Network Working Group JM. Valin
Internet-Draft Octasic Inc.
Intended status: Standards Track K. Vos
Expires: December 18, 2011 Skype Technologies S.A.
T. Terriberry
Mozilla Corporation
June 16, 2011
Definition of the Opus Audio Codec
draft-ietf-codec-opus-06
Abstract
This document defines the Opus codec, designed for interactive speech
and audio transmission over the Internet.
Status of this Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at http://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on December 18, 2011.
Copyright Notice
Copyright (c) 2011 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. Code Components extracted from this document must
include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1. Notation and Conventions . . . . . . . . . . . . . . . . 5
1.1.1. min(x,y) . . . . . . . . . . . . . . . . . . . . . . 5
1.1.2. max(x,y) . . . . . . . . . . . . . . . . . . . . . . 5
1.1.3. clamp(lo,x,hi) . . . . . . . . . . . . . . . . . . . 5
1.1.4. sign(x) . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.5. log2(f) . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.6. ilog(n) . . . . . . . . . . . . . . . . . . . . . . . 6
2. Opus Codec Overview . . . . . . . . . . . . . . . . . . . . . 7
3. Codec Modes . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1. Examples . . . . . . . . . . . . . . . . . . . . . . . . 15
4. Opus Decoder . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1. Range Decoder . . . . . . . . . . . . . . . . . . . . . . 17
4.1.1. Decoding Symbols . . . . . . . . . . . . . . . . . . 18
4.1.2. Alternate Decoding Methods . . . . . . . . . . . . . 20
4.1.3. Decoding Raw Bits . . . . . . . . . . . . . . . . . . 21
4.1.4. Decoding Uniformly Distributed Integers . . . . . . . 21
4.1.5. Current Bit Usage . . . . . . . . . . . . . . . . . . 22
4.2. SILK Decoder . . . . . . . . . . . . . . . . . . . . . . 24
4.2.1. Decoder Modules . . . . . . . . . . . . . . . . . . . 25
4.2.2. Header Bits . . . . . . . . . . . . . . . . . . . . . 27
4.2.3. LBRR Flags . . . . . . . . . . . . . . . . . . . . . 27
4.2.4. SILK/LBRR Frame Contents . . . . . . . . . . . . . . 27
4.2.5. LBRR Information . . . . . . . . . . . . . . . . . . 55
4.3. CELT Decoder . . . . . . . . . . . . . . . . . . . . . . 55
4.3.1. Transient Decoding . . . . . . . . . . . . . . . . . 56
4.3.2. Energy Envelope Decoding . . . . . . . . . . . . . . 57
4.3.3. Bit allocation . . . . . . . . . . . . . . . . . . . 58
4.3.4. Shape Decoder . . . . . . . . . . . . . . . . . . . . 62
4.3.5. Anti-collapse processing . . . . . . . . . . . . . . 64
4.3.6. Denormalization . . . . . . . . . . . . . . . . . . . 64
4.3.7. Inverse MDCT . . . . . . . . . . . . . . . . . . . . 64
4.3.8. Packet Loss Concealment (PLC) . . . . . . . . . . . . 65
5. Codec Encoder . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1. Range Coder . . . . . . . . . . . . . . . . . . . . . . . 66
5.1.1. Encoding Symbols . . . . . . . . . . . . . . . . . . 66
5.1.2. Encoding Raw Bits . . . . . . . . . . . . . . . . . . 67
5.1.3. Encoding Uniformly Distributed Integers . . . . . . . 68
5.1.4. Finalizing the Stream . . . . . . . . . . . . . . . . 68
5.1.5. Current Bit Usage . . . . . . . . . . . . . . . . . . 68
5.2. SILK Encoder . . . . . . . . . . . . . . . . . . . . . . 69
5.2.1. Voice Activity Detection . . . . . . . . . . . . . . 70
5.2.2. High-Pass Filter . . . . . . . . . . . . . . . . . . 71
5.2.3. Pitch Analysis . . . . . . . . . . . . . . . . . . . 71
5.2.4. Noise Shaping Analysis . . . . . . . . . . . . . . . 73
5.2.5. Prefilter . . . . . . . . . . . . . . . . . . . . . . 77
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5.2.6. Prediction Analysis . . . . . . . . . . . . . . . . . 77
5.2.7. LSF Quantization . . . . . . . . . . . . . . . . . . 78
5.2.8. LTP Quantization . . . . . . . . . . . . . . . . . . 81
5.2.9. Noise Shaping Quantizer . . . . . . . . . . . . . . . 82
5.2.10. Range Encoder . . . . . . . . . . . . . . . . . . . . 83
5.3. CELT Encoder . . . . . . . . . . . . . . . . . . . . . . 83
5.3.1. Pre-filter . . . . . . . . . . . . . . . . . . . . . 83
5.3.2. Forward MDCT . . . . . . . . . . . . . . . . . . . . 83
5.3.3. Bands and Normalization . . . . . . . . . . . . . . . 83
5.3.4. Energy Envelope Quantization . . . . . . . . . . . . 84
5.3.5. Spherical Vector Quantization . . . . . . . . . . . . 85
5.3.6. Stereo support . . . . . . . . . . . . . . . . . . . 86
5.3.7. Synthesis . . . . . . . . . . . . . . . . . . . . . . 86
5.3.8. Variable Bitrate (VBR) . . . . . . . . . . . . . . . 87
6. Conformance . . . . . . . . . . . . . . . . . . . . . . . . . 88
7. Security Considerations . . . . . . . . . . . . . . . . . . . 89
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 90
9. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 91
10. Informative References . . . . . . . . . . . . . . . . . . . 92
Appendix A. Reference Implementation . . . . . . . . . . . . . . 94
A.1. Extracting the source . . . . . . . . . . . . . . . . . . 94
A.2. Development Versions . . . . . . . . . . . . . . . . . . 94
A.3. Base64-encoded source code . . . . . . . . . . . . . . . 94
Appendix B. opus_compare.c . . . . . . . . . . . . . . . . . . . 239
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 245
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1. Introduction
The Opus codec is a real-time interactive audio codec composed of a
linear prediction (LP)-based layer and a Modified Discrete Cosine
Transform (MDCT)-based layer. The main idea behind using two layers
is that in speech, linear prediction techniques (such as CELP) code
low frequencies more efficiently than transform (e.g., MDCT) domain
techniques, while the situation is reversed for music and higher
speech frequencies. Thus a codec with both layers available can
operate over a wider range than either one alone and, by combining
them, achieve better quality than either one individually.
The primary normative part of this specification is provided by the
source code in Appendix A. In general, only the decoder portion of
this software is normative, though a significant amount of code is
shared by both the encoder and decoder. The decoder contains
significant amounts of integer and fixed-point arithmetic which must
be performed exactly, including all rounding considerations, so any
useful specification must make extensive use of domain-specific
symbolic language to adequately define these operations.
Additionally, any conflict between the symbolic representation and
the included reference implementation must be resolved. For the
practical reasons of compatibility and testability it would be
advantageous to give the reference implementation to have priority in
any disagreement. The C language is also one of the most widely
understood human-readable symbolic representations for machine
behavior. For these reasons this RFC uses the reference
implementation as the sole symbolic representation of the codec.
While the symbolic representation is unambiguous and complete it is
not always the easiest way to understand the codec's operation. For
this reason this document also describes significant parts of the
codec in English and takes the opportunity to explain the rationale
behind many of the more surprising elements of the design. These
descriptions are intended to be accurate and informative, but the
limitations of common English sometimes result in ambiguity, so it is
expected that the reader will always read them alongside the symbolic
representation. Numerous references to the implementation are
provided for this purpose. The descriptions sometimes differ from
the reference in ordering or through mathematical simplification
wherever such deviation makes an explanation easier to understand.
For example, the right shift and left shift operations in the
reference implementation are often described using division and
multiplication in the text. In general, the text is focused on the
"what" and "why" while the symbolic representation most clearly
provides the "how".
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1.1. Notation and Conventions
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119.
Even when using floating-point, various operations in the codec
require bit-exact fixed-point behavior. The notation "Q_n_", where
_n_ is an integer, denotes the number of binary digits to the right
of the decimal point in a fixed-point number. For example, a signed
Q14 value in a 16-bit word can represent values from -2.0 to
1.99993896484375, inclusive. This notation is for informational
purposes only. Arithmetic, when described, always operates on the
underlying integer. E.g., the text will explicitly indicate any
shifts required after a multiplication.
Expressions, where included in the text, follow C operator rules and
precedence, with the exception that syntax like "2**n" is used to
indicate 2 raised to the power n. The text also makes use of the
following functions:
1.1.1. min(x,y)
The smallest of two values x and y.
1.1.2. max(x,y)
The largest of two values x and y.
1.1.3. clamp(lo,x,hi)
clamp(lo,x,hi) = max(lo,min(x,hi))
With this definition, if lo>hi, the lower bound is the one that is
enforced.
1.1.4. sign(x)
The sign of x, i.e.,
( -1, x < 0 ,
sign(x) = < 0, x == 0 ,
( 1, x > 0 .
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1.1.5. log2(f)
The base-two logarithm of f.
1.1.6. ilog(n)
The minimum number of bits required to store a positive integer n in
two's complement notation, or 0 for a non-positive integer n.
( 0, n <= 0,
ilog(n) = <
( floor(log2(n))+1, n > 0
Examples:
o ilog(-1) = 0
o ilog(0) = 0
o ilog(1) = 1
o ilog(2) = 2
o ilog(3) = 2
o ilog(4) = 3
o ilog(7) = 3
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2. Opus Codec Overview
The Opus codec scales from 6 kb/s narrowband mono speech to 510 kb/s
fullband stereo music, with algorithmic delays ranging from 5 ms to
65.2 ms. At any given time, either the LP layer, the MDCT layer, or
both, may be active. It can seamlessly switch between all of its
various operating modes, giving it a great deal of flexibility to
adapt to varying content and network conditions without renegotiating
the current session. Internally, the codec always operates at a
48 kHz sampling rate, though it allows input and output of various
bandwidths, defined as follows:
+----------------------+-----------------+--------------------------+
| Abbreviation | Audio Bandwidth | Sampling Rate |
| | | (Effective) |
+----------------------+-----------------+--------------------------+
| NB (narrowband) | 4 kHz | 8 kHz |
| | | |
| MB (medium-band) | 6 kHz | 12 kHz |
| | | |
| WB (wideband) | 8 kHz | 16 kHz |
| | | |
| SWB (super-wideband) | 12 kHz | 24 kHz |
| | | |
| FB (fullband) | 20 kHz | 48 kHz |
+----------------------+-----------------+--------------------------+
These can be chosen independently on the encoder and decoder side,
e.g., a fullband signal can be decoded as wideband, or vice versa.
This approach ensures a sender and receiver can always interoperate,
regardless of the capabilities of their actual audio hardware.
The LP layer is based on the SILK [1] codec [SILK]. It supports NB,
MB, or WB audio and frame sizes from 10 ms to 60 ms, and requires an
additional 5.2 ms look-ahead for noise shaping estimation (5 ms) and
internal resampling (0.2 ms). Like Vorbis and many other modern
codecs, SILK is inherently designed for variable-bitrate (VBR)
coding, though an encoder can with sufficient effort produce
constant-bitrate (CBR) or near-CBR streams.
The MDCT layer is based on the CELT [2] codec [CELT]. It supports
sampling NB, WB, SWB, or FB audio and frame sizes from 2.5 ms to
20 ms, and requires an additional 2.5 ms look-ahead due to the
overlapping MDCT windows. The CELT codec is inherently designed for
CBR coding, but unlike many CBR codecs it is not limited to a set of
predetermined rates. It internally allocates bits to exactly fill
any given target budget, and an encoder can produce a VBR stream by
varying the target on a per-frame basis. The MDCT layer is not used
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for speech when the audio bandwidth is WB or less, as it is not
useful there. On the other hand, non-speech signals are not always
adequately coded using linear prediction, so for music only the MDCT
layer should be used.
A hybrid mode allows the use of both layers simultaneously with a
frame size of 10 or 20 ms and a SWB or FB audio bandwidth. Each
frame is split into a low frequency signal and a high frequency
signal, with a cutoff of 8 kHz. The LP layer then codes the low
frequency signal, followed by the MDCT layer coding the high
frequency signal. In the MDCT layer, all bands below 8 kHz are
discarded, so there is no coding redundancy between the two layers.
At the decoder, the two decoder outputs are simply added together.
To compensate for the different look-aheads required by each layer,
the CELT encoder input is delayed by an additional 2.7 ms. This
ensures that low frequencies and high frequencies arrive at the same
time. This extra delay MAY be reduced by an encoder by using less
lookahead for noise shaping or using a simpler resampler in the LP
layer, but this will reduce quality. However, the base 2.5 ms look-
ahead in the CELT layer cannot be reduced in the encoder because it
is needed for the MDCT overlap, whose size is fixed by the decoder.
Both layers use the same entropy coder, avoiding any waste from
"padding bits" between them. The hybrid approach makes it easy to
support both CBR and VBR coding. Although the LP layer is VBR, the
bit allocation of the MDCT layer can produce a final stream that is
CBR by using all the bits left unused by the LP layer.
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3. Codec Modes
As described, the two layers can be combined in three possible
operating modes:
1. A LP-only mode for use in low bitrate connections with an audio
bandwidth of WB or less,
2. A hybrid (LP+MDCT) mode for SWB or FB speech at medium bitrates,
and
3. An MDCT-only mode for very low delay speech transmission as well
as music transmission.
A single packet may contain multiple audio frames, however they must
share a common set of parameters, including the operating mode, audio
bandwidth, frame size, and channel count. A single-byte table-of-
contents (TOC) header signals which of the various modes and
configurations a given packet uses. It is composed of a frame count
code, "c", a stereo flag, "s", and a configuration number, "config",
arranged as illustrated in Figure 1. A description of each of these
fields follows.
0
0 1 2 3 4 5 6 7
+-+-+-+-+-+-+-+-+
| c |s| config |
+-+-+-+-+-+-+-+-+
Figure 1: The TOC byte
The top five bits of the TOC byte, labeled "config", encode one of 32
possible configurations of operating mode, audio bandwidth, and frame
size. Table 1 lists the parameters for each configuration.
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+-----------------------+-----------+-----------+-------------------+
| Configuration | Mode | Bandwidth | Frame Size(s) |
| Number(s) | | | |
+-----------------------+-----------+-----------+-------------------+
| 0...3 | LP-only | NB | 10, 20, 40, 60 ms |
| | | | |
| 4...7 | LP-only | MB | 10, 20, 40, 60 ms |
| | | | |
| 8...11 | LP-only | WB | 10, 20, 40, 60 ms |
| | | | |
| 12...13 | Hybrid | SWB | 10, 20 ms |
| | | | |
| 14...15 | Hybrid | FB | 10, 20 ms |
| | | | |
| 16...19 | MDCT-only | NB | 2.5, 5, 10, 20 ms |
| | | | |
| 20...23 | MDCT-only | WB | 2.5, 5, 10, 20 ms |
| | | | |
| 24...27 | MDCT-only | SWB | 2.5, 5, 10, 20 ms |
| | | | |
| 28...31 | MDCT-only | FB | 2.5, 5, 10, 20 ms |
+-----------------------+-----------+-----------+-------------------+
Table 1: TOC Byte Configuration Parameters
One additional bit, labeled "s", is used to signal mono vs. stereo,
with 0 indicating mono and 1 indicating stereo. The remaining two
bits, labeled "c", code the number of frames per packet (codes 0 to
3) as follows:
o 0: 1 frame in the packet
o 1: 2 frames in the packet, each with equal compressed size
o 2: 2 frames in the packet, with different compressed sizes
o 3: an arbitrary number of frames in the packet
A well-formed Opus packet MUST contain at least one byte with the TOC
information, though the frame(s) within a packet MAY be zero bytes
long. It must also obey various additional rules indicated by
"MUST", "MUST NOT", etc., in this section. A receiver MUST NOT
process packets which violate these rules as normal Opus packets.
They are reserved for future applications, such as in-band headers
(containing metadata, etc.) or multichannel support.
When a packet contains multiple VBR frames, the compressed length of
one or more of these frames is indicated with a one or two byte
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sequence, with the meaning of the first byte as follows:
o 0: No frame (DTX or lost packet)
o 1...251: Size of the frame in bytes
o 252...255: A second byte is needed. The total size is
(size[1]*4)+size[0]
The maximum representable size is 255*4+255=1275 bytes. For 20 ms
frames, this represents a bitrate of 510 kb/s, which is approximately
the highest useful rate for lossily compressed fullband stereo music.
Beyond that point, lossless codecs would be more appropriate. It is
also roughly the maximum useful rate of the MDCT layer, as shortly
thereafter additional bits no longer improve quality due to
limitations on the codebook sizes. No length is transmitted for the
last frame in a VBR packet, or any of the frames in a CBR packet, as
it can be inferred from the total size of the packet and the size of
all other data in the packet. However, it MUST NOT exceed
1275 bytes, to allow for repacketization by gateways, conference
bridges, or other software.
For code 0 packets, the TOC byte is immediately followed by N-1 bytes
of compressed data for a single frame (where N is the size of the
packet), as illustrated in Figure 2.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|0|0|s| config | |
+-+-+-+-+-+-+-+-+ |
| Compressed frame 1 (N-1 bytes)... :
: |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 2: A Code 0 Packet
For code 1 packets, the TOC byte is immediately followed by the
(N-1)/2 bytes of compressed data for the first frame, followed by
(N-1)/2 bytes of compressed data for the second frame, as illustrated
in Figure 3. The number of payload bytes available for compressed
data, N-1, MUST be even for all code 1 packets.
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0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|1|0|s| config | |
+-+-+-+-+-+-+-+-+ :
| Compressed frame 1 ((N-1)/2 bytes)... |
: +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ :
| Compressed frame 2 ((N-1)/2 bytes)... |
: +-+-+-+-+-+-+-+-+
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: A Code 1 Packet
For code 2 packets, the TOC byte is followed by a one or two byte
sequence indicating the the length of the first frame (marked N1 in
the figure below), followed by N1 bytes of compressed data for the
first frame. The remaining N-N1-2 or N-N1-3 bytes are the compressed
data for the second frame. This is illustrated in Figure 4. The
length of the first frame, N1, MUST be no larger than the size of the
payload remaining after decoding that length for all code 2 packets.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|0|1|s| config | N1 (1-2 bytes): |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ :
| Compressed frame 1 (N1 bytes)... |
: +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |
| Compressed frame 2... :
: |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 4: A Code 2 Packet
For code 3 packets, the TOC byte is followed by a byte encoding the
number of frames in the packet in bits 0 to 5 (marked "M" in the
figure below), with bit 6 indicating whether or not padding is
inserted (marked "p" in the figure below), and bit 7 indicating VBR
(marked "v" in the figure below). M MUST NOT be zero, and the audio
duration contained within a packet MUST NOT exceed 120&nbps;ms. This
limits the maximum frame count for any frame size to 48 (for 2.5 ms
frames), with lower limits for longer frame sizes. Figure 5
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illustrates the layout of the frame count byte.
0
0 1 2 3 4 5 6 7
+-+-+-+-+-+-+-+-+
| M |p|v|
+-+-+-+-+-+-+-+-+
Figure 5: The frame count byte
When padding is used, the number of bytes of padding is encoded in
the bytes following the frame count byte. Values from 0...254
indicate that 0...254 bytes of padding are included, in addition to
the byte(s) used to indicate the size of the padding. If the value
is 255, then the size of the additional padding is 254 bytes, plus
the padding value encoded in the next byte. The additional padding
bytes appear at the end of the packet, and SHOULD be set to zero by
the encoder, however the decoder MUST accept any value for the
padding bytes. By using code 255 multiple times, it is possible to
create a packet of any specific, desired size. Let P be the total
amount of padding, including both the trailing padding bytes
themselves and the header bytes used to indicate how many there are.
Then P MUST be no more than N-2 for CBR packets, or N-M-1 for VBR
packets.
In the CBR case, the compressed length of each frame in bytes is
equal to the number of remaining bytes in the packet after
subtracting the (optional) padding, (N-2-P), divided by M. This
number MUST be an integer multiple of M. The compressed data for all
M frames then follows, each of size (N-2-P)/M bytes, as illustrated
in Figure 6.
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0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|1|1|s| config | M |p|0| Padding length (Optional) :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 1 ((N-2-P)/M bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 2 ((N-2-P)/M bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: ... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame M ((N-2-P)/M bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: Padding (Optional)... |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 6: A CBR Code 3 Packet
In the VBR case, the (optional) padding length is followed by M-1
frame lengths (indicated by "N1" to "N[M-1]" in the figure below),
each encoded in a one or two byte sequence as described above. The
packet MUST contain enough data for the M-1 lengths after the
(optional) padding, and the sum of these lengths MUST be no larger
than the number of bytes remaining in the packet after decoding them.
The compressed data for all M frames follows, each frame consisting
of the indicated number of bytes, with the final frame consuming any
remaining bytes before the final padding, as illustrated in Figure 6.
The number of header bytes (TOC byte, frame count byte, padding
length bytes, and frame length bytes), plus the length of the first
M-1 frames themselves, plus the length of the padding MUST be no
larger than N, the total size of the packet.
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0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|1|1|s| config | M |p|1| Padding length (Optional) :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: N1 (1-2 bytes): N2 (1-2 bytes): ... : N[M-1] |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 1 (N1 bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 2 (N2 bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: ... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame M... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: Padding (Optional)... |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 7: A VBR Code 3 Packet
3.1. Examples
Simplest case, one NB mono 20 ms SILK frame:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|0|0|0| 1 | compressed data... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Two FB mono 5 ms CELT frames of the same compressed size:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|1|0|0| 29 | compressed data... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Two FB mono 20 ms hybrid frames of different compressed size:
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0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|1|1|0| 15 | 2 |0|1| N1 | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |
| compressed data... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Four FB stereo 20 ms CELT frames of the same compressed size:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|1|1|1| 31 | 4 |0|0| compressed data... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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4. Opus Decoder
The Opus decoder consists of two main blocks: the SILK decoder and
the CELT decoder. The output of the Opus decode is the sum of the
outputs from the SILK and CELT decoders with proper sample rate
conversion and delay compensation as illustrated in the block diagram
below. At any given time, one or both of the SILK and CELT decoders
may be active.
+-------+ +----------+
| SILK | | sample |
+->|encoder|--->| rate |----+
bit- +-------+ | | | |conversion| v
stream | Range |---+ +-------+ +----------+ /---\ audio
------->|decoder| | + |------>
| |---+ +-------+ +----------+ \---/
+-------+ | | CELT | | Delay | ^
+->|decoder|----| compens- |----+
| | | ation |
+-------+ +----------+
4.1. Range Decoder
Opus uses an entropy coder based on [range-coding], which is itself a
rediscovery of the FIFO arithmetic code introduced by
[coding-thesis]. It is very similar to arithmetic encoding, except
that encoding is done with digits in any base instead of with bits,
so it is faster when using larger bases (i.e., an octet). All of the
calculations in the range coder must use bit-exact integer
arithmetic.
Symbols may also be coded as _raw bits_ packed directly into the
bitstream, bypassing the range coder. These are packed backwards
starting at the end of the frame. This reduces complexity and makes
the stream more resilient to bit errors, as corruption in the raw
bits will not desynchronize the decoding process, unlike corruption
in the input to the range decoder. Raw bits are only used in the
CELT layer.
Each symbol coded by the range coder is drawn from a finite alphabet
and coded in a separate _context_, which describes the size of the
alphabet and the relative frequency of each symbol in that alphabet.
Opus only uses static contexts. They are not adapted to the
statistics of the data as it is coded.
The parameters needed to encode or decode a symbol in a given context
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are represented by a three-tuple (fl,fh,ft), with 0 <= fl < fh <= ft
<= 65535. The values of this tuple are derived from the probability
model for the symbol, represented by traditional _frequency counts_
(although, since Opus uses static contexts, these are not updated as
symbols are decoded). Let f[i] be the frequency of the _i_th symbol
in a context with _n_ symbols total. Then the three-tuple
corresponding to the _k_th symbol is given by
k-1 n-1
__ __
fl = \ f[i], fh = fl + f[k], ft = \ f[i]
/_ /_
i=0 i=0
The range decoder extracts the symbols and integers encoded using the
range encoder in Section 5.1. The range decoder maintains an
internal state vector composed of the two-tuple (val,rng),
representing the difference between the high end of the current range
and the actual coded value, minus one, and the size of the current
range, respectively. Both val and rng are 32-bit unsigned integer
values. The decoder initializes rng to 128 and initializes val to
127 minus the top 7 bits of the first input octet. It then
immediately normalizes the range using the procedure described in
Section 4.1.1.1.
4.1.1. Decoding Symbols
Decoding a symbol is a two-step process. The first step determines a
16-bit unsigned value fs, which lies within the range of some symbol
in the current context. The second step updates the range decoder
state with the three-tuple (fl,fh,ft) corresponding to that symbol.
The first step is implemented by ec_decode() (entdec.c), which
computes fs = ft - min(val/(rng/ft)+1, ft). The divisions here are
exact integer division.
The decoder then identifies the symbol in the current context
corresponding to fs; i.e., the one whose three-tuple (fl,fh,ft)
satisfies fl <= fs < fh. It uses this tuple to update val according
to val = val - (rng/ft)*(ft-fh). If fl is greater than zero, then
the decoder updates rng using rng = (rng/ft)*(fh-fl). Otherwise, it
updates rng using rng = rng - (rng/ft)*(ft-fh). After these updates,
implemented by ec_dec_update() (entdec.c), it normalizes the range
using the procedure in the next section, and returns the index of the
identified symbol.
With this formulation, all the truncation error from using finite
precision arithmetic accumulates in symbol 0. This makes the cost of
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coding a 0 slightly smaller, on average, than the negative log of its
estimated probability and makes the cost of coding any other symbol
slightly larger. When contexts are designed so that 0 is the most
probable symbol, which is often the case, this strategy minimizes the
inefficiency introduced by the finite precision.
4.1.1.1. Renormalization
To normalize the range, the decoder repeats the following process,
implemented by ec_dec_normalize() (entdec.c), until rng > 2**23. If
rng is already greater than 2**23, the entire process is skipped.
First, it sets rng to (rng<<8). Then it reads the next 8 bits of
input into sym, using the remaining bit from the previous input octet
as the high bit of sym, and the top 7 bits of the next octet as the
remaining bits of sym. If no more input octets remain, it uses zero
bits instead. Then, it sets val to (val<<8)+(255-sym)&0x7FFFFFFF.
It is normal and expected that the range decoder will read several
bytes into the raw bits data (if any) at the end of the packet by the
time the frame is completely decoded, as illustrated in Figure 8.
This same data MUST also be returned as raw bits when requested. The
encoder is expected to terminate the stream in such a way that the
decoder will decode the intended values regardless of the data
contained in the raw bits. Section 5.1.4 describes a procedure for
doing this. If the range decoder consumes all of the bytes belonging
to the current frame, it MUST continue to use zero when any further
input bytes are required, even if there is additional data in the
current packet from padding or other frames.
n n+1 n+2 n+3
7 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: | <----------- Overlap region ------------> | :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
^ ^
| End of data buffered by the range coder |
...-----------------------------------------------+
|
| End of data consumed by raw bits
+-------------------------------------------------------...
Figure 8: Illustrative example of raw bits overlapping range coder
data
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4.1.2. Alternate Decoding Methods
The reference implementation uses three additional decoding methods
that are exactly equivalent to the above, but make assumptions and
simplifications that allow for a more efficient implementation.
4.1.2.1. ec_decode_bin()
The first is ec_decode_bin() (entdec.c), defined using the parameter
ftb instead of ft. It is mathematically equivalent to calling
ec_decode() with ft = (1<<ftb), but avoids one of the divisions.
4.1.2.2. ec_dec_bit_logp()
The next is ec_dec_bit_logp() (entdec.c), which decodes a single
binary symbol, replacing both the ec_decode() and ec_dec_update()
steps. The context is described by a single parameter, logp, which
is the absolute value of the base-2 logarithm of the probability of a
"1". It is mathematically equivalent to calling ec_decode() with ft
= (1<<logp), followed by ec_dec_update() with fl = 0, fh =
(1<<logp)-1, ft = (1<<logp) if the returned value of fs is less than
(1<<logp)-1 (a "0" was decoded), and with fl = (1<<logp)-1, fh = ft =
(1<<logp) otherwise (a "1" was decoded). The implementation requires
no multiplications or divisions.
4.1.2.3. ec_dec_icdf()
The last is ec_dec_icdf() (entdec.c), which decodes a single symbol
with a table-based context of up to 8 bits, also replacing both the
ec_decode() and ec_dec_update() steps, as well as the search for the
decoded symbol in between. The context is described by two
parameters, an icdf (_inverse_ cumulative distribution function)
table and ftb. As with ec_decode_bin(), (1<<ftb) is equivalent to
ft. idcf[k], on the other hand, stores (1<<ftb)-fh for the kth symbol
in the context, which is equal to (1<<ftb)-fl for the (k+1)st symbol.
fl for the 0th symbol is assumed to be 0, and the table is terminated
by a value of 0 (where fh == ft).
The function is mathematically equivalent to calling ec_decode() with
ft = (1<<ftb), using the returned value fs to search the table for
the first entry where fs < (1<<ftb)-icdf[k], and calling
ec_dec_update() with fl = (1<<ftb)-icdf[k-1] (or 0 if k == 0), fh =
(1<<ftb)-idcf[k], and ft = (1<<ftb). Combining the search with the
update allows the division to be replaced by a series of
multiplications (which are usually much cheaper), and using an
inverse CDF allows the use of an ftb as large as 8 in an 8-bit table
without any special cases. This is the primary interface with the
range decoder in the SILK layer, though it is used in a few places in
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the CELT layer as well.
Although icdf[k] is more convenient for the code, the frequency
counts, f[k], are a more natural representation of the probability
distribution function (PDF) for a given symbol. Therefore this draft
lists the latter, not the former, when describing the context in
which a symbol is coded as a list, e.g., {4, 4, 4, 4}/16 for a
uniform context with four possible values and ft=16. The value of ft
after the slash is always the sum of the entries in the PDF, but is
included for convenience. Contexts with identical probabilities,
f[k]/ft, but different values of ft (or equivalently, ftb) are not
the same, and cannot, in general, be used in place of one another.
An icdf table is also not capable of representing a PDF where the
first symbol has 0 probability. In such contexts, ec_dec_icdf() can
decode the symbol by using a table that drops the entries for any
initial zero-probability values and adding the constant offset of the
first value with a non-zero probability to its return value.
4.1.3. Decoding Raw Bits
The raw bits used by the CELT layer are packed at the end of the
packet, with the least significant bit of the first value to be
packed in the least significant bit of the last byte, filling up to
the most significant bit in the last byte, and continuing on to the
least significant bit of the penultimate byte, and so on. The
reference implementation reads them using ec_dec_bits() (entdec.c).
Because the range decoder must read several bytes ahead in the
stream, as described in Section 4.1.1.1, the input consumed by the
raw bits MAY overlap with the input consumed by the range coder, and
a decoder MUST allow this. The format should render it impossible to
attempt to read more raw bits than there are actual bits in the
frame, though a decoder MAY wish to check for this and report an
error.
4.1.4. Decoding Uniformly Distributed Integers
The ec_dec_uint() (entdec.c) function decodes one of ft equiprobable
values in the range 0 to ft-1, inclusive, each with a frequency of 1,
where ft may be as large as 2**32-1. Because ec_decode() is limited
to a total frequency of 2**16-1, this is split up into a range coded
symbol representing up to 8 of the high bits of the value, and, if
necessary, raw bits representing the remaining bits. The limit of 8
bits in the range coded symbol is a trade-off between implementation
complexity, modeling error (since the symbols no longer truly have
equal coding cost) and rounding error introduced by the range coder
itself (which gets larger as more bits are included). Using raw bits
reduces the maximum number of divisions required in the worst case,
but means that it may be possible to decode a value outside the range
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0 to ft-1, inclusive.
ec_dec_uint() takes a single, positive parameter, ft, which is not
necessarily a power of two, and returns an integer, t, whose value
lies between 0 and ft-1, inclusive. Let ftb = ilog(ft-1), i.e., the
number of bits required to store ft-1 in two's complement notation.
If ftb is 8 or less, then t is decoded with t = ec_decode(ft), and
the range coder state is updated using the three-tuple (t,t+1,ft).
If ftb is greater than 8, then the top 8 bits of t are decoded using
t = ec_decode((ft-1>>ftb-8)+1), the decoder state is updated using
the three-tuple (t,t+1,(ft-1>>ftb-8)+1), and the remaining bits are
decoded as raw bits, setting t = t<<ftb-8|ec_dec_bits(ftb-8). If, at
this point, t >= ft, then the current frame is corrupt. In that
case, the decoder should assume there has been an error in the
coding, decoding, or transmission and SHOULD take measures to conceal
the error and/or report to the application that a problem has
occurred.
4.1.5. Current Bit Usage
The bit allocation routines in the CELT decoder need a conservative
upper bound on the number of bits that have been used from the
current frame thus far, including both range coder bits and raw bits.
This drives allocation decisions that must match those made in the
encoder. The upper bound is computed in the reference implementation
to whole-bit precision by the function ec_tell() (entcode.h) and to
fractional 1/8th bit precision by the function ec_tell_frac()
(entcode.c). Like all operations in the range coder, it must be
implemented in a bit-exact manner, and must produce exactly the same
value returned by the same functions in the encoder after encoding
the same symbols.
ec_tell() is guaranteed to return ceil(ec_tell_frac()/8.0). In
various places the codec will check to ensure there is enough room to
contain a symbol before attempting to decode it. In practice,
although the number of bits used so far is an upper bound, decoding a
symbol whose probability model suggests it has a worst-case cost of p
1/8th bits may actually advance the return value of ec_tell_frac() by
p-1, p, or p+1 1/8th bits, due to approximation error in that upper
bound, truncation error in the range coder, and for large values of
ft, modeling error in ec_dec_uint().
However, this error is bounded, and periodic calls to ec_tell() or
ec_tell_frac() at precisely defined points in the decoding process
prevent it from accumulating. For a symbol that requires a whole
number of bits (i.e., ft/(fh-fl) is a power of two, including values
of ft larger than 2**8 with ec_dec_uint()), and there are at least p
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1/8th bits available, decoding the symbol will never advance the
decoder past the end of the frame, i.e., will never _bust_ the
budget. Frames contain a whole number of bits, and the return value
of ec_tell_frac() will only advance by more than p 1/8th bits in this
case if there was a fractional number of bits remaining, and by no
more than the fractional part. However, when p is not a whole number
of bits, an extra 1/8th bit is required to ensure decoding the symbol
will not bust.
The reference implementation keeps track of the total number of whole
bits that have been processed by the decoder so far in a variable
nbits_total, including the (possibly fractional number of bits) that
are currently buffered (but not consumed) inside the range coder.
nbits_total is initialized to 33 just after the initial range
renormalization process completes (or equivalently, it can be
initialized to 9 before the first renormalization). The extra two
bits over the actual amount buffered by the range coder guarantees
that it is an upper bound and that there is enough room for the
encoder to terminate the stream. Each iteration through the range
coder's renormalization loop increases nbits_total by 8. Reading raw
bits increases nbits_total by the number of raw bits read.
4.1.5.1. ec_tell()
The whole number of bits buffered in rng may be estimated via l =
ilog(rng). ec_tell() then becomes a simple matter of removing these
bits from the total. It returns (nbits_total - l).
In a newly initialized decoder, before any symbols have been read,
this reports that 1 bit has been used. This is the bit reserved for
termination of the encoder.
4.1.5.2. ec_tell_frac()
ec_tell_frac() estimates the number of bits buffered in rng to
fractional precision. Since rng must be greater than 2**23 after
renormalization, l must be at least 24. Let r = rng>>(l-16), so that
32768 <= r < 65536, an unsigned Q15 value representing the fractional
part of rng. Then the following procedure can be used to add one bit
of precision to l. First, update r = r*r>>15. Then add the 16th bit
of r to l via l = 2*l + (r>>16). Finally, if this bit was a 1,
reduce r by a factor of two via r = r>>1, so that it once again lies
in the range 32768 <= r < 65536.
This procedure is repeated three times to extend l to 1/8th bit
precision. ec_tell_frac() then returns (nbits_total*8 - l).
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4.2. SILK Decoder
The LP layer uses a modified version of the SILK codec (herein simply
called "SILK"), which has a relatively traditional Code-Excited
Linear Prediction (CELP) structure. It runs in NB, MB, and WB modes
internally. When used in a hybrid frame in SWB or FB mode, the LP
layer itself still only runs in WB mode.
Internally, the LP layer of a single Opus frame is composed of either
a single 10 ms SILK frame or between one and three 20 ms SILK frames.
Each SILK frame is in turn composed of either two or four 5 ms
subframes. Optional Low Bit-Rate Redundancy (LBRR) frames, which are
redundant copies of the previous SILK frames, may appear to aid in
recovery from packet loss. If present, these appear before the
regular SILK frames. All of these frames and subframes are decoded
from the same range coder, with no padding between them. Thus
packing multiple SILK frames in a single Opus frame saves, on
average, half a byte per SILK frame. It also allows some parameters
to be predicted from prior SILK frames in the same Opus frame, since
this does not degrade packet loss robustness (beyond any penalty for
merely using larger packets).
Stereo support in SILK uses a variant of mid-side coding, allowing a
mono decoder to simply decode the mid channel. However, the data for
the two channels is interleaved, so a mono decoder must still unpack
the data for the side channel. It would be required to do so anyway
for hybrid Opus frames, or to support decoding individual 20 ms
frames.
+----------------------+-----------------+---------------+
| Symbol(s) | PDF | Condition |
+----------------------+-----------------+---------------+
| VAD flags | {1, 1}/2 | |
| | | |
| LBRR flag | {1, 1}/2 | |
| | | |
| Per-frame LBRR flags | Section 4.2.3 | Section 4.2.3 |
| | | |
| Frame Type | Section 4.2.4.1 | |
| | | |
| Gain index | Section 4.2.4.2 | |
+----------------------+-----------------+---------------+
Order of the symbols in the SILK section of the bit-stream.
Table 2
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4.2.1. Decoder Modules
An overview of the decoder is given in Figure 9.
+---------+ +------------+
-->| Range |--->| Decode |---------------------------+
1 | Decoder | 2 | Parameters |----------+ 5 |
+---------+ +------------+ 4 | |
3 | | |
\/ \/ \/
+------------+ +------------+ +------------+
| Generate |-->| LTP |-->| LPC |-->
| Excitation | | Synthesis | | Synthesis | 6
+------------+ +------------+ +------------+
1: Range encoded bitstream
2: Coded parameters
3: Pulses and gains
4: Pitch lags and LTP coefficients
5: LPC coefficients
6: Decoded signal
Decoder block diagram.
Figure 9
4.2.1.1. Range Decoder
The range decoder decodes the encoded parameters from the received
bitstream. Output from this function includes the pulses and gains
for the excitation signal generation, as well as LTP and LSF codebook
indices, which are needed for decoding LTP and LPC coefficients
needed for LTP and LPC synthesis filtering the excitation signal,
respectively.
4.2.1.2. Decode Parameters
Pulses and gains are decoded from the parameters that were decoded by
the range decoder.
When a voiced frame is decoded and LTP codebook selection and indices
are received, LTP coefficients are decoded using the selected
codebook by choosing the vector that corresponds to the given
codebook index in that codebook. This is done for each of the four
subframes. The LPC coefficients are decoded from the LSF codebook by
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first adding the chosen vectors, one vector from each stage of the
codebook. The resulting LSF vector is stabilized using the same
method that was used in the encoder, see Section 5.2.7.5. The LSF
coefficients are then converted to LPC coefficients, and passed on to
the LPC synthesis filter.
4.2.1.3. Generate Excitation
The pulses signal is multiplied with the quantization gain to create
the excitation signal.
4.2.1.4. LTP Synthesis
For voiced speech, the excitation signal e(n) is input to an LTP
synthesis filter that will recreate the long term correlation that
was removed in the LTP analysis filter and generate an LPC excitation
signal e_LPC(n), according to
d
__
e_LPC(n) = e(n) + \ e_LPC(n - L - i) * b_i,
/_
i=-d
using the pitch lag L, and the decoded LTP coefficients b_i. For
unvoiced speech, the output signal is simply a copy of the excitation
signal, i.e., e_LPC(n) = e(n).
4.2.1.5. LPC Synthesis
In a similar manner, the short-term correlation that was removed in
the LPC analysis filter is recreated in the LPC synthesis filter.
The LPC excitation signal e_LPC(n) is filtered using the LTP
coefficients a_i, according to
d_LPC
__
y(n) = e_LPC(n) + \ y(n - i) * a_i,
/_
i=1
where d_LPC is the LPC synthesis filter order, and y(n) is the
decoded output signal.
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4.2.2. Header Bits
The LP layer begins with two to eight header bits, decoded in
silk_Decode() (silk_dec_API.c). These consist of one Voice Activity
Detection (VAD) bit per frame (up to 3), followed by a single flag
indicating the presence of LBRR frames. For a stereo packet, these
flags correspond to the mid channel, and a second set of flags is
included for the side channel.
Because these are the first symbols decoded by the range coder, they
can be extracted directly from the upper bits of the first byte of
compressed data. Thus, a receiver can determine if an Opus frame
contains any active SILK frames or if it contains LBRR frames without
the overhead of using the range decoder.
4.2.3. LBRR Flags
If an Opus frame contains more than one SILK frame, then for each
channel that has its LBRR flag set, a set of per-frame LBRR flags is
decoded. When there are two SILK frames present, the 2-frame LBRR
flag PDF from Table 2 is used, and when there are three SILK frames
the 3-frame LBRR flag PDF is used. For each channel, the resulting
2- or 3-bit integer contains the corresponding LBRR flag for each
frame, packed in order from the LSb to the MSb.
LBRR frames do not include their own separate VAD flags. An LBRR
frame is only meant to be transmitted for active speech, thus all
LBRR frames are treated as active.
4.2.4. SILK/LBRR Frame Contents
Each SILK frame or LBRR frame includes a set of side information...
4.2.4.1. Frame Type
Each SILK frame or LBRR frame begins with a single _frame type_
symbol that jointly codes the signal type and quantization offset
type of the corresponding frame. If the current frame is an normal
SILK frame whose VAD bit was not set (an _inactive_ frame), then the
frame type symbol takes on the value either 0 or 1 and is decoded
using the first PDF in Table 3. If the frame is an LBRR frame or a
normal SILK frame whose VAD flag was set (an _active_ frame), then
the symbol ranges from 2 to 5, inclusive, and is decoded using the
second PDF in Table 3. Table 4 translates between the value of the
frame type symbol and the corresponding signal type and quantization
offset type.
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+----------------+-----------------------------+
| VAD Flag | PDF |
+----------------+-----------------------------+
| Inactive | {26, 230, 0, 0, 0, 0}/256 |
| | |
| Active or LBRR | {0, 0, 24, 74, 148, 10}/256 |
+----------------+-----------------------------+
Table 3: Frame Type PDFs
+------------+-------------+--------------------------+
| Frame Type | Signal Type | Quantization Offset Type |
+------------+-------------+--------------------------+
| 0 | Non-speech | 0 |
| | | |
| 1 | Non-speech | 1 |
| | | |
| 2 | Unvoiced | 0 |
| | | |
| 3 | Unvoiced | 1 |
| | | |
| 4 | Voiced | 0 |
| | | |
| 5 | Voiced | 1 |
+------------+-------------+--------------------------+
Table 4: Signal Type and Quantization Offset Type from Frame Type
4.2.4.2. Sub-Frame Gains
A separate quantization gain is coded for each 5 ms subframe. These
gains control the step size between quantization levels of the
excitation signal and, therefore, the quality of the reconstruction.
They are independent of the pitch gains coded for voiced frames. The
quantization gains are themselves uniformly quantized to 6 bits on a
log scale, giving them a resolution of approximately 1.369 dB and a
range of approximately 1.94 dB to 88.21 dB. For the first SILK
frame, the first LBRR frame, or an LBRR frame where the previous LBRR
frame was not coded, an independent coding method is used for the
first subframe. The 3 most significant bits of the quantization gain
are decoded using a PDF selected from Table 5 based on the decoded
signal type.
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+-------------+------------------------------------+
| Signal Type | PDF |
+-------------+------------------------------------+
| Non-speech | {32, 112, 68, 29, 12, 1, 1, 1}/256 |
| | |
| Unvoiced | {2, 17, 45, 60, 62, 47, 19, 4}/256 |
| | |
| Voiced | {1, 3, 26, 71, 94, 50, 9, 2}/256 |
+-------------+------------------------------------+
Table 5: PDFs for Independent Quantization Gain MSb Coding
The 3 least significant bits are decoded using a uniform PDF:
+--------------------------------------+
| PDF |
+--------------------------------------+
| {32, 32, 32, 32, 32, 32, 32, 32}/256 |
+--------------------------------------+
Table 6: PDF for Independent Quantization Gain LSb Coding
For all other subframes (including the first subframe of the frame
when not using independent coding), the quantization gain is coded
relative to the gain from the previous subframe. The PDF in Table 7
yields a delta gain index between 0 and 40, inclusive.
+-------------------------------------------------------------------+
| PDF |
+-------------------------------------------------------------------+
| {6, 5, 11, 31, 132, 21, 8, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, |
| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
| 1}/256 |
+-------------------------------------------------------------------+
Table 7: PDF for Delta Quantization Gain Coding
The following formula translates this index into a quantization gain
for the current subframe using the gain from the previous subframe:
log_gain = min(max(2*gain_index - 16,
previous_log_gain + gain_index - 4), 63)
silk_gains_dequant() (silk_gain_quant.c) dequantizes the gain for the
_k_th subframe and converts it into a linear Q16 scale factor via
gain_Q16[k] = silk_log2lin((0x1D1C71*log_gain>>16) + 2090)
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The function silk_log2lin() (silk_log2lin.c) computes an
approximation of of 2**(inLog_Q7/128.0), where inLog_Q7 is its Q7
input. Let i = inLog_Q7>>7 be the integer part of inLogQ7 and f =
inLog_Q7&127 be the fractional part. Then, if i < 16, then
(1<<i) + (((-174*f*(128-f)>>16)+f)>>7)*(1<<i)
yields the approximate exponential. Otherwise, silk_log2lin uses
(1<<i) + ((-174*f*(128-f)>>16)+f)*((1<<i)>>7) .
4.2.4.3. Normalized Line Spectral Frequencies
Normalized Line Spectral Frequencies (LSFs) follow the quantization
gains in the bitstream, and represent the Linear Prediction
Coefficients (LPCs) for the current SILK frame. Once decoded, they
form an increasing list of Q15 values between 0 and 1. These
represent the interleaved zeros on the unit circle between 0 and pi
(hence "normalized") in the standard decomposition of the LPC filter
into a symmetric part and an anti-symmetric part (P and Q in
Section 4.2.4.3.3). Because of non-linear effects in the decoding
process, an implementation SHOULD match the fixed-point arithmetic
described in this section exactly. The reference decoder uses fixed-
point arithmetic for this even when running in floating point mode,
for this reason. An encoder SHOULD also use the same process.
The normalized LSFs are coded using a two-stage vector quantizer
(VQ). NB and MB frames use an order-10 predictor, while WB frames
use an order-16 predictor, and thus have different sets of tables.
The first VQ stage uses a 32-element codebook, coded with one of the
PDFs in Table 8, depending on the audio bandwidth and the signal type
of the current SILK or LBRR frame. This yields a single index, _I1_,
for the entire frame. This indexes an element in a coarse codebook,
selects the PDFs for the second stage of the VQ, and selects the
prediction weights used to remove intra-frame redundancy from the
second stage. The actual codebook elements are listed in Table 17
and Table 18, but they are not needed until the last stages of
reconstructing the LSF coefficients.
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+-----------+------------+------------------------------------------+
| Audio | Signal | PDF |
| Bandwidth | Type | |
+-----------+------------+------------------------------------------+
| NB or MB | Non-speech | {44, 34, 30, 19, 21, 12, 11, 3, 3, 2, |
| | or | 16, 2, 2, 1, 5, 2, 1, 3, 3, 1, 1, 2, 2, |
| | unvoiced | 2, 3, 1, 9, 9, 2, 7, 2, 1}/256 |
| | | |
| NB or MB | Voiced | {1, 10, 1, 8, 3, 8, 8, 14, 13, 14, 1, |
| | | 14, 12, 13, 11, 11, 12, 11, 10, 10, 11, |
| | | 8, 9, 8, 7, 8, 1, 1, 6, 1, 6, 5}/256 |
| | | |
| WB | Non-speech | {31, 21, 3, 17, 1, 8, 17, 4, 1, 18, 16, |
| | or | 4, 2, 3, 1, 10, 1, 3, 16, 11, 16, 2, 2, |
| | unvoiced | 3, 2, 11, 1, 4, 9, 8, 7, 3}/256 |
| | | |
| WB | Voiced | {1, 4, 16, 5, 18, 11, 5, 14, 15, 1, 3, |
| | | 12, 13, 14, 14, 6, 14, 12, 2, 6, 1, 12, |
| | | 12, 11, 10, 3, 10, 5, 1, 1, 1, 3}/256 |
+-----------+------------+------------------------------------------+
Table 8: PDFs for Normalized LSF Index Stage-1 Decoding
A total of 16 PDFs, each with a different PDF, are available for the
LSF residual in the second stage: the 8 (a...h) for NB and MB frames
given in Table 9, and the 8 (i...p) for WB frames given in Table 10.
Which PDF is used for which coefficient is driven by the index, I1,
decoded in the first stage. Table 11 lists the letter of the
corresponding PDF for each normalized LSF coefficient for NB and MB,
and Table 12 lists them for WB.
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+----------+--------------------------------------+
| Codebook | PDF |
+----------+--------------------------------------+
| a | {1, 1, 1, 15, 224, 11, 1, 1, 1}/256 |
| | |
| b | {1, 1, 2, 34, 183, 32, 1, 1, 1}/256 |
| | |
| c | {1, 1, 4, 42, 149, 55, 2, 1, 1}/256 |
| | |
| d | {1, 1, 8, 52, 123, 61, 8, 1, 1}/256 |
| | |
| e | {1, 3, 16, 53, 101, 74, 6, 1, 1}/256 |
| | |
| f | {1, 3, 17, 55, 90, 73, 15, 1, 1}/256 |
| | |
| g | {1, 7, 24, 53, 74, 67, 26, 3, 1}/256 |
| | |
| h | {1, 1, 18, 63, 78, 58, 30, 6, 1}/256 |
+----------+--------------------------------------+
Table 9: PDFs for NB/MB Normalized LSF Index Stage-2 Decoding
+----------+---------------------------------------+
| Codebook | PDF |
+----------+---------------------------------------+
| i | {1, 1, 1, 9, 232, 9, 1, 1, 1}/256 |
| | |
| j | {1, 1, 2, 28, 186, 35, 1, 1, 1}/256 |
| | |
| k | {1, 1, 3, 42, 152, 53, 2, 1, 1}/256 |
| | |
| l | {1, 1, 10, 49, 126, 65, 2, 1, 1}/256 |
| | |
| m | {1, 4, 19, 48, 100, 77, 5, 1, 1}/256 |
| | |
| n | {1, 1, 14, 54, 100, 72, 12, 1, 1}/256 |
| | |
| o | {1, 1, 15, 61, 87, 61, 25, 4, 1}/256 |
| | |
| p | {1, 7, 21, 50, 77, 81, 17, 1, 1}/256 |
+----------+---------------------------------------+
Table 10: PDFs for WB Normalized LSF Index Stage-2 Decoding
+----+---------------------+
| I1 | Coefficient |
+----+---------------------+
| | 0 1 2 3 4 5 6 7 8 9 |
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| 0 | a a a a a a a a a a |
| | |
| 1 | b d b c c b c b b b |
| | |
| 2 | c b b b b b b b b b |
| | |
| 3 | b c c c c b c b b b |
| | |
| 4 | c d d d d c c c c c |
| | |
| 5 | a f d d c c c c b b |
| | |
| g | a c c c c c c c c b |
| | |
| 7 | c d g e e e f e f f |
| | |
| 8 | c e f f e f e g e e |
| | |
| 9 | c e e h e f e f f e |
| | |
| 10 | e d d d c d c c c c |
| | |
| 11 | b f f g e f e f f f |
| | |
| 12 | c h e g f f f f f f |
| | |
| 13 | c h f f f f f g f e |
| | |
| 14 | d d f e e f e f e e |
| | |
| 15 | c d d f f e e e e e |
| | |
| 16 | c e e g e f e f f f |
| | |
| 17 | c f e g f f f e f e |
| | |
| 18 | c h e f e f e f f f |
| | |
| 19 | c f e g h g f g f e |
| | |
| 20 | d g h e g f f g e f |
| | |
| 21 | c h g e e e f e f f |
| | |
| 22 | e f f e g g f g f e |
| | |
| 23 | c f f g f g e g e e |
| | |
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| 24 | e f f f d h e f f e |
| | |
| 25 | c d e f f g e f f e |
| | |
| 26 | c d c d d e c d d d |
| | |
| 27 | b b c c c c c d c c |
| | |
| 28 | e f f g g g f g e f |
| | |
| 29 | d f f e e e e d d c |
| | |
| 30 | c f d h f f e e f e |
| | |
| 31 | e e f e f g f g f e |
+----+---------------------+
Table 11: Codebook Selection for NB/MB Normalized LSF Index Stage 2
Decoding
+----+------------------------------------------------+
| I1 | Coefficient |
+----+------------------------------------------------+
| | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
| | |
| 0 | i i i i i i i i i i i i i i i i |
| | |
| 1 | k l l l l l k k k k k j j j i l |
| | |
| 2 | k n n l p m m n k n m n n m l l |
| | |
| 3 | i k j k k j j j j j i i i i i j |
| | |
| 4 | i o n m o m p n m m m n n m m l |
| | |
| 5 | i l n n m l l n l l l l l l k m |
| | |
| 6 | i i i i i i i i i i i i i i i i |
| | |
| 7 | i k o l p k n l m n n m l l k l |
| | |
| 8 | i o k o o m n m o n m m n l l l |
| | |
| 9 | k j i i i i i i i i i i i i i i |
| | |
| j0 | i j i i i i i i i i i i i i i j |
| | |
| 11 | k k l m n l l l l l l l k k j l |
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| 12 | k k l l m l l l l l l l l k j l |
| | |
| 13 | l m m m o m m n l n m m n m l m |
| | |
| 14 | i o m n m p n k o n p m m l n l |
| | |
| 15 | i j i j j j j j j j i i i i j i |
| | |
| 16 | j o n p n m n l m n m m m l l m |
| | |
| 17 | j l l m m l l n k l l n n n l m |
| | |
| 18 | k l l k k k l k j k j k j j j m |
| | |
| 19 | i k l n l l k k k j j i i i i i |
| | |
| 20 | l m l n l l k k j j j j j k k m |
| | |
| 21 | k o l p p m n m n l n l l k l l |
| | |
| 22 | k l n o o l n l m m l l l l k m |
| | |
| 23 | j l l m m m m l n n n l j j j j |
| | |
| 24 | k n l o o m p m m n l m m l l l |
| | |
| 25 | i o j j i i i i i i i i i i i i |
| | |
| 26 | i o o l n k n n l m m p p m m m |
| | |
| 27 | l l p l n m l l l k k l l l k l |
| | |
| 28 | i i j i i i k j k j j k k k j j |
| | |
| 29 | i l k n l l k l k j i i j i i j |
| | |
| 30 | l n n m p n l l k l k k j i j i |
| | |
| 31 | k l n l m l l l k j k o m i i i |
+----+------------------------------------------------+
Table 12: Codebook Selection for WB Normalized LSF Index Stage 2
Decoding
Decoding the second stage residual proceeds as follows. For each
coefficient, the decoder reads a symbol using the PDF corresponding
to I1 from either Table 11 or Table 12, and subtracts 4 from the
result to given an index in the range -4 to 4, inclusive. If the
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index is either -4 or 4, it reads a second symbol using the PDF in
Table 13, and adds the value of this second symbol to the index,
using the same sign. This gives the index, I2[k], a total range of
-10 to 10, inclusive.
+-------------------------------+
| PDF |
+-------------------------------+
| {156, 60, 24, 9, 4, 2, 1}/256 |
+-------------------------------+
Table 13: PDF for Normalized LSF Index Extension Decoding
The decoded indices from both stages are translated back into
normalized LSF coefficients in silk_NLSF_decode()
(silk_NLSF_decode.c). The stage-2 indices represent residuals after
both the first stage of the VQ and a separate backwards-prediction
step. The backwards prediction process in the encoder subtracts a
prediction from each residual formed by a multiple of the coefficient
that follows it. The decoder must undo this process. Table 14
contains lists of prediction weights for each coefficient. There are
two lists for NB and MB, and another two lists for WB, giving two
possible prediction weights for each coefficient.
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+-------------+-----+-----+-----+-----+
| Coefficient | A | B | C | D |
+-------------+-----+-----+-----+-----+
| 0 | 179 | 116 | 175 | 68 |
| | | | | |
| 1 | 138 | 67 | 148 | 62 |
| | | | | |
| 2 | 140 | 82 | 160 | 66 |
| | | | | |
| 3 | 148 | 59 | 176 | 60 |
| | | | | |
| 4 | 151 | 92 | 178 | 72 |
| | | | | |
| 5 | 149 | 72 | 173 | 117 |
| | | | | |
| 6 | 153 | 100 | 174 | 85 |
| | | | | |
| 7 | 151 | 89 | 164 | 90 |
| | | | | |
| 8 | 163 | 92 | 177 | 118 |
| | | | | |
| 9 | | | 174 | 136 |
| | | | | |
| 10 | | | 196 | 151 |
| | | | | |
| 11 | | | 182 | 142 |
| | | | | |
| 12 | | | 198 | 160 |
| | | | | |
| 13 | | | 192 | 142 |
| | | | | |
| 14 | | | 182 | 155 |
+-------------+-----+-----+-----+-----+
Table 14: Prediction Weights for Normalized LSF Decoding
The prediction is undone using the procedure implemented in
silk_NLSF_residual_dequant() (silk_NLSF_decode.c), which is as
follows. Each coefficient selects its prediction weight from one of
the two lists based on the stage-1 index, I1. Table 15 gives the
selections for each coefficient for NB and MB, and Table 16 gives the
selections for WB. Let d_LPC be the order of the codebook, i.e., 10
for NB and MB, and 16 for WB, and let pred_Q8[k] be the weight for
the _k_th coefficient selected by this process for 0 <= k < d_LPC-1.
Then, the stage-2 residual for each coefficient is computed via
res_Q10[k] = (k+1 < d_LPC ? (res_Q10[k+1]*pred_Q8[k])>>8 : 0)
+ ((((I2[k]<<10) + sign(I2[k])*102)*qstep)>>16) ,
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where qstep is the Q16 quantization step size, which is 11796 for NB
and MB and 9830 for WB (representing step sizes of approximately 0.18
and 0.15, respectively).
+----+-------------------+
| I1 | Coefficient |
+----+-------------------+
| | 0 1 2 3 4 5 6 7 8 |
| | |
| 0 | A B A A A A A A A |
| | |
| 1 | B A A A A A A A A |
| | |
| 2 | A A A A A A A A A |
| | |
| 3 | B B B A A A A B A |
| | |
| 4 | A B A A A A A A A |
| | |
| 5 | A B A A A A A A A |
| | |
| 6 | B A B B A A A B A |
| | |
| 7 | A B B A A B B A A |
| | |
| 8 | A A B B A B A B B |
| | |
| 9 | A A B B A A B B B |
| | |
| 10 | A A A A A A A A A |
| | |
| 11 | A B A B B B B B A |
| | |
| 12 | A B A B B B B B A |
| | |
| 13 | A B B B B B B B A |
| | |
| 14 | B A B B A B B B B |
| | |
| 15 | A B B B B B A B A |
| | |
| 16 | A A B B A B A B A |
| | |
| 17 | A A B B B A B B B |
| | |
| 18 | A B B A A B B B A |
| | |
| 19 | A A A B B B A B A |
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| 20 | A B B A A B A B A |
| | |
| 21 | A B B A A A B B A |
| | |
| 22 | A A A A A B B B B |
| | |
| 23 | A A B B A A A B B |
| | |
| 24 | A A A B A B B B B |
| | |
| 25 | A B B B B B B B A |
| | |
| 26 | A A A A A A A A A |
| | |
| 27 | A A A A A A A A A |
| | |
| 28 | A A B A B B A B A |
| | |
| 29 | A A A B A A A A A |
| | |
| 30 | A A A B B A B A B |
| | |
| 31 | B A B B A B B B B |
+----+-------------------+
Table 15: Prediction Weight Selection for NB/MB Normalized LSF
Decoding
+----+---------------------------------------------+
| I1 | Coefficient |
+----+---------------------------------------------+
| | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
| | |
| 0 | C C C C C C C C C C C C C C D |
| | |
| 1 | C C C C C C C C C C C C C C C |
| | |
| 2 | C C D C C D D D C D D D D C C |
| | |
| 3 | C C C C C C C C C C C C D C C |
| | |
| 4 | C D D C D C D D C D D D D D C |
| | |
| 5 | C D C C C C C C C C C C C C C |
| | |
| 6 | D C C C C C C C C C C D C D C |
| | |
| 7 | C D D C C C D C D D D C D C D |
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| 8 | C D C D D C D C D C D D D D D |
| | |
| 9 | C C C C C C C C C C C C C C D |
| | |
| 10 | C D C C C C C C C C C C C C C |
| | |
| 11 | C C D C D D D D D D D C D C C |
| | |
| 12 | C C D C C D C D C D C C D C C |
| | |
| 13 | C C C C D D C D C D D D D C C |
| | |
| 14 | C D C C C D D C D D D C D D D |
| | |
| 15 | C C D D C C C C C C C C D D C |
| | |
| 16 | C D D C D C D D D D D C D C C |
| | |
| 17 | C C D C C C C D C C D D D C C |
| | |
| 18 | C C C C C C C C C C C C C C D |
| | |
| 19 | C C C C C C C C C C C C D C C |
| | |
| 20 | C C C C C C C C C C C C C C C |
| | |
| 21 | C D C D C D D C D C D C D D C |
| | |
| 22 | C C D D D D C D D C C D D C C |
| | |
| 23 | C D D C D C D C D C C C C D C |
| | |
| 24 | C C C D D C D C D D D D D D D |
| | |
| 25 | C C C C C C C C C C C C C C D |
| | |
| 26 | C D D C C C D D C C D D D D D |
| | |
| 27 | C C C C C D C D D D D C D D D |
| | |
| 28 | C C C C C C C C C C C C C C D |
| | |
| 29 | C C C C C C C C C C C C C C D |
| | |
| 30 | D C C C C C C C C C C D C C C |
| | |
| 31 | C C D C C D D D C C D C C D C |
+----+---------------------------------------------+
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Table 16: Prediction Weight Selection for WB Normalized LSF Decoding
The spectral distortion introduced by the quantization of each LSF
coefficient varies, so the stage-2 residual is weighted accordingly,
using the low-complexity weighting function proposed in
[laroia-icassp]. The weights are derived directly from the stage-1
codebook vector. Let cb1_Q8[k] be the _k_th entry of the stage-1
codebook vector from Table 17 or Table 18. Then for 0 <= k < d_LPC
the following expression computes the square of the weight as a Q18
value:
w2_Q18[k] = (1024/(cb1_Q8[k] - cb1_Q8[k-1])
+ 1024/(cb1_Q8[k+1] - cb1_Q8[k])) << 16 ,
where cb1_Q8[-1] = 0 and cb1_Q8[d_LPC] = 256, and the division is
exact integer division. This is reduced to an unsquared, Q9 value
using the following square-root approximation:
i = ilog(w2_Q18[k])
f = (w2_Q18[k]>>(i-8)) & 127
y = ((i&1) ? 32768 : 46214) >> ((32-i)>>1)
w_Q9[k] = y + ((213*f*y)>>16)
The cb1_Q8[] vector completely determines these weights, and they may
be tabulated and stored as 13-bit unsigned values (with a range of
1819 to 5227) to avoid computing them when decoding. The reference
implementation computes them on the fly in
silk_NLSF_VQ_weights_laroia() (silk_NLSF_VQ_weights_laroia.c) and its
caller, to reduce the amount of ROM required.
+----+----------------------------------------+
| I1 | Codebook |
+----+----------------------------------------+
| | 0 1 2 3 4 5 6 7 8 9 |
| | |
| 0 | 12 35 60 83 108 132 157 180 206 228 |
| | |
| 1 | 15 32 55 77 101 125 151 175 201 225 |
| | |
| 2 | 19 42 66 89 114 137 162 184 209 230 |
| | |
| 3 | 12 25 50 72 97 120 147 172 200 223 |
| | |
| 4 | 26 44 69 90 114 135 159 180 205 225 |
| | |
| 5 | 13 22 53 80 106 130 156 180 205 228 |
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| 6 | 15 25 44 64 90 115 142 168 196 222 |
| | |
| 7 | 19 24 62 82 100 120 145 168 190 214 |
| | |
| 8 | 22 31 50 79 103 120 151 170 203 227 |
| | |
| 9 | 21 29 45 65 106 124 150 171 196 224 |
| | |
| 10 | 30 49 75 97 121 142 165 186 209 229 |
| | |
| 11 | 19 25 52 70 93 116 143 166 192 219 |
| | |
| 12 | 26 34 62 75 97 118 145 167 194 217 |
| | |
| 13 | 25 33 56 70 91 113 143 165 196 223 |
| | |
| 14 | 21 34 51 72 97 117 145 171 196 222 |
| | |
| 15 | 20 29 50 67 90 117 144 168 197 221 |
| | |
| 16 | 22 31 48 66 95 117 146 168 196 222 |
| | |
| 17 | 24 33 51 77 116 134 158 180 200 224 |
| | |
| 18 | 21 28 70 87 106 124 149 170 194 217 |
| | |
| 19 | 26 33 53 64 83 117 152 173 204 225 |
| | |
| 20 | 27 34 65 95 108 129 155 174 210 225 |
| | |
| 21 | 20 26 72 99 113 131 154 176 200 219 |
| | |
| 22 | 34 43 61 78 93 114 155 177 205 229 |
| | |
| 23 | 23 29 54 97 124 138 163 179 209 229 |
| | |
| 24 | 30 38 56 89 118 129 158 178 200 231 |
| | |
| 25 | 21 29 49 63 85 111 142 163 193 222 |
| | |
| 26 | 27 48 77 103 133 158 179 196 215 232 |
| | |
| 27 | 29 47 74 99 124 151 176 198 220 237 |
| | |
| 28 | 33 42 61 76 93 121 155 174 207 225 |
| | |
| 29 | 29 53 87 112 136 154 170 188 208 227 |
| | |
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| 30 | 24 30 52 84 131 150 166 186 203 229 |
| | |
| 31 | 37 48 64 84 104 118 156 177 201 230 |
+----+----------------------------------------+
Table 17: Codebook Vectors for NB/MB Normalized LSF Stage 1 Decoding
+----+------------------------------------------------------------+
| I1 | Codebook |
+----+------------------------------------------------------------+
| | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
| | |
| 0 | 7 23 38 54 69 85 100 116 131 147 162 178 193 208 223 239 |
| | |
| 1 | 13 25 41 55 69 83 98 112 127 142 157 171 187 203 220 236 |
| | |
| 2 | 15 21 34 51 61 78 92 106 126 136 152 167 185 205 225 240 |
| | |
| 3 | 10 21 36 50 63 79 95 110 126 141 157 173 189 205 221 237 |
| | |
| 4 | 17 20 37 51 59 78 89 107 123 134 150 164 184 205 224 240 |
| | |
| 5 | 10 15 32 51 67 81 96 112 129 142 158 173 189 204 220 236 |
| | |
| 6 | 8 21 37 51 65 79 98 113 126 138 155 168 179 192 209 218 |
| | |
| 7 | 12 15 34 55 63 78 87 108 118 131 148 167 185 203 219 236 |
| | |
| 8 | 16 19 32 36 56 79 91 108 118 136 154 171 186 204 220 237 |
| | |
| 9 | 11 28 43 58 74 89 105 120 135 150 165 180 196 211 226 241 |
| | |
| 10 | 6 16 33 46 60 75 92 107 123 137 156 169 185 199 214 225 |
| | |
| 11 | 11 19 30 44 57 74 89 105 121 135 152 169 186 202 218 234 |
| | |
| 12 | 12 19 29 46 57 71 88 100 120 132 148 165 182 199 216 233 |
| | |
| 13 | 17 23 35 46 56 77 92 106 123 134 152 167 185 204 222 237 |
| | |
| 14 | 14 17 45 53 63 75 89 107 115 132 151 171 188 206 221 240 |
| | |
| 15 | 9 16 29 40 56 71 88 103 119 137 154 171 189 205 222 237 |
| | |
| 16 | 16 19 36 48 57 76 87 105 118 132 150 167 185 202 218 236 |
| | |
| 17 | 12 17 29 54 71 81 94 104 126 136 149 164 182 201 221 237 |
| | |
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| 18 | 15 28 47 62 79 97 115 129 142 155 168 180 194 208 223 238 |
| | |
| 19 | 8 14 30 45 62 78 94 111 127 143 159 175 192 207 223 239 |
| | |
| 20 | 17 30 49 62 79 92 107 119 132 145 160 174 190 204 220 235 |
| | |
| 21 | 14 19 36 45 61 76 91 108 121 138 154 172 189 205 222 238 |
| | |
| 22 | 12 18 31 45 60 76 91 107 123 138 154 171 187 204 221 236 |
| | |
| 23 | 13 17 31 43 53 70 83 103 114 131 149 167 185 203 220 237 |
| | |
| 24 | 17 22 35 42 58 78 93 110 125 139 155 170 188 206 224 240 |
| | |
| 25 | 8 15 34 50 67 83 99 115 131 146 162 178 193 209 224 239 |
| | |
| 26 | 13 16 41 66 73 86 95 111 128 137 150 163 183 206 225 241 |
| | |
| 27 | 17 25 37 52 63 75 92 102 119 132 144 160 175 191 212 231 |
| | |
| 28 | 19 31 49 65 83 100 117 133 147 161 174 187 200 213 227 242 |
| | |
| 29 | 18 31 52 68 88 103 117 126 138 149 163 177 192 207 223 239 |
| | |
| 30 | 16 29 47 61 76 90 106 119 133 147 161 176 193 209 224 240 |
| | |
| 31 | 15 21 35 50 61 73 86 97 110 119 129 141 175 198 218 237 |
+----+------------------------------------------------------------+
Table 18: Codebook Vectors for WB Normalized LSF Stage 1 Decoding
Given the stage-1 codebook entry cb1_Q8[], the stage-2 residual
res_Q10[], and their corresponding weights, w_Q9[], the reconstructed
normalized LSF coefficients are
NLSF_Q15[k] = (cb1_Q8[k]<<7) + (res_Q10[k]<<14)/w_Q9[k] ,
where the division is exact integer division. However, nothing thus
far in the reconstruction process, nor in the quantization process in
the encoder, guarantees that the coefficients are monotonically
increasing and separated well enough to ensure a stable filter. When
using the reference encoder, roughly 2% of frames violate this
constraint. The next section describes a stabilization procedure
used to make these guarantees.
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4.2.4.3.1. Normalized LSF Stabilization
The normalized LSF stabilization procedure is implemented in
silk_NLSF_stabilize() (silk_NLSF_stabilize.c). This process ensures
that consecutive values of the normalized LSF coefficients,
NLSF_Q15[], are spaced some minimum distance apart (predetermined to
be the 0.01 percentile of a large training set). Table 19 gives the
minimum spacings for NB and MB and those for WB, where row k is the
minimum allowed value of NLSF_Q[k]-NLSF_Q[k-1]. For the purposes of
computing this spacing for the first and last coefficient,
NLSF_Q15[-1] is taken to be 0, and NLSF_Q15[d_LPC] is taken to be
32768.
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+-------------+-----------+-----+
| Coefficient | NB and MB | WB |
+-------------+-----------+-----+
| 0 | 250 | 100 |
| | | |
| 1 | 3 | 3 |
| | | |
| 2 | 6 | 40 |
| | | |
| 3 | 3 | 3 |
| | | |
| 4 | 3 | 3 |
| | | |
| 5 | 3 | 3 |
| | | |
| 6 | 4 | 5 |
| | | |
| 7 | 3 | 14 |
| | | |
| 8 | 3 | 14 |
| | | |
| 9 | 3 | 10 |
| | | |
| 10 | 461 | 11 |
| | | |
| 11 | | 3 |
| | | |
| 12 | | 8 |
| | | |
| 13 | | 9 |
| | | |
| 14 | | 7 |
| | | |
| 15 | | 3 |
| | | |
| 16 | | 347 |
+-------------+-----------+-----+
Table 19: Minimum Spacing for Normalized LSF Coefficients
The procedure starts off by trying to make small adjustments which
attempt to minimize the amount of distortion introduced. After 20
such adjustments, it falls back to a more direct method which
guarantees the constraints are enforced but may require large
adjustments.
Let NDeltaMin_Q15[k] be the minimum required spacing for the current
audio bandwidth from Table 19. First, the procedure finds the index
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i where NLSF_Q15[i] - NLSF_Q15[i-1] - NDeltaMin_Q15[i] is the
smallest, breaking ties by using the lower value of i. If this value
is non-negative, then the stabilization stops; the coefficients
satisfy all the constraints. Otherwise, if i == 0, it sets
NLSF_Q15[0] to NDeltaMin_Q15[0], and if i == d_LPC, it sets
NLSF_Q15[d_LPC-1] to (32768 - NDeltaMin_Q15[d_LPC]). For all other
values of i, both NLSF_Q15[i-1] and NLSF_Q15[i] are updated as
follows:
i-1
__
min_center_Q15 = (NDeltaMin[i]>>1) + \ NDeltaMin[k]
/_
k=0
d_LPC
__
max_center_Q15 = 32768 - (NDeltaMin[i]>>1) - \ NDeltaMin[k]
/_
k=i+1
center_freq_Q15 = clamp(min_center_Q15[i],
(NLSF_Q15[i-1] + NLSF_Q15[i] + 1)>>1,
max_center_Q15[i])
NLSF_Q15[i-1] = center_freq_Q15 - (NDeltaMin_Q15[i]>>1)
NLSF_Q15[i] = NLSF_Q15[i-1] + NDeltaMin_Q15[i] .
Then the procedure repeats again, until it has executed 20 times, or
until it stops because the coefficients satisfy all the constraints.
After the 20th repetition of the above, the following fallback
procedure executes once. First, the values of NLSF_Q15[k] for
0 <= k < d_LPC are sorted in ascending order. Then for each value of
k from 0 to d_LPC-1, NLSF_Q15[k] is set to
max(NLSF_Q15[k], NLSF_Q15[k-1] + NDeltaMin_Q15[k]) .
Next, for each value of k from d_LPC-1 down to 0, NLSF_Q15[k] is set
to
min(NLSF_Q15[k], NLSF_Q15[k+1] - NDeltaMin_Q15[k+1]) .
4.2.4.3.2. Normalized LSF Interpolation
For 20 ms SILK frames, the first half of the frame (i.e., the first
two sub-frames) may use normalized LSF coefficients that are
interpolated between the decoded LSFs for the previous frame and the
current frame. A Q2 interpolation factor follows the LSF coefficient
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indices in the bitstream, which is decoded using the PDF in Table 20.
This happens in silk_decode_indices() (silk_decode_indices.c). For
the first frame after a decoder reset, when no prior LSF coefficients
are available, the decoder still decodes this factor, but ignores its
value and always uses 4 instead. For 10 ms SILK frames, this factor
is not stored at all.
+---------------------------+
| PDF |
+---------------------------+
| {13, 22, 29, 11, 181}/256 |
+---------------------------+
Table 20: PDF for Normalized LSF Interpolation Index
Let n2_Q15[k] be the normalized LSF coefficients decoded by the
procedure in Section 4.2.4.3, n0_Q15[k] be the LSF coefficients
decoded for the prior frame, and w_Q2 be the interpolation factor.
Then the normalized LSF coefficients used for the first half of a
20 ms frame, n1_Q15[k], are
n1_Q15[k] = n0_Q15[k] + (w_Q2*(n2_Q15[k] - n0_Q15[k]) >> 2) .
This interpolation is performed in silk_decode_parameters()
(silk_decode_parameters.c).
4.2.4.3.3. Converting Normalized LSF Coefficients to LPCs
Any LPC filter A(z) can be split into a symmetric part P(z) and an
anti-symmetric part Q(z) such that
d_LPC
__ -k 1
A(z) = 1 - \ a[k] * z = - * (P(z) + Q(z))
/_ 2
k=1
with
-d_LPC-1 -1
P(z) = A(z) + z * A(z )
-d_LPC-1 -1
Q(z) = A(z) - z * A(z ) .
The even normalized LSF coefficients correspond to a pair of
conjugate roots of P(z), while the odd coefficients correspond to a
pair of conjugate roots of Q(z), all of which lie on the unit circle.
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In addition, P(z) has a root at pi and Q(z) has a root at 0. Thus,
they may be reconstructed mathematically from a set of normalized LSF
coefficients, n[k], as
d_LPC/2-1
-1 ___ -1 -2
P(z) = (1 + z ) * | | (1 - 2*cos(pi*n[2*k])*z + z )
k=0
d_LPC/2-1
-1 ___ -1 -2
Q(z) = (1 - z ) * | | (1 - 2*cos(pi*n[2*k+1])*z + z )
k=0
However, SILK performs this reconstruction using a fixed-point
approximation that can be reproduced in a bit-exact manner in all
decoders to avoid prediction drift. The function silk_NLSF2A()
(silk_NLSF2A.c) implements this procedure.
To start, it approximates cos(pi*n[k]) using a table lookup with
linear interpolation. The encoder SHOULD use the inverse of this
piecewise linear approximation, rather than true the inverse of the
cosine function, when deriving the normalized LSF coefficients.
The top 7 bits of each normalized LSF coefficient index a value in
the table, and the next 8 bits interpolate between it and the next
value. Let i = n[k]>>8 be the integer index and f = n[k]&255 be the
fractional part of a given coefficient. Then the approximated
cosine, c_Q17[k], is
c_Q17[k] = (cos_Q13[i]*256 + (cos_Q13[i+1]-cos_Q13[i])*f + 8) >> 4 ,
where cos_Q13[i] is the corresponding entry of Table 21.
+-----+-------+-------+-------+-------+
| | 0 | 1 | 2 | 3 |
+-----+-------+-------+-------+-------+
| 0 | 8192 | 8190 | 8182 | 8170 |
| | | | | |
| 4 | 8152 | 8130 | 8104 | 8072 |
| | | | | |
| 8 | 8034 | 7994 | 7946 | 7896 |
| | | | | |
| 12 | 7840 | 7778 | 7714 | 7644 |
| | | | | |
| 16 | 7568 | 7490 | 7406 | 7318 |
| | | | | |
| 20 | 7226 | 7128 | 7026 | 6922 |
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| 24 | 6812 | 6698 | 6580 | 6458 |
| | | | | |
| 28 | 6332 | 6204 | 6070 | 5934 |
| | | | | |
| 32 | 5792 | 5648 | 5502 | 5352 |
| | | | | |
| 36 | 5198 | 5040 | 4880 | 4718 |
| | | | | |
| 40 | 4552 | 4382 | 4212 | 4038 |
| | | | | |
| 44 | 3862 | 3684 | 3502 | 3320 |
| | | | | |
| 48 | 3136 | 2948 | 2760 | 2570 |
| | | | | |
| 52 | 2378 | 2186 | 1990 | 1794 |
| | | | | |
| 56 | 1598 | 1400 | 1202 | 1002 |
| | | | | |
| 60 | 802 | 602 | 402 | 202 |
| | | | | |
| 64 | 0 | -202 | -402 | -602 |
| | | | | |
| 68 | -802 | -1002 | -1202 | -1400 |
| | | | | |
| 72 | -1598 | -1794 | -1990 | -2186 |
| | | | | |
| 76 | -2378 | -2570 | -2760 | -2948 |
| | | | | |
| 80 | -3136 | -3320 | -3502 | -3684 |
| | | | | |
| 84 | -3862 | -4038 | -4212 | -4382 |
| | | | | |
| 88 | -4552 | -4718 | -4880 | -5040 |
| | | | | |
| 92 | -5198 | -5352 | -5502 | -5648 |
| | | | | |
| 96 | -5792 | -5934 | -6070 | -6204 |
| | | | | |
| 100 | -6332 | -6458 | -6580 | -6698 |
| | | | | |
| 104 | -6812 | -6922 | -7026 | -7128 |
| | | | | |
| 108 | -7226 | -7318 | -7406 | -7490 |
| | | | | |
| 112 | -7568 | -7644 | -7714 | -7778 |
| | | | | |
| 116 | -7840 | -7896 | -7946 | -7994 |
| | | | | |
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| 120 | -8034 | -8072 | -8104 | -8130 |
| | | | | |
| 124 | -8152 | -8170 | -8182 | -8190 |
| | | | | |
| 128 | -8192 | | | |
+-----+-------+-------+-------+-------+
Table 21: Q13 Cosine Table for LSF Conversion
Given the list of cosine values, silk_NLSF2A_find_poly()
(silk_NLSF2A.c) computes the coefficients of P and Q, described here
via a simple recurrence. Let p_Q16[k][j] and q_Q16[k][j] be the
coefficients of the products of the first (k+1) root pairs for P and
Q, with j indexing the coefficient number. Only the first (k+2)
coefficients are needed, as the products are symmetric. Let
p_Q16[0][0] = q_Q16[0][0] = 1<<16, p_Q16[0][1] = -c_Q17[0],
q_Q16[0][1] = -c_Q17[1], and d2 = d_LPC/2. As boundary conditions,
assume p_Q16[k][j] = q_Q16[k][j] = 0 for all j < 0. Also, assume
p_Q16[k][k+2] = p_Q16[k][k] and q_Q16[k][k+2] = q_Q16[k][k] (because
of the symmetry). Then, for 0 <k < d2 and 0 <= j <= k+1,
p_Q16[k][j] = p_Q16[k-1][j] + p_Q16[k-1][j-2]
- ((c_Q17[2*k]*p_Q16[k-1][j-1] + 32768)>>16) ,
q_Q16[k][j] = q_Q16[k-1][j] + q_Q16[k-1][j-2]
- ((c_Q17[2*k+1]*q_Q16[k-1][j-1] + 32768)>>16) .
The use of Q17 values for the cosine terms in an otherwise Q16
expression implicitly scales them by a factor of 2. The
multiplications in this recurrence may require up to 48 bits of
precision in the result to avoid overflow. In practice, each row of
the recurrence only depends on the previous row, so an implementation
does not need to store all of them.
silk_NLSF2A() uses the values from the last row of this recurrence to
reconstruct a 32-bit version of the LPC filter (without the leading
1.0 coefficient), a32_Q17[k], 0 <= k < d2:
a32_Q17[k] = -(q_Q16[d2-1][k+1] - q_Q16[d2-1][k])
- (p_Q16[d2-1][k+1] + p_Q16[d2-1][k])) ,
a32_Q17[d_LPC-k-1] = (q_Q16[d2-1][k+1] - q_Q16[d2-1][k])
- (p_Q16[d2-1][k+1] + p_Q16[d2-1][k])) .
The sum and difference of two terms from each of the p_Q16 and q_Q16
coefficient lists reflect the (z**-1 + 1) and (z**-1 - 1) factors of
P and Q, respectively. The promotion of the expression from Q16 to
Q17 implicitly scales the result by 1/2.
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4.2.4.3.4. Limiting the Range of the LPC Coefficients
The a32_Q17[] coefficients are too large to fit in a 16-bit value,
which significantly increases the cost of applying this filter in
fixed-point decoders. Reducing them to Q12 precision doesn't incur
any significant quality loss, but still does not guarantee they will
fit. silk_NLSF2A() applies up to 10 rounds of bandwidth expansion to
limit the dynamic range of these coefficients. Even floating-point
decoders SHOULD perform these steps, to avoid mismatch.
For each round, the process first finds the index k such that
abs(a32_Q17[k]) is the largest, breaking ties by using the lower
value of k. Then, it computes the corresponding Q12 precision value,
maxabs_Q12, subject to an upper bound to avoid overflow when
computing the chirp factor:
maxabs_Q12 = min((maxabs_Q17 + 16) >> 5, 163838) .
If this is larger than 32767, the procedure derives the chirp factor,
sc_Q16[0], to use in the bandwidth expansion as
(maxabs_Q12 - 32767) << 14
sc_Q16[0] = 65470 - -------------------------- ,
(maxabs_Q12 * (k+1)) >> 2
where the division here is exact integer division. This is an
approximation of the chirp factor needed to reduce the target
coefficient to 32767, though it is both less than 0.999 and, for
k > 0 when maxabs_Q12 is much greater than 32767, still slightly too
large.
silk_bwexpander_32() (silk_bwexpander_32.c) peforms the bandwidth
expansion (again, only when maxabs_Q12 is greater than 32767) using
the following recurrence:
a32_Q17[k] = (a32_Q17[k]*sc_Q16[k]) >> 16
sc_Q16[k+1] = (sc_Q16[0]*sc_Q16[k] + 32768) >> 16
The first multiply may require up to 48 bits of precision in the
result to avoid overflow. The second multiply must be unsigned to
avoid overflow with only 32 bits of precision. The reference
implementation uses a slightly more complex formulation that avoids
the 32-bit overflow using signed multiplication, but is otherwise
equivalent.
After 10 rounds of bandwidth expansion are performed, they are simply
saturated to 16 bits:
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a32_Q17[k] = clamp(-32768, (a32_Q17[k]+16) >> 5, 32767) << 5 .
Because this performs the actual saturation in the Q12 domain, but
converts the coefficients back to the Q17 domain for the purposes of
prediction gain limiting, this step must be performed after the 10th
round of bandwidth expansion, regardless of whether or not the Q12
version of any of the coefficients still overflow a 16-bit integer.
This saturation is not performed if maxabs_Q12 drops to 32767 or less
prior to the 10th round.
4.2.4.3.5. Limiting the Prediction Gain of the LPC Filter
Even if the Q12 coefficients would fit, the resulting filter may
still have a significant gain (especially for voiced sounds), making
the filter unstable. silk_NLSF2A() applies up to 18 additional rounds
of bandwidth expansion to limit the prediction gain. Instead of
controlling the amount of bandwidth expansion using the prediction
gain itself (which may diverge to infinity for an unstable filter),
silk_NLSF2A() uses LPC_inverse_pred_gain_QA()
(silk_LPC_inv_pred_gain.c) to compute the reflection coefficients
associated with the filter. The filter is stable if and only if the
magnitude of these coefficients is sufficiently less than one. The
reflection coefficients can be computed using a simple Levinson
recurrence, initialized with the LPC coefficients a[d_LPC-
1][n] = a[n], and then updated via
rc[k] = -a[k][k] ,
a[k][n] - a[k][k-n-1]*rc[k]
a[k-1][n] = --------------------------- .
2
1 - rc[k]
However, LPC_inverse_pred_gain_QA() approximates this using fixed-
point arithmetic to guarantee reproducible results across platforms
and implementations. It is important to run on the real Q12
coefficients that will be used during reconstruction, because small
changes in the coefficients can make a stable filter unstable, but
increasing the precision back to Q16 allows more accurate computation
of the reflection coefficients. Thus, let
a32_Q16[d_LPC-1][n] = ((a32_Q17[n] + 16) >> 5) << 4
be the Q16 representation of the Q12 version of the LPC coefficients
that will eventually be used. Then for each k from d_LPC-1 down to
0, if abs(a32_Q16[k][k]) > 65520, the filter is unstable and the
recurrence stops. Otherwise, the row k-1 of a32_Q16 is computed from
row k as
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rc_Q31[k] = -a32_Q16[k][k] << 15 ,
div_Q30[k] = (1<<30) - 1 - (rc_Q31[k]*rc_Q31[k] >> 32) ,
b1[k] = ilog(div_Q30[k]) - 16 ,
(1<<29) - 1
inv_Qb1[k] = ----------------------- ,
div_Q30[k] >> (b1[k]+1)
err_Q29[k] = (1<<29)
- ((div_Q30[k]<<(15-b1[k]))*inv_Qb1[k] >> 16) ,
mul_Q16[k] = ((inv_Qb1[k] << 16)
+ (err_Q29[k]*inv_Qb1[k] >> 13)) >> b1[k] ,
b2[k] = ilog(mul_Q16[k]) - 15 ,
t_Q16[k-1][n] = a32_Q16[k][n]
- ((a32_Q16[k][k-n-1]*rc_Q31[k] >> 32) << 1) ,
a32_Q16[k-1][n] = ((t_Q16[k-1][n] *
(mul_Q16[k] << (16-b2[k]))) >> 32) << b2[k] .
Here, rc_Q30[k] are the reflection coefficients. div_Q30[k] is the
denominator for each iteration, and mul_Q16[k] is its multiplicative
inverse. inv_Qb1[k], which ranges from 16384 to 32767, is a low-
precision version of that inverse (with b1[k] fractional bits, where
b1[k] ranges from 3 to 14). err_Q29[k] is the residual error, ranging
from -32392 to 32763, which is used to improve the accuracy.
t_Q16[k-1][n], 0 <= n < k, are the numerators for the next row of
coefficients in the recursion, and a32_Q16[k-1][n] is the final
version of that row. Every multiply in this procedure except the one
used to compute mul_Q16[k] requires more than 32 bits of precision,
but otherwise all intermediate results fit in 32 bits or less. In
practice, because each row only depends on the next one, an
implementation does not need to store them all. If
abs(a32_Q16[k][k]) <= 65520 for 0 <= k < d_LPC, then the filter is
considerd stable.
On round i, 1 <= i <= 18, if the filter passes this stability check,
then this procedure stops, and
a_Q12[k] = (a32_Q17[k] + 16) >> 5
are the final LPC coefficients to use for reconstruction. Otherwise,
a round of bandwidth expansion is applied using the same procedure as
in Section 4.2.4.3.4, with
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sc_Q16[0] = 65536 - i*(i+9) .
If, after the 18th round, the filter still fails the stability check,
then a_Q12[k] is set to 0 for all k.
4.2.4.4. Long-Term Prediction (LTP) Paramters
After the normalized LSF indices and, for 20 ms frames, the LSF
interpolation index, voiced frames (see Section 4.2.4.1) include
additional Long-Term Prediction (LTP) parameters.
4.2.5. LBRR Information
The Low Bit-Rate Redundancy (LBRR) information, if present,
immediately follows the header bits. Each frame whose LBRR flag was
set includes a separate set of data for each channel.
4.3. CELT Decoder
Insert decoder figure.
+---------------+-----------------------------------+---------------+
| Symbol(s) | PDF | Condition |
+---------------+-----------------------------------+---------------+
| silence | {32767, 1}/32768 | |
| | | |
| post-filter | {1, 1}/2 | |
| | | |
| octave | uniform (6) | post-filter |
| | | |
| period | raw bits (4+octave) | post-filter |
| | | |
| gain | raw bits (3) | post-filter |
| | | |
| tapset | {2, 1, 1}/4 | post-filter |
| | | |
| transient | {7, 1}/8 | |
| | | |
| intra | {7, 1}/8 | |
| | | |
| coarse energy | Section 4.3.2 | |
| | | |
| tf_change | Section 4.3.1 | |
| | | |
| tf_select | {1, 1}/2 | Section 4.3.1 |
| | | |
| spread | {7, 2, 21, 2}/32 | |
| | | |
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| dyn. alloc. | Section 4.3.3 | |
| | | |
| alloc. trim | {2, 2, 5, 10, 22, 46, 22, 10, 5, | |
| | 2, 2}/128 | |
| | | |
| skip | {1, 1}/2 | Section 4.3.3 |
| | | |
| intensity | uniform | Section 4.3.3 |
| | | |
| dual | {1, 1}/2 | |
| | | |
| fine energy | Section 4.3.2 | |
| | | |
| residual | Section 4.3.4 | |
| | | |
| anti-collapse | {1, 1}/2 | Section 4.3.5 |
| | | |
| finalize | Section 4.3.2 | |
+---------------+-----------------------------------+---------------+
Order of the symbols in the CELT section of the bit-stream.
Table 22
The decoder extracts information from the range-coded bit-stream in
the order described in the figure above. In some circumstances, it
is possible for a decoded value to be out of range due to a very
small amount of redundancy in the encoding of large integers by the
range coder. In that case, the decoder should assume there has been
an error in the coding, decoding, or transmission and SHOULD take
measures to conceal the error and/or report to the application that a
problem has occurred.
4.3.1. Transient Decoding
The _transient_ flag encoded in the bit-stream has a probability of
1/8. When it is set, then the MDCT coefficients represent multiple
short MDCTs in the frame. When not set, the coefficients represent a
single long MDCT for the frame. In addition to the global transient
flag is a per-band binary flag to change the time-frequency (tf)
resolution independently in each band. The change in tf resolution
is defined in tf_select_table[][] in celt.c and depends on the frame
size, whether the transient flag is set, and the value of tf_select.
The tf_select flag uses a 1/2 probability, but is only decoded if it
can have an impact on the result knowing the value of all per-band
tf_change flags.
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4.3.2. Energy Envelope Decoding
It is important to quantize the energy with sufficient resolution
because any energy quantization error cannot be compensated for at a
later stage. Regardless of the resolution used for encoding the
shape of a band, it is perceptually important to preserve the energy
in each band. CELT uses a three-step coarse-fine-fine strategy for
encoding the energy in the base-2 log domain, as implemented in
quant_bands.c
4.3.2.1. Coarse energy decoding
Coarse quantization of the energy uses a fixed resolution of 6 dB
(integer part of base-2 log). To minimize the bitrate, prediction is
applied both in time (using the previous frame) and in frequency
(using the previous bands). The part of the prediction that is based
on the previous frame can be disabled, creating an "intra" frame
where the energy is coded without reference to prior frames. The
decoder first reads the intra flag to determine what prediction is
used. The 2-D z-transform of the prediction filter is: A(z_l,
z_b)=(1-a*z_l^-1)*(1-z_b^-1)/(1-b*z_b^-1) where b is the band index
and l is the frame index. The prediction coefficients applied depend
on the frame size in use when not using intra energy and a=0 b=4915/
32768 when using intra energy. The time-domain prediction is based
on the final fine quantization of the previous frame, while the
frequency domain (within the current frame) prediction is based on
coarse quantization only (because the fine quantization has not been
computed yet). The prediction is clamped internally so that fixed
point implementations with limited dynamic range to not suffer
desynchronization. We approximate the ideal probability distribution
of the prediction error using a Laplace distribution with seperate
parameters for each frame size in intra and inter-frame modes. The
coarse energy quantization is performed by unquant_coarse_energy()
and unquant_coarse_energy_impl() (quant_bands.c). The encoding of
the Laplace-distributed values is implemented in ec_laplace_decode()
(laplace.c).
4.3.2.2. Fine energy quantization
The number of bits assigned to fine energy quantization in each band
is determined by the bit allocation computation described in
Section 4.3.3. Let B_i be the number of fine energy bits for band i;
the refinement is an integer f in the range [0,2^B_i-1]. The mapping
between f and the correction applied to the coarse energy is equal to
(f+1/2)/2^B_i - 1/2. Fine energy quantization is implemented in
quant_fine_energy() (quant_bands.c).
When some bits are left "unused" after all other flags have been
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decoded, these bits are assigned to a "final" step of fine
allocation. In effect, these bits are used to add one extra fine
energy bit per band per channel. The allocation process determines
two _priorities_ for the final fine bits. Any remaining bits are
first assigned only to bands of priority 0, starting from band 0 and
going up. If all bands of priority 0 have received one bit per
channel, then bands of priority 1 are assigned an extra bit per
channel, starting from band 0. If any bit is left after this, they
are left unused. This is implemented in unquant_energy_finalise()
(quant_bands.c).
4.3.3. Bit allocation
Many codecs transmit significant amounts of side information for the
purpose of controlling bit allocation within a frame. Often this
side information controls bit usage indirectly and must be carefully
selected to achieve the desired rate constraints.
The band-energy normalized structure of Opus MDCT mode ensures that a
constant bit allocation for the shape content of a band will result
in a roughly constant tone to noise ratio, which provides for fairly
consistent perceptual performance. The effectiveness of this
approach is the result of two factors: The band energy, which is
understood to be perceptually important on its own, is always
preserved regardless of the shape precision and because the constant
tone-to-noise ratio implies a constant intra-band noise to masking
ratio. Intra-band masking is the strongest of the perceptual masking
effects. This structure means that the ideal allocation is more
consistent from frame to frame than it is for other codecs without an
equivalent structure.
Because the bit allocation is used to drive the decoding of the
range-coder stream it MUST be recovered exactly so that identical
coding decisions are made in the encoder and decoder. Any deviation
from the reference's resulting bit allocation will result in
corrupted output, though implementers are free to implement the
procedure in any way which produces identical results.
Because all of the information required to decode a frame must be
derived from that frame alone in order to retain robustness to packet
loss the overhead of explicitly signaling the allocation would be
considerable, especially for low-latency (small frame size)
applications, even though the allocation is relatively static.
For this reason, in the MDCT mode Opus uses a primarily implicit bit
allocation. The available bit-stream capacity is known in advance to
both the encoder and decoder without additional signaling, ultimately
from the packet sizes expressed by a higher level protocol. Using
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this information the codec interpolates an allocation from a hard-
coded table.
While the band-energy structure effectively models intra-band
masking, it ignores the weaker inter-band masking, band-temporal
masking, and other less significant perceptual effects. While these
effects can often be ignored they can become significant for
particular samples. One mechanism available to encoders would be to
simply increase the overall rate for these frames, but this is not
possible in a constant rate mode and can be fairly inefficient. As a
result three explicitly signaled mechanisms are provided to alter the
implicit allocation:
o Band boost
o Allocation trim
o band skipping
The first of these mechanisms, band boost, allows an encoder to boost
the allocation in specific bands. The second, allocation trim, works
by biasing the overall allocation towards higher or lower frequency
bands. The third, band skipping, selects which low-precision high
frequency bands will be allocated no shape bits at all.
In stereo mode there are also two additional parameters potentially
coded as part of the allocation procedure: a parameter to allow the
selective elimination of allocation for the 'side' in jointly coded
bands, and a flag to deactivate joint coding. These values are not
signaled if they would be meaningless in the overall context of the
allocation.
Because every signaled adjustment increases overhead and
implementation complexity none were included speculatively: The
reference encoder makes use of all of these mechanisms. While the
decision logic in the reference was found to be effective enough to
justify the overhead and complexity further analysis techniques may
be discovered which increase the effectiveness of these parameters.
As with other signaled parameters, encoder is free to choose the
values in any manner but unless a technique is known to deliver
superior perceptual results the methods used by the reference
implementation should be used.
The process of allocation consists of the following steps:
determining the per-band maximum allocation vector, decoding the
boosts, decoding the tilt, determining the remaining capacity the
frame, searching the mode table for the entry nearest but not
exceeding the available space (subject to the tilt, boosts, band
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maximums, and band minimums), linear interpolation, reallocation of
unused bits with concurrent skip decoding, determination of the fine-
energy vs shape split, and final reallocation. This process results
in an shape allocation per-band (in 1/8th bit units), a per-band
fine-energy allocation (in 1 bit per channel units), a set of band
priorities for controlling the use of remaining bits at the end of
the frame, and a remaining balance of unallocated space which is
usually zero except at very high rates.
The maximum allocation vector is an approximation of the maximum
space which can be used by each band for a given mode. The value is
approximate because the shape encoding is variable rate (due to
entropy coding of splitting parameters). Setting the maximum too low
reduces the maximum achievable quality in a band while setting it too
high may result in waste: bit-stream capacity available at the end of
the frame which can not be put to any use. The maximums specified by
the codec reflect the average maximum. In the reference the maximums
are provided partially computed form, in order to fit in less memory,
as a static table (XXX cache.caps). Implementations are expected to
simply use the same table data but the procedure for generating this
table is included in rate.c as part of compute_pulse_cache().
To convert the values in cache.caps into the actual maximums: First
set nbBands to the maximum number of bands for this mode and stereo
to zero if stereo is not in use and one otherwise. For each band
assign N to the number of MDCT bins covered by the band (for one
channel), set LM to the shift value for the frame size (e.g. 0 for
120, 1 for 240, 3 for 480) then set i to nbBands*(2*LM+stereo). Then
set the maximum for the band to the i-th index of cache.caps + 64 and
multiply by the number of channels in the current frame (one or two)
and by N then divide the result by 4 using truncating integer
division. The resulting vector will be called cap[]. The elements
fit in signed 16 bit integers but do not fit in 8 bits. This
procedure is implemented in the reference in the function init_caps()
in celt.c.
The band boosts are represented by a series of binary symbols which
are coded with very low probability. Each band can potentially be
boosted multiple times, subject to the frame actually having enough
room to obey the boost and having enough room to code the boost
symbol. The default coding cost for a boost starts out at six bits,
but subsequent boosts in a band cost only a single bit and every time
a band is boosted the initial cost is reduced (down to a minimum of
two). Since the initial cost of coding a boost is 6 bits the coding
cost of the boost symbols when completely unused is 0.48 bits/frame
for a 21 band mode (21*-log2(1-1/2^6)).
To decode the band boosts: First set 'dynalloc_logp' to 6, the
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initial amount of storage required to signal a boost in bits,
'total_bits' to the size of the frame in 8th-bits, 'total_boost' to
zero, and 'tell' to the total number of 8th bits decoded so far. For
each band from the coding start (0 normally, but 17 in hybrid mode)
to the coding end (which changes depending on the signaled
bandwidth): Set 'width' to the number of MDCT bins in this band for
all channels. Take the larger of width and 64, then the minimum of
that value and the width times eight and set 'quanta' to the result.
This represents a boost step size of six bits subject to limits of
1/bit/sample and 1/8th bit/sample. Set 'boost' to zero and
'dynalloc_loop_logp' to dynalloc_logp. While dynalloc_loop_log (the
current worst case symbol cost) in 8th bits plus tell is less than
total_bits plus total_boost and boost is less than cap[] for this
band: Decode a bit from the bitstream with a with dynalloc_loop_logp
as the cost of a one, update tell to reflect the current used
capacity, if the decoded value is zero break the loop otherwise add
quanta to boost and total_boost, subtract quanta from total_bits, and
set dynalloc_loop_log to 1. When the while loop finishes boost
contains the boost for this band. If boost is non-zero and
dynalloc_logp is greater than 2 decrease dynalloc_logp. Once this
process has been execute on all bands the band boosts have been
decoded. This procedure is implemented around line 2352 of celt.c.
At very low rates it's possible that there won't be enough available
space to execute the inner loop even once. In these cases band boost
is not possible but its overhead is completely eliminated. Because
of the high cost of band boost when activated a reasonable encoder
should not be using it at very low rates. The reference implements
its dynalloc decision logic at around 1269 of celt.c
The allocation trim is a integer value from 0-10. The default value
of 5 indicates no trim. The trim parameter is entropy coded in order
to lower the coding cost of less extreme adjustments. Values lower
than 5 bias the allocation towards lower frequencies and values above
5 bias it towards higher frequencies. Like other signaled
parameters, signaling of the trim is gated so that it is not included
if there is insufficient space available in the bitstream. To decode
the trim first set the trim value to 5 then iff the count of decoded
8th bits so far (ec_tell_frac) plus 48 (6 bits) is less than or equal
to the total frame size in 8th bits minus total_boost (a product of
the above band boost procedure) then decode the trim value using the
inverse CDF {127, 126, 124, 119, 109, 87, 41, 19, 9, 4, 2, 0}.
Stereo parameters
Anti-collapse reservation
The allocation computation first begins by setting up some initial
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conditions. 'total' is set to the available remaining 8th bits,
computed by taking the size of the coded frame times 8 and
subtracting ec_tell_frac(). From this value one (8th bit) is
subtracted to assure that the resulting allocation will be
conservative. 'anti_collapse_rsv' is set to 8 (8th bits) iff the
frame is a transient, LM is greater than 1, and total is greater than
or equal to (LM+2) * 8. Total is then decremented by
anti_collapse_rsv and clamped to be equal to or greater than zero.
'skip_rsv' is set to 8 (8th bits) if total is greater than 8,
otherwise it is zero. Total is then decremented by skip_rsv. This
reserves space for the final skipping flag.
If the current frame is stereo intensity_rsv is set to the
conservative log2 in 8th bits of the number of coded bands for this
frame (given by the table LOG2_FRAC_TABLE). If intensity_rsv is
greater than total then intensity_rsv is set to zero otherwise total
is decremented by intensity_rsv, and if total is still greater than 8
dual_stereo_rsv is set to 8 and total is decremented by
dual_stereo_rsv.
The allocation process then computes a vector representing the hard
minimum amounts allocation any band will receive for shape. This
minimum is higher than the technical limit of the PVQ process, but
very low rate allocations produce excessively an sparse spectrum and
these bands are better served by having no allocation at all. For
each coded band set thresh[band] to twenty-four times the number of
MDCT bins in the band and divide by 16. If 8 times the number of
channels is greater, use that instead. This sets the minimum
allocation to one bit per channel or 48 128th bits per MDCT bin,
whichever is greater. The band size dependent part of this value is
not scaled by the channel count because at the very low rates where
this limit is applicable there will usually be no bits allocated to
the side.
The previously decoded allocation trim is used to derive a vector of
per-band adjustments, 'trim_offsets[]'. For each coded band take the
alloc_trim and subtract 5 and LM then multiply the result by number
of channels, the number MDCT bins in the shortest frame size for this
mode, the number remaining bands, 2^LM, and 8. Then divide this
value by 64. Finally, if the number of MDCT bins in the band per
channel is only one 8 times the number of channels is subtracted in
order to diminish the allocation by one bit because width 1 bands
receive greater benefit from the coarse energy coding.
4.3.4. Shape Decoder
In each band, the normalized _shape_ is encoded using a vector
quantization scheme called a "Pyramid vector quantizer".
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In the simplest case, the number of bits allocated in Section 4.3.3
is converted to a number of pulses as described by Section 4.3.4.1.
Knowing the number of pulses and the number of samples in the band,
the decoder calculates the size of the codebook as detailed in
Section 4.3.4.2. The size is used to decode an unsigned integer
(uniform probability model), which is the codeword index. This index
is converted into the corresponding vector as explained in
Section 4.3.4.2. This vector is then scaled to unit norm.
4.3.4.1. Bits to Pulses
Although the allocation is performed in 1/8th bit units, the
quantization requires an integer number of pulses K. To do this, the
encoder searches for the value of K that produces the number of bits
that is the nearest to the allocated value (rounding down if exactly
half-way between two values), subject to not exceeding the total
number of bits available. For efficiency reasons the search is
performed against a precomputated allocation table which only permits
some K values for each N. The number of codebooks entries can be
computed as explained in Section 5.3.5.2. The difference between the
number of bits allocated and the number of bits used is accumulated
to a _balance_ (initialised to zero) that helps adjusting the
allocation for the next bands. One third of the balance is applied
to the bit allocation of the each band to help achieving the target
allocation. The only exceptions are the band before the last and the
last band, for which half the balance and the whole balance are
applied, respectively.
4.3.4.2. Index Decoding
The codeword is decoded as a uniformly-distributed integer value by
decode_pulses() (cwrs.c). The codeword is converted from a unique
index in the same way as specified in [PVQ]. The indexing is based
on the calculation of V(N,K) (denoted N(L,K) in [PVQ]), which is the
number of possible combinations of K pulses in N samples. The number
of combinations can be computed recursively as V(N,K) = V(N-1,K) +
V(N,K-1) + V(N-1,K-1), with V(N,0) = 1 and V(0,K) = 0, K != 0. There
are many different ways to compute V(N,K), including pre-computed
tables and direct use of the recursive formulation. The reference
implementation applies the recursive formulation one line (or column)
at a time to save on memory use, along with an alternate, univariate
recurrence to initialise an arbitrary line, and direct polynomial
solutions for small N. All of these methods are equivalent, and have
different trade-offs in speed, memory usage, and code size.
Implementations MAY use any methods they like, as long as they are
equivalent to the mathematical definition.
The decoding of the codeword from the index is performed as specified
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in [PVQ], as implemented in function decode_pulses() (cwrs.c).
4.3.4.3. Spreading
4.3.4.4. Split decoding
To avoid the need for multi-precision calculations when decoding PVQ
codevectors, the maximum size allowed for codebooks is 32 bits. When
larger codebooks are needed, the vector is instead split in two sub-
vectors of size N/2. A quantized gain parameter with precision
derived from the current allocation is entropy coded to represent the
relative gains of each side of the split and the entire decoding
process is recursively applied. Multiple levels of splitting may be
applied up to a frame size dependent limit. The same recursive
mechanism is applied for the joint coding of stereo audio.
4.3.4.5. Time-Frequency change
4.3.5. Anti-collapse processing
When the frame has the transient bit set...
4.3.6. Denormalization
Just like each band was normalized in the encoder, the last step of
the decoder before the inverse MDCT is to denormalize the bands.
Each decoded normalized band is multiplied by the square root of the
decoded energy. This is done by denormalise_bands() (bands.c).
4.3.7. Inverse MDCT
The inverse MDCT implementation has no special characteristics. The
input is N frequency-domain samples and the output is 2*N time-domain
samples, while scaling by 1/2. The output is windowed using the same
window as the encoder. The IMDCT and windowing are performed by
mdct_backward (mdct.c). If a time-domain pre-emphasis window was
applied in the encoder, the (inverse) time-domain de-emphasis window
is applied on the IMDCT result.
4.3.7.1. Post-filter
The output of the inverse MDCT (after weighted overlap-add) is sent
to the post-filter. Although the post-filter is applied at the end,
the post-filter parameters are encoded at the beginning, just after
the silence flag. The post-filter can be switched on or off using
one bit (logp=1). If the post-filter is enabled, then the octave is
decoded as an integer value between 0 and 6 of uniform probability.
Once the octave is known, the fine pitch within the octave is decoded
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using 4+octave raw bits. The final pitch period is equal to
(16<<octave)+fine_pitch-1 so it is bounded between 15 and 1022,
inclusively. Next, the gain is decoded as three raw bits and is
equal to G=3*(int_gain+1)/32. The set of post-filter taps is decoded
last using a pdf equal to {2, 1, 1}/4. Tapset zero corresponds to
the filter coefficients g0 = 0.3066406250, g1 = 0.2170410156, g2 =
0.1296386719. Tapset one corresponds to the filter coefficients g0 =
0.4638671875, g1 = 0.2680664062, g2 = 0, and tapset two uses filter
coefficients g0 = 0.7998046875, g1 = 0.1000976562, g2 = 0.
The post-filter response is thus computed as:
y(n) = x(n) + G*(g0*y(n-T) + g1*(y(n-T+1)+y(n-T+1))
+ g2*(y(n-T+2)+y(n-T+2)))
During a transition between different gains, a smooth transition is
calculated using the square of the MDCT window. It is important that
values of y(n) be interpolated one at a time such that the past value
of y(n) used is interpolated.
4.3.7.2. De-emphasis
After the post-filter, the signal is de-emphasized using the inverse
of the pre-emphasis filter used in the encoder: 1/A(z)=1/
(1-alpha_p*z^-1), where alpha_p=0.8500061035.
4.3.8. Packet Loss Concealment (PLC)
Packet loss concealment (PLC) is an optional decoder-side feature
which SHOULD be included when transmitting over an unreliable
channel. Because PLC is not part of the bit-stream, there are
several possible ways to implement PLC with different complexity/
quality trade-offs. The PLC in the reference implementation finds a
periodicity in the decoded signal and repeats the windowed waveform
using the pitch offset. The windowed waveform is overlapped in such
a way as to preserve the time-domain aliasing cancellation with the
previous frame and the next frame. This is implemented in
celt_decode_lost() (mdct.c).
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5. Codec Encoder
Opus encoder block diagram.
+----------+ +-------+
| sample | | SILK |
+->| rate |--->|encoder|--+
| |conversion| | | |
audio | +----------+ +-------+ | +-------+
------+ +--->| Range |
| +-------+ |encoder|---->
| | CELT | +--->| | bit-stream
+->|encoder|------------------+ +-------+
| |
+-------+
5.1. Range Coder
The range coder also acts as the bit-packer for Opus. It is used in
three different ways, to encode:
o entropy-coded symbols with a fixed probability model using
ec_encode(), (entenc.c)
o integers from 0 to 2**M-1 using ec_enc_uint() or ec_enc_bits(),
(entenc.c)
o integers from 0 to N-1 (where N is not a power of two) using
ec_enc_uint(). (entenc.c)
The range encoder maintains an internal state vector composed of the
four-tuple (low,rng,rem,ext), representing the low end of the current
range, the size of the current range, a single buffered output octet,
and a count of additional carry-propagating output octets. Both rng
and low are 32-bit unsigned integer values, rem is an octet value or
the special value -1, and ext is an integer with at least 16 bits.
This state vector is initialized at the start of each each frame to
the value (0,2**31,-1,0). The reference implementation re-uses the
'val' field of the entropy coder structure to hold low, in order to
allow the same structure to be used for encoding and decoding, but we
maintain the distinction here for clarity.
5.1.1. Encoding Symbols
The main encoding function is ec_encode() (entenc.c), which takes as
an argument a three-tuple (fl,fh,ft) describing the range of the
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symbol to be encoded in the current context, with 0 <= fl < fh <= ft
<= 65535. The values of this tuple are derived from the probability
model for the symbol. Let f(i) be the frequency of the ith symbol in
the current context. Then the three-tuple corresponding to the kth
symbol is given by fl=sum(f(i),i<k), fh=fl+f(i), and ft=sum(f(i)).
ec_encode() updates the state of the encoder as follows. If fl is
greater than zero, then low = low + rng - (rng/ft)*(ft-fl) and rng =
(rng/ft)*(fh-fl). Otherwise, low is unchanged and rng = rng - (rng/
ft)*(fh-fl). The divisions here are exact integer division. After
this update, the range is normalized.
To normalize the range, the following process is repeated until rng >
2**23. First, the top 9 bits of low, (low>>23), are placed into a
carry buffer. Then, low is set to (low << 8 & 0x7FFFFFFF) and rng is
set to (rng<<8). This process is carried out by ec_enc_normalize()
(entenc.c).
The 9 bits produced in each iteration of the normalization loop
consist of 8 data bits and a carry flag. The final value of the
output bits is not determined until carry propagation is accounted
for. Therefore the reference implementation buffers a single (non-
propagating) output octet and keeps a count of additional propagating
(0xFF) output octets. An implementation MAY choose to use any
mathematically equivalent scheme to perform carry propagation.
The function ec_enc_carry_out() (entenc.c) performs this buffering.
It takes a 9-bit input value, c, from the normalization: 8 bits of
output and a carry bit. If c is 0xFF, then ext is incremented and no
octets are output. Otherwise, if rem is not the special value -1,
then the octet (rem+(c>>8)) is output. Then ext octets are output
with the value 0 if the carry bit is set, or 0xFF if it is not, and
rem is set to the lower 8 bits of c. After this, ext is set to zero.
In the reference implementation, a special version of ec_encode()
called ec_encode_bin() (entenc.c) is defined to take a two-tuple
(fl,ftb), where 0 <= fl < 2**ftb and ftb < 16. It is mathematically
equivalent to calling ec_encode() with the three-tuple (fl,fl+
1,1<<ftb), but avoids using division.
5.1.2. Encoding Raw Bits
The CELT layer also allows directly encoding a series of raw bits,
outside of the range coder, implemented in ec_enc_bits() (entenc.c).
The raw bits are packed at the end of the packet, starting by storing
the least significant bit of the value to be packed in the least
significant bit of the last byte, filling up to the most significant
bit in the last byte, and the continuing in the least significant bit
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of the penultimate byte, and so on. This packing may continue into
the last byte output by the range coder, though the format should
render it impossible to overwrite any set bit produced by the range
coder when the procedure in Section 5.1.4 is followed to finalize the
stream.
5.1.3. Encoding Uniformly Distributed Integers
The function ec_enc_uint() is based on ec_encode() and encodes one of
N equiprobable symbols, each with a frequency of 1, where N may be as
large as 2**32-1. Because ec_encode() is limited to a total
frequency of 2**16-1, this is done by encoding a series of symbols in
smaller contexts.
ec_enc_uint() (entenc.c) takes a two-tuple (fl,ft), where ft is not
necessarily a power of two. Let ftb be the location of the highest 1
bit in the two's-complement representation of (ft-1), or -1 if no
bits are set. If ftb>8, then the top 8 bits of fl are encoded using
ec_encode() with the three-tuple (fl>>ftb-8,(fl>>ftb-8)+
1,(ft-1>>ftb-8)+1), and the remaining bits are encoded as raw bits.
Otherwise, fl is encoded with ec_encode() directly using the three-
tuple (fl,fl+1,ft).
5.1.4. Finalizing the Stream
After all symbols are encoded, the stream must be finalized by
outputting a value inside the current range. Let end be the integer
in the interval [low,low+rng) with the largest number of trailing
zero bits, b, such that end+(1<<b)-1 is also in the interval
[low,low+rng). Then while end is not zero, the top 9 bits of end,
e.g., (end>>23), are sent to the carry buffer, and end is replaced by
(end<<8&0x7FFFFFFF). Finally, if the value in carry buffer, rem, is
neither zero nor the special value -1, or the carry count, ext, is
greater than zero, then 9 zero bits are sent to the carry buffer.
After the carry buffer is finished outputting octets, the rest of the
output buffer (if any) is padded with zero bits, until it reaches the
raw bits. Finally, rem is set to the special value -1. This process
is implemented by ec_enc_done() (entenc.c).
5.1.5. Current Bit Usage
The bit allocation routines in Opus need to be able to determine a
conservative upper bound on the number of bits that have been used to
encode the current frame thus far. This drives allocation decisions
and ensures that the range coder and raw bits will not overflow the
output buffer. This is computed in the reference implementation to
whole-bit precision by the function ec_tell() (entcode.h) and to
fractional 1/8th bit precision by the function ec_tell_frac()
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(entcode.c). Like all operations in the range coder, it must be
implemented in a bit-exact manner, and must produce exactly the same
value returned by the same functions in the decoder after decoding
the same symbols.
5.2. SILK Encoder
In the following, we focus on the core encoder and describe its
components. For simplicity, we will refer to the core encoder simply
as the encoder in the remainder of this document. An overview of the
encoder is given in Figure 10.
+---+
+----------------------------->| |
+---------+ | +---------+ | |
|Voice | | |LTP | | |
+----->|Activity |-----+ +---->|Scaling |---------+--->| |
| |Detector | 3 | | |Control |<+ 12 | | |
| +---------+ | | +---------+ | | | |
| | | +---------+ | | | |
| | | |Gains | | 11 | | |
| | | +->|Processor|-|---+---|--->| R |
| | | | | | | | | | a |
| \/ | | +---------+ | | | | n |
| +---------+ | | +---------+ | | | | g |
| |Pitch | | | |LSF | | | | | e |
| +->|Analysis |-+ | |Quantizer|-|---|---|--->| |
| | | |4| | | | | 8 | | | E |->
| | +---------+ | | +---------+ | | | | n |14
| | | | 9/\ 10| | | | | c |
| | | | | \/ | | | | o |
| | +---------+ | | +----------+| | | | d |
| | |Noise | +--|->|Prediction|+---|---|--->| e |
| +->|Shaping |-|--+ |Analysis || 7 | | | r |
| | |Analysis |5| | | || | | | |
| | +---------+ | | +----------+| | | | |
| | | | /\ | | | | |
| | +---------|--|-------+ | | | | |
| | | \/ \/ \/ \/ \/ | |
| +---------+ | | +---------+ +------------+ | |
| |High-Pass| | | | | |Noise | | |
-+->|Filter |-+----+----->|Prefilter|------>|Shaping |->| |
1 | | 2 | | 6 |Quantization|13| |
+---------+ +---------+ +------------+ +---+
1: Input speech signal
2: High passed input signal
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3: Voice activity estimate
4: Pitch lags (per 5 ms) and voicing decision (per 20 ms)
5: Noise shaping quantization coefficients
- Short term synthesis and analysis
noise shaping coefficients (per 5 ms)
- Long term synthesis and analysis noise
shaping coefficients (per 5 ms and for voiced speech only)
- Noise shaping tilt (per 5 ms)
- Quantizer gain/step size (per 5 ms)
6: Input signal filtered with analysis noise shaping filters
7: Short and long term prediction coefficients
LTP (per 5 ms) and LPC (per 20 ms)
8: LSF quantization indices
9: LSF coefficients
10: Quantized LSF coefficients
11: Processed gains, and synthesis noise shape coefficients
12: LTP state scaling coefficient. Controlling error propagation
/ prediction gain trade-off
13: Quantized signal
14: Range encoded bitstream
Encoder block diagram.
Figure 10
5.2.1. Voice Activity Detection
The input signal is processed by a VAD (Voice Activity Detector) to
produce a measure of voice activity, and also spectral tilt and
signal-to-noise estimates, for each frame. The VAD uses a sequence
of half-band filterbanks to split the signal in four subbands: 0 -
Fs/16, Fs/16 - Fs/8, Fs/8 - Fs/4, and Fs/4 - Fs/2, where Fs is the
sampling frequency, that is, 8, 12, 16, or 24 kHz. The lowest
subband, from 0 - Fs/16 is high-pass filtered with a first-order MA
(Moving Average) filter (with transfer function H(z) = 1-z^(-1)) to
reduce the energy at the lowest frequencies. For each frame, the
signal energy per subband is computed. In each subband, a noise
level estimator tracks the background noise level and an SNR (Signal-
to-Noise Ratio) value is computed as the logarithm of the ratio of
energy to noise level. Using these intermediate variables, the
following parameters are calculated for use in other SILK modules:
o Average SNR. The average of the subband SNR values.
o Smoothed subband SNRs. Temporally smoothed subband SNR values.
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o Speech activity level. Based on the average SNR and a weighted
average of the subband energies.
o Spectral tilt. A weighted average of the subband SNRs, with
positive weights for the low subbands and negative weights for the
high subbands.
5.2.2. High-Pass Filter
The input signal is filtered by a high-pass filter to remove the
lowest part of the spectrum that contains little speech energy and
may contain background noise. This is a second order ARMA (Auto
Regressive Moving Average) filter with a cut-off frequency around
70 Hz.
In the future, a music detector may also be used to lower the cut-off
frequency when the input signal is detected to be music rather than
speech.
5.2.3. Pitch Analysis
The high-passed input signal is processed by the open loop pitch
estimator shown in Figure 11.
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+--------+ +----------+
|2 x Down| |Time- |
+->|sampling|->|Correlator| |
| | | | | |4
| +--------+ +----------+ \/
| | 2 +-------+
| | +-->|Speech |5
+---------+ +--------+ | \/ | |Type |->
|LPC | |Down | | +----------+ | |
+->|Analysis | +->|sample |-+------------->|Time- | +-------+
| | | | |to 8 kHz| |Correlator|----------->
| +---------+ | +--------+ |__________| 6
| | | |3
| \/ | \/
| +---------+ | +----------+
| |Whitening| | |Time- |
-+->|Filter |-+--------------------------->|Correlator|----------->
1 | | | | 7
+---------+ +----------+
1: Input signal
2: Lag candidates from stage 1
3: Lag candidates from stage 2
4: Correlation threshold
5: Voiced/unvoiced flag
6: Pitch correlation
7: Pitch lags
Block diagram of the pitch estimator.
Figure 11
The pitch analysis finds a binary voiced/unvoiced classification,
and, for frames classified as voiced, four pitch lags per frame - one
for each 5 ms subframe - and a pitch correlation indicating the
periodicity of the signal. The input is first whitened using a
Linear Prediction (LP) whitening filter, where the coefficients are
computed through standard Linear Prediction Coding (LPC) analysis.
The order of the whitening filter is 16 for best results, but is
reduced to 12 for medium complexity and 8 for low complexity modes.
The whitened signal is analyzed to find pitch lags for which the time
correlation is high. The analysis consists of three stages for
reducing the complexity:
o In the first stage, the whitened signal is downsampled to 4 kHz
(from 8 kHz) and the current frame is correlated to a signal
delayed by a range of lags, starting from a shortest lag
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corresponding to 500 Hz, to a longest lag corresponding to 56 Hz.
o The second stage operates on a 8 kHz signal ( downsampled from 12,
16, or 24 kHz ) and measures time correlations only near the lags
corresponding to those that had sufficiently high correlations in
the first stage. The resulting correlations are adjusted for a
small bias towards short lags to avoid ending up with a multiple
of the true pitch lag. The highest adjusted correlation is
compared to a threshold depending on:
* Whether the previous frame was classified as voiced
* The speech activity level
* The spectral tilt.
If the threshold is exceeded, the current frame is classified as
voiced and the lag with the highest adjusted correlation is stored
for a final pitch analysis of the highest precision in the third
stage.
o The last stage operates directly on the whitened input signal to
compute time correlations for each of the four subframes
independently in a narrow range around the lag with highest
correlation from the second stage.
5.2.4. Noise Shaping Analysis
The noise shaping analysis finds gains and filter coefficients used
in the prefilter and noise shaping quantizer. These parameters are
chosen such that they will fulfil several requirements:
o Balancing quantization noise and bitrate. The quantization gains
determine the step size between reconstruction levels of the
excitation signal. Therefore, increasing the quantization gain
amplifies quantization noise, but also reduces the bitrate by
lowering the entropy of the quantization indices.
o Spectral shaping of the quantization noise; the noise shaping
quantizer is capable of reducing quantization noise in some parts
of the spectrum at the cost of increased noise in other parts
without substantially changing the bitrate. By shaping the noise
such that it follows the signal spectrum, it becomes less audible.
In practice, best results are obtained by making the shape of the
noise spectrum slightly flatter than the signal spectrum.
o Deemphasizing spectral valleys; by using different coefficients in
the analysis and synthesis part of the prefilter and noise shaping
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quantizer, the levels of the spectral valleys can be decreased
relative to the levels of the spectral peaks such as speech
formants and harmonics. This reduces the entropy of the signal,
which is the difference between the coded signal and the
quantization noise, thus lowering the bitrate.
o Matching the levels of the decoded speech formants to the levels
of the original speech formants; an adjustment gain and a first
order tilt coefficient are computed to compensate for the effect
of the noise shaping quantization on the level and spectral tilt.
/ \ ___
| // \\
| // \\ ____
|_// \\___// \\ ____
| / ___ \ / \\ // \\
P |/ / \ \_/ \\_____// \\
o | / \ ____ \ / \\
w | / \___/ \ \___/ ____ \\___ 1
e |/ \ / \ \
r | \_____/ \ \__ 2
| \
| \___ 3
|
+---------------------------------------->
Frequency
1: Input signal spectrum
2: Deemphasized and level matched spectrum
3: Quantization noise spectrum
Noise shaping and spectral de-emphasis illustration.
Figure 12
Figure 12 shows an example of an input signal spectrum (1). After
de-emphasis and level matching, the spectrum has deeper valleys (2).
The quantization noise spectrum (3) more or less follows the input
signal spectrum, while having slightly less pronounced peaks. The
entropy, which provides a lower bound on the bitrate for encoding the
excitation signal, is proportional to the area between the
deemphasized spectrum (2) and the quantization noise spectrum (3).
Without de-emphasis, the entropy is proportional to the area between
input spectrum (1) and quantization noise (3) - clearly higher.
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The transformation from input signal to deemphasized signal can be
described as a filtering operation with a filter
Wana(z)
H(z) = G * ( 1 - c_tilt * z^(-1) ) * -------
Wsyn(z),
having an adjustment gain G, a first order tilt adjustment filter
with tilt coefficient c_tilt, and where
16 d
__ __
Wana(z) = (1 - \ (a_ana(k) * z^(-k))*(1 - z^(-L) \ b_ana(k)*z^(-k)),
/_ /_
k=1 k=-d
is the analysis part of the de-emphasis filter, consisting of the
short-term shaping filter with coefficients a_ana(k), and the long-
term shaping filter with coefficients b_ana(k) and pitch lag L. The
parameter d determines the number of long-term shaping filter taps.
Similarly, but without the tilt adjustment, the synthesis part can be
written as
16 d
__ __
Wsyn(z) = (1 - \ (a_syn(k) * z^(-k))*(1 - z^(-L) \ b_syn(k)*z^(-k)).
/_ /_
k=1 k=-d
All noise shaping parameters are computed and applied per subframe of
5 milliseconds. First, an LPC analysis is performed on a windowed
signal block of 15 milliseconds. The signal block has a look-ahead
of 5 milliseconds relative to the current subframe, and the window is
an asymmetric sine window. The LPC analysis is done with the
autocorrelation method, with an order of 16 for best quality or 12 in
low complexity operation. The quantization gain is found as the
square-root of the residual energy from the LPC analysis, multiplied
by a value inversely proportional to the coding quality control
parameter and the pitch correlation.
Next we find the two sets of short-term noise shaping coefficients
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a_ana(k) and a_syn(k), by applying different amounts of bandwidth
expansion to the coefficients found in the LPC analysis. This
bandwidth expansion moves the roots of the LPC polynomial towards the
origo, using the formulas
a_ana(k) = a(k)*g_ana^k, and
a_syn(k) = a(k)*g_syn^k,
where a(k) is the k'th LPC coefficient and the bandwidth expansion
factors g_ana and g_syn are calculated as
g_ana = 0.94 - 0.02*C, and
g_syn = 0.94 + 0.02*C,
where C is the coding quality control parameter between 0 and 1.
Applying more bandwidth expansion to the analysis part than to the
synthesis part gives the desired de-emphasis of spectral valleys in
between formants.
The long-term shaping is applied only during voiced frames. It uses
three filter taps, described by
b_ana = F_ana * [0.25, 0.5, 0.25], and
b_syn = F_syn * [0.25, 0.5, 0.25].
For unvoiced frames these coefficients are set to 0. The
multiplication factors F_ana and F_syn are chosen between 0 and 1,
depending on the coding quality control parameter, as well as the
calculated pitch correlation and smoothed subband SNR of the lowest
subband. By having F_ana less than F_syn, the pitch harmonics are
emphasized relative to the valleys in between the harmonics.
The tilt coefficient c_tilt is for unvoiced frames chosen as
c_tilt = 0.4, and as
c_tilt = 0.04 + 0.06 * C
for voiced frames, where C again is the coding quality control
parameter and is between 0 and 1.
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The adjustment gain G serves to correct any level mismatch between
original and decoded signal that might arise from the noise shaping
and de-emphasis. This gain is computed as the ratio of the
prediction gain of the short-term analysis and synthesis filter
coefficients. The prediction gain of an LPC synthesis filter is the
square-root of the output energy when the filter is excited by a
unit-energy impulse on the input. An efficient way to compute the
prediction gain is by first computing the reflection coefficients
from the LPC coefficients through the step-down algorithm, and
extracting the prediction gain from the reflection coefficients as
K
___
predGain = ( | | 1 - (r_k)^2 )^(-0.5),
k=1
where r_k is the k'th reflection coefficient.
Initial values for the quantization gains are computed as the square-
root of the residual energy of the LPC analysis, adjusted by the
coding quality control parameter. These quantization gains are later
adjusted based on the results of the prediction analysis.
5.2.5. Prefilter
In the prefilter the input signal is filtered using the spectral
valley de-emphasis filter coefficients from the noise shaping
analysis, see Section 5.2.4. By applying only the noise shaping
analysis filter to the input signal, it provides the input to the
noise shaping quantizer.
5.2.6. Prediction Analysis
The prediction analysis is performed in one of two ways depending on
how the pitch estimator classified the frame. The processing for
voiced and unvoiced speech are described in Section 5.2.6.1 and
Section 5.2.6.2, respectively. Inputs to this function include the
pre-whitened signal from the pitch estimator, see Section 5.2.3.
5.2.6.1. Voiced Speech
For a frame of voiced speech the pitch pulses will remain dominant in
the pre-whitened input signal. Further whitening is desirable as it
leads to higher quality at the same available bitrate. To achieve
this, a Long-Term Prediction (LTP) analysis is carried out to
estimate the coefficients of a fifth order LTP filter for each of
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four subframes. The LTP coefficients are used to find an LTP
residual signal with the simulated output signal as input to obtain
better modelling of the output signal. This LTP residual signal is
the input to an LPC analysis where the LPCs are estimated using Burgs
method, such that the residual energy is minimized. The estimated
LPCs are converted to a Line Spectral Frequency (LSF) vector, and
quantized as described in Section 5.2.7. After quantization, the
quantized LSF vector is converted to LPC coefficients and hence by
using these quantized coefficients the encoder remains fully
synchronized with the decoder. The LTP coefficients are quantized
using a method described in Section 5.2.8. The quantized LPC and LTP
coefficients are now used to filter the high-pass filtered input
signal and measure a residual energy for each of the four subframes.
5.2.6.2. Unvoiced Speech
For a speech signal that has been classified as unvoiced there is no
need for LTP filtering as it has already been determined that the
pre-whitened input signal is not periodic enough within the allowed
pitch period range for an LTP analysis to be worth-while the cost in
terms of complexity and rate. Therefore, the pre-whitened input
signal is discarded and instead the high-pass filtered input signal
is used for LPC analysis using Burgs method. The resulting LPC
coefficients are converted to an LSF vector, quantized as described
in the following section and transformed back to obtain quantized LPC
coefficients. The quantized LPC coefficients are used to filter the
high-pass filtered input signal and measure a residual energy for
each of the four subframes.
5.2.7. LSF Quantization
The purpose of quantization in general is to significantly lower the
bit rate at the cost of some introduced distortion. A higher rate
should always result in lower distortion, and lowering the rate will
generally lead to higher distortion. A commonly used but generally
sub-optimal approach is to use a quantization method with a constant
rate where only the error is minimized when quantizing.
5.2.7.1. Rate-Distortion Optimization
Instead, we minimize an objective function that consists of a
weighted sum of rate and distortion, and use a codebook with an
associated non-uniform rate table. Thus, we take into account that
the probability mass function for selecting the codebook entries are
by no means guaranteed to be uniform in our scenario. The advantage
of this approach is that it ensures that rarely used codebook vector
centroids, which are modelling statistical outliers in the training
set can be quantized with a low error but with a relatively high cost
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in terms of a high rate. At the same time this approach also
provides the advantage that frequently used centroids are modelled
with low error and a relatively low rate. This approach will lead to
equal or lower distortion than the fixed rate codebook at any given
average rate, provided that the data is similar to the data used for
training the codebook.
5.2.7.2. Error Mapping
Instead of minimizing the error in the LSF domain, we map the errors
to better approximate spectral distortion by applying an individual
weight to each element in the error vector. The weight vectors are
calculated for each input vector using the Inverse Harmonic Mean
Weighting (IHMW) function proposed by Laroia et al., see
[laroia-icassp]. Consequently, we solve the following minimization
problem, i.e.,
LSF_q = argmin { (LSF - c)' * W * (LSF - c) + mu * rate },
c in C
where LSF_q is the quantized vector, LSF is the input vector to be
quantized, and c is the quantized LSF vector candidate taken from the
set C of all possible outcomes of the codebook.
5.2.7.3. Multi-Stage Vector Codebook
We arrange the codebook in a multiple stage structure to achieve a
quantizer that is both memory efficient and highly scalable in terms
of computational complexity, see e.g. [sinervo-norsig]. In the first
stage the input is the LSF vector to be quantized, and in any other
stage s > 1, the input is the quantization error from the previous
stage, see Figure 13.
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Stage 1: Stage 2: Stage S:
+----------+ +----------+ +----------+
| c_{1,1} | | c_{2,1} | | c_{S,1} |
LSF +----------+ res_1 +----------+ res_{S-1} +----------+
--->| c_{1,2} |------>| c_{2,2} |--> ... --->| c_{S,2} |--->
+----------+ +----------+ +----------+ res_S =
... ... ... LSF-LSF_q
+----------+ +----------+ +----------+
|c_{1,M1-1}| |c_{2,M2-1}| |c_{S,MS-1}|
+----------+ +----------+ +----------+
| c_{1,M1} | | c_{2,M2} | | c_{S,MS} |
+----------+ +----------+ +----------+
Multi-Stage LSF Vector Codebook Structure.
Figure 13
By storing total of M codebook vectors, i.e.,
S
__
M = \ Ms,
/_
s=1
where M_s is the number of vectors in stage s, we obtain a total of
S
___
T = | | Ms
s=1
possible combinations for generating the quantized vector. It is for
example possible to represent 2**36 uniquely combined vectors using
only 216 vectors in memory, as done in SILK for voiced speech at all
sample frequencies above 8 kHz.
5.2.7.4. Survivor Based Codebook Search
This number of possible combinations is far too high for a full
search to be carried out for each frame so for all stages but the
last, i.e., s smaller than S, only the best min( L, Ms ) centroids
are carried over to stage s+1. In each stage the objective function,
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i.e., the weighted sum of accumulated bitrate and distortion, is
evaluated for each codebook vector entry and the results are sorted.
Only the best paths and the corresponding quantization errors are
considered in the next stage. In the last stage S the single best
path through the multistage codebook is determined. By varying the
maximum number of survivors from each stage to the next L, the
complexity can be adjusted in real-time at the cost of a potential
increase when evaluating the objective function for the resulting
quantized vector. This approach scales all the way between the two
extremes, L=1 being a greedy search, and the desirable but infeasible
full search, L=T/MS. In fact, a performance almost as good as what
can be achieved with the infeasible full search can be obtained at a
substantially lower complexity by using this approach, see e.g.
[leblanc-tsap].
5.2.7.5. LSF Stabilization
If the input is stable, finding the best candidate will usually
result in the quantized vector also being stable, but due to the
multi-stage approach it could in theory happen that the best
quantization candidate is unstable and because of this there is a
need to explicitly ensure that the quantized vectors are stable.
Therefore we apply a LSF stabilization method which ensures that the
LSF parameters are within valid range, increasingly sorted, and have
minimum distances between each other and the border values that have
been pre-determined as the 0.01 percentile distance values from a
large training set.
5.2.7.6. Off-Line Codebook Training
The vectors and rate tables for the multi-stage codebook have been
trained by minimizing the average of the objective function for LSF
vectors from a large training set.
5.2.8. LTP Quantization
For voiced frames, the prediction analysis described in
Section 5.2.6.1 resulted in four sets (one set per subframe) of five
LTP coefficients, plus four weighting matrices. Also, the LTP
coefficients for each subframe are quantized using entropy
constrained vector quantization. A total of three vector codebooks
are available for quantization, with different rate-distortion trade-
offs. The three codebooks have 10, 20 and 40 vectors and average
rates of about 3, 4, and 5 bits per vector, respectively.
Consequently, the first codebook has larger average quantization
distortion at a lower rate, whereas the last codebook has smaller
average quantization distortion at a higher rate. Given the
weighting matrix W_ltp and LTP vector b, the weighted rate-distortion
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measure for a codebook vector cb_i with rate r_i is give by
RD = u * (b - cb_i)' * W_ltp * (b - cb_i) + r_i,
where u is a fixed, heuristically-determined parameter balancing the
distortion and rate. Which codebook gives the best performance for a
given LTP vector depends on the weighting matrix for that LTP vector.
For example, for a low valued W_ltp, it is advantageous to use the
codebook with 10 vectors as it has a lower average rate. For a large
W_ltp, on the other hand, it is often better to use the codebook with
40 vectors, as it is more likely to contain the best codebook vector.
The weighting matrix W_ltp depends mostly on two aspects of the input
signal. The first is the periodicity of the signal; the more
periodic the larger W_ltp. The second is the change in signal energy
in the current subframe, relative to the signal one pitch lag
earlier. A decaying energy leads to a larger W_ltp than an
increasing energy. Both aspects do not fluctuate very fast which
causes the W_ltp matrices for different subframes of one frame often
to be similar. As a result, one of the three codebooks typically
gives good performance for all subframes. Therefore the codebook
search for the subframe LTP vectors is constrained to only allow
codebook vectors to be chosen from the same codebook, resulting in a
rate reduction.
To find the best codebook, each of the three vector codebooks is used
to quantize all subframe LTP vectors and produce a combined weighted
rate-distortion measure for each vector codebook and the vector
codebook with the lowest combined rate-distortion over all subframes
is chosen. The quantized LTP vectors are used in the noise shaping
quantizer, and the index of the codebook plus the four indices for
the four subframe codebook vectors are passed on to the range
encoder.
5.2.9. Noise Shaping Quantizer
The noise shaping quantizer independently shapes the signal and
coding noise spectra to obtain a perceptually higher quality at the
same bitrate.
The prefilter output signal is multiplied with a compensation gain G
computed in the noise shaping analysis. Then the output of a
synthesis shaping filter is added, and the output of a prediction
filter is subtracted to create a residual signal. The residual
signal is multiplied by the inverse quantized quantization gain from
the noise shaping analysis, and input to a scalar quantizer. The
quantization indices of the scalar quantizer represent a signal of
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pulses that is input to the pyramid range encoder. The scalar
quantizer also outputs a quantization signal, which is multiplied by
the quantized quantization gain from the noise shaping analysis to
create an excitation signal. The output of the prediction filter is
added to the excitation signal to form the quantized output signal
y(n). The quantized output signal y(n) is input to the synthesis
shaping and prediction filters.
5.2.10. Range Encoder
Range encoding is a well known method for entropy coding in which a
bitstream sequence is continually updated with every new symbol,
based on the probability for that symbol. It is similar to
arithmetic coding but rather than being restricted to generating
binary output symbols, it can generate symbols in any chosen number
base. In SILK all side information is range encoded. Each quantized
parameter has its own cumulative density function based on histograms
for the quantization indices obtained by running a training database.
5.2.10.1. Bitstream Encoding Details
TBD.
5.3. CELT Encoder
Copy from CELT draft.
5.3.1. Pre-filter
Inverse of the post-filter
5.3.2. Forward MDCT
The MDCT implementation has no special characteristics. The input is
a windowed signal (after pre-emphasis) of 2*N samples and the output
is N frequency-domain samples. A _low-overlap_ window is used to
reduce the algorithmic delay. It is derived from a basic (full
overlap) window that is the same as the one used in the Vorbis codec:
W(n)=[sin(pi/2*sin(pi/2*(n+.5)/L))]^2. The low-overlap window is
created by zero-padding the basic window and inserting ones in the
middle, such that the resulting window still satisfies power
complementarity. The MDCT is computed in mdct_forward() (mdct.c),
which includes the windowing operation and a scaling of 2/N.
5.3.3. Bands and Normalization
The MDCT output is divided into bands that are designed to match the
ear's critical bands for the smallest (2.5ms) frame size. The larger
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frame sizes use integer multiplies of the 2.5ms layout. For each
band, the encoder computes the energy that will later be encoded.
Each band is then normalized by the square root of the *non-
quantized* energy, such that each band now forms a unit vector X. The
energy and the normalization are computed by compute_band_energies()
and normalise_bands() (bands.c), respectively.
5.3.4. Energy Envelope Quantization
It is important to quantize the energy with sufficient resolution
because any energy quantization error cannot be compensated for at a
later stage. Regardless of the resolution used for encoding the
shape of a band, it is perceptually important to preserve the energy
in each band. CELT uses a coarse-fine strategy for encoding the
energy in the base-2 log domain, as implemented in quant_bands.c
5.3.4.1. Coarse energy quantization
The coarse quantization of the energy uses a fixed resolution of 6
dB. To minimize the bitrate, prediction is applied both in time
(using the previous frame) and in frequency (using the previous
bands). The prediction using the previous frame can be disabled,
creating an "intra" frame where the energy is coded without reference
to prior frames. An encoder is able to choose the mode used at will
based on both loss robustness and efficiency considerations. The 2-D
z-transform of the prediction filter is: A(z_l, z_b)=(1-a*z_l^-1)*(1-
z_b^-1)/(1-b*z_b^-1) where b is the band index and l is the frame
index. The prediction coefficients applied depend on the frame size
in use when not using intra energy and a=0 b=4915/32768 when using
intra energy. The time-domain prediction is based on the final fine
quantization of the previous frame, while the frequency domain
(within the current frame) prediction is based on coarse quantization
only (because the fine quantization has not been computed yet). The
prediction is clamped internally so that fixed point implementations
with limited dynamic range to not suffer desynchronization.
Identical prediction clamping must be implemented in all encoders and
decoders. We approximate the ideal probability distribution of the
prediction error using a Laplace distribution with seperate
parameters for each frame size in intra and inter-frame modes. The
coarse energy quantization is performed by quant_coarse_energy() and
quant_coarse_energy() (quant_bands.c). The encoding of the Laplace-
distributed values is implemented in ec_laplace_encode() (laplace.c).
5.3.4.2. Fine energy quantization
After the coarse energy quantization and encoding, the bit allocation
is computed (Section 4.3.3) and the number of bits to use for
refining the energy quantization is determined for each band. Let
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B_i be the number of fine energy bits for band i; the refinement is
an integer f in the range [0,2^B_i-1]. The mapping between f and the
correction applied to the coarse energy is equal to (f+1/2)/2^B_i -
1/2. Fine energy quantization is implemented in quant_fine_energy()
(quant_bands.c).
If any bits are unused at the end of the encoding process, these bits
are used to increase the resolution of the fine energy encoding in
some bands. Priority is given to the bands for which the allocation
(Section 4.3.3) was rounded down. At the same level of priority,
lower bands are encoded first. Refinement bits are added until there
is no more room for fine energy or until each band has gained an
additional bit of precision or has the maximum fine energy precision.
This is implemented in quant_energy_finalise() (quant_bands.c).
5.3.5. Spherical Vector Quantization
CELT uses a Pyramid Vector Quantization (PVQ) [PVQ] codebook for
quantizing the details of the spectrum in each band that have not
been predicted by the pitch predictor. The PVQ codebook consists of
all sums of K signed pulses in a vector of N samples, where two
pulses at the same position are required to have the same sign. Thus
the codebook includes all integer codevectors y of N dimensions that
satisfy sum(abs(y(j))) = K.
In bands where there are sufficient bits allocated the PVQ is used to
encode the unit vector that results from the normalization in
Section 5.3.3 directly. Given a PVQ codevector y, the unit vector X
is obtained as X = y/||y||, where ||.|| denotes the L2 norm.
5.3.5.1. PVQ Search
The search for the best codevector y is performed by alg_quant()
(vq.c). There are several possible approaches to the search with a
tradeoff between quality and complexity. The method used in the
reference implementation computes an initial codeword y1 by
projecting the residual signal R = X - p' onto the codebook pyramid
of K-1 pulses:
y0 = round_towards_zero( (K-1) * R / sum(abs(R)))
Depending on N, K and the input data, the initial codeword y0 may
contain from 0 to K-1 non-zero values. All the remaining pulses,
with the exception of the last one, are found iteratively with a
greedy search that minimizes the normalized correlation between y and
R:
J = -R^T*y / ||y||
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The search described above is considered to be a good trade-off
between quality and computational cost. However, there are other
possible ways to search the PVQ codebook and the implementors MAY use
any other search methods.
5.3.5.2. Index Encoding
The best PVQ codeword is encoded as a uniformly-distributed integer
value by encode_pulses() (cwrs.c). The codeword is converted from a
unique index in the same way as specified in [PVQ]. The indexing is
based on the calculation of V(N,K) (denoted N(L,K) in [PVQ]), which
is the number of possible combinations of K pulses in N samples.
5.3.6. Stereo support
When encoding a stereo stream, some parameters are shared across the
left and right channels, while others are transmitted separately for
each channel, or jointly encoded. Only one copy of the flags for the
features, transients and pitch (pitch period and filter parameters)
are transmitted. The coarse and fine energy parameters are
transmitted separately for each channel. Both the coarse energy and
fine energy (including the remaining fine bits at the end of the
stream) have the left and right bands interleaved in the stream, with
the left band encoded first.
The main difference between mono and stereo coding is the PVQ coding
of the normalized vectors. In stereo mode, a normalized mid-side
(M-S) encoding is used. Let L and R be the normalized vector of a
certain band for the left and right channels, respectively. The mid
and side vectors are computed as M=L+R and S=L-R and no longer have
unit norm.
From M and S, an angular parameter theta=2/pi*atan2(||S||, ||M||) is
computed. The theta parameter is converted to a Q14 fixed-point
parameter itheta, which is quantized on a scale from 0 to 1 with an
interval of 2^-qb, where qb is based the number of bits allocated to
the band. From here on, the value of itheta MUST be treated in a
bit-exact manner since both the encoder and decoder rely on it to
infer the bit allocation.
Let m=M/||M|| and s=S/||S||; m and s are separately encoded with the
PVQ encoder described in Section 5.3.5. The number of bits allocated
to m and s depends on the value of itheta.
5.3.7. Synthesis
After all the quantization is completed, the quantized energy is used
along with the quantized normalized band data to resynthesize the
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MDCT spectrum. The inverse MDCT (Section 4.3.7) and the weighted
overlap-add are applied and the signal is stored in the _synthesis
buffer_. The encoder MAY omit this step of the processing if it does
not need the decoded output.
5.3.8. Variable Bitrate (VBR)
Each CELT frame can be encoded in a different number of octets,
making it possible to vary the bitrate at will. This property can be
used to implement source-controlled variable bitrate (VBR). Support
for VBR is OPTIONAL for the encoder, but a decoder MUST be prepared
to decode a stream that changes its bitrate dynamically. The method
used to vary the bitrate in VBR mode is left to the implementor, as
long as each frame can be decoded by the reference decoder.
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6. Conformance
It is the intention to allow the greatest possible choice of freedom
in implementing the specification. For this reason, outside of a few
exceptions noted in this section, conformance is defined through the
reference implementation of the decoder provided in Appendix
Appendix A. Although this document includes an English description
of the codec, should the description contradict the source code of
the reference implementation, the latter shall take precedence.
Compliance with this specification means that a decoder's output MUST
be within the thresholds specified compared to the reference
implementation using the opus_compare.m tool in Appendix Appendix B.
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7. Security Considerations
The codec needs to take appropriate security considerations into
account, as outlined in [DOS] and [SECGUIDE]. It is extremely
important for the decoder to be robust against malicious payloads.
Malicious payloads must not cause the decoder to overrun its
allocated memory or to take much more resources to decode. Although
problems in encoders are typically rarer, the same applies to the
encoder. Malicious audio stream must not cause the encoder to
misbehave because this would allow an attacker to attack transcoding
gateways.
The reference implementation contains no known buffer overflow or
cases where a specially crafter packet or audio segment could cause a
significant increase in CPU load. However, on certain CPU
architectures where denormalized floating-point operations are much
slower it is possible for some audio content (e.g. silence or near-
silence) to cause such an increase in CPU load. For such
architectures, it is RECOMMENDED to add very small floating-point
offsets to prevent significant numbers of denormalized operations or
to configure the hardware to zeroize denormal numbers. No such issue
exists for the fixed-point reference implementation.
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8. IANA Considerations
This document has no actions for IANA.
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9. Acknowledgments
Thanks to all other developers, including Raymond Chen, Soeren Skak
Jensen, Gregory Maxwell, Christopher Montgomery, Karsten Vandborg
Soerensen, and Timothy Terriberry. We would also like to thank Igor
Dyakonov, Jan Skoglund for their help with subjective testing of the
Opus codec. Thanks to John Ridges, Keith Yan and many others on the
Opus and CELT mailing lists for their bug reports and feeback.
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10. Informative References
[SILK] Vos, K., Jensen, S., and K. Soerensen, "SILK Speech
Codec", draft-vos-silk-01 (work in progress), March 2010.
[laroia-icassp]
Laroia, R., Phamdo, N., and N. Farvardin, "Robust and
Efficient Quantization of Speech LSP Parameters Using
Structured Vector Quantization", ICASSP-1991, Proc. IEEE
Int. Conf. Acoust., Speech, Signal Processing, pp. 641-
644, October 1991.
[sinervo-norsig]
Sinervo, U., Nurminen, J., Heikkinen, A., and J. Saarinen,
"Evaluation of Split and Multistage Techniques in LSF
Quantization", NORSIG-2001, Norsk symposium i
signalbehandling, Trondheim, Norge, October 2001.
[leblanc-tsap]
LeBlanc, W., Bhattacharya, B., Mahmoud, S., and V.
Cuperman, "Efficient Search and Design Procedures for
Robust Multi-Stage VQ of LPC Parameters for 4 kb/s Speech
Coding", IEEE Transactions on Speech and Audio Processing,
Vol. 1, No. 4, October 1993.
[CELT] Valin, J-M., Terriberry, T., Maxwell, G., and C.
Montgomery, "Constrained-Energy Lapped Transform (CELT)
Codec", draft-valin-celt-codec-02 (work in progress),
July 2010.
[DOS] Handley, M., Rescorla, E., and IAB, "Internet Denial-of-
Service Considerations", RFC 4732, December 2006.
[SECGUIDE]
Rescorla, E. and B. Korver, "Guidelines for Writing RFC
Text on Security Considerations", BCP 72, RFC 3552,
July 2003.
[range-coding]
Nigel, G. and N. Martin, "Range encoding: An algorithm for
removing redundancy from a digitised message", Proc.
Institution of Electronic and Radio Engineers
International Conference on Video and Data Recording ,
1979.
[coding-thesis]
Pasco, R., "Source coding algorithms for fast data
compression", Ph.D. thesis Dept. of Electrical
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Engineering, Stanford University, May 1976.
[PVQ] Fischer, T., "A Pyramid Vector Quantizer", IEEE Trans. on
Information Theory, Vol. 32 pp. 568-583, July 1986.
[1] <http://developer.skype.com/silk>
[2] <http://www.celt-codec.org/>
[3] <git://git.opus-codec.org/opus.git>
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Appendix A. Reference Implementation
This appendix contains the complete source code for the reference
implementation of the Opus codec written in C. This implementation
can be compiled for either floating-point or fixed-point
architectures.
The implementation can be compiled with either a C89 or a C99
compiler. It is reasonably optimized for most platforms such that
only architecture-specific optimizations are likely to be useful.
The FFT used is a slightly modified version of the KISS-FFT package,
but it is easy to substitute any other FFT library.
A.1. Extracting the source
The complete source code can be extracted from this draft, by running
the following command line:
o cat draft-ietf-codec-opus.txt | grep '^\ \ \ ###' | sed
's/\s\s\s###//' | base64 -d > opus_source.tar.gz
o tar xzvf opus_source.tar.gz
o cd opus_source
o make
A.2. Development Versions
The current development version of the source code is available in a
Git repository [3]. Development snapshots are provided at
<http://opus-codec.org/>.
A.3. Base64-encoded source code
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Valin, et al. Expires December 18, 2011 [Page 105]
Internet-Draft Interactive Audio Codec June 2011
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Valin, et al. Expires December 18, 2011 [Page 106]
Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Valin, et al. Expires December 18, 2011 [Page 108]
Internet-Draft Interactive Audio Codec June 2011
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Valin, et al. Expires December 18, 2011 [Page 109]
Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Valin, et al. Expires December 18, 2011 [Page 139]
Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Valin, et al. Expires December 18, 2011 [Page 234]
Internet-Draft Interactive Audio Codec June 2011
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Internet-Draft Interactive Audio Codec June 2011
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Appendix B. opus_compare.c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#define OPUS_PI (3.14159265F)
#define OPUS_MIN(_x,_y) ((_x)<(_y)?(_x):(_y))
#define OPUS_MAX(_x,_y) ((_x)>(_y)?(_x):(_y))
#define OPUS_CLAMP(_a,_b,_c) OPUS_MAX(_a,OPUS_MIN(_b,_c))
#define OPUS_COSF(_x) ((float)cos(_x))
#define OPUS_SINF(_x) ((float)sin(_x))
#define OPUS_SQRTF(_x) ((float)sqrt(_x))
#define OPUS_LOG10F(_x) ((float)log10(_x))
static void *check_alloc(void *_ptr){
if(_ptr==NULL){
fprintf(stderr,"Out of memory.\n");
exit(EXIT_FAILURE);
}
return _ptr;
}
static void *opus_malloc(size_t _size){
return check_alloc(malloc(_size));
}
static void *opus_realloc(void *_ptr,size_t _size){
return check_alloc(realloc(_ptr,_size));
}
static size_t read_pcm16(float **_samples,FILE *_fin,
int _nchannels){
unsigned char buf[1024];
float *samples;
size_t nsamples;
size_t csamples;
size_t xi;
size_t nread;
samples=NULL;
nsamples=csamples=0;
for(;;){
nread=fread(buf,2*_nchannels,1024/(2*_nchannels),_fin);
if(nread<=0)break;
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if(nsamples+nread>csamples){
do csamples=csamples<<1|1;
while(nsamples+nread>csamples);
samples=(float *)opus_realloc(samples,
_nchannels*csamples*sizeof(*samples));
}
for(xi=0;xi<nread;xi++){
int ci;
for(ci=0;ci<_nchannels;ci++){
int s;
s=buf[2*(xi*_nchannels+ci)+1]<<8|buf[2*(xi*_nchannels+ci)];
s=((s&0xFFFF)^0x8000)-0x8000;
samples[(nsamples+xi)*_nchannels+ci]=s;
}
}
nsamples+=nread;
}
*_samples=(float *)opus_realloc(samples,
_nchannels*nsamples*sizeof(*samples));
return nsamples;
}
static void band_energy(float *_out,const int *_bands,int _nbands,
const float *_in,int _nchannels,size_t _nframes,int _window_sz,
int _step){
float *window;
float *x;
float *c;
float *s;
size_t xi;
int xj;
window=(float *)opus_malloc((3+_nchannels)*_window_sz
*sizeof(*window));
c=window+_window_sz;
s=c+_window_sz;
x=s+_window_sz;
for(xj=0;xj<_window_sz;xj++){
window[xj]=0.5F-0.5F*OPUS_COSF((2*OPUS_PI/(_window_sz-1))*xj);
}
for(xj=0;xj<_window_sz;xj++)
c[xj]=OPUS_COSF((2*OPUS_PI/_window_sz)*xj);
for(xj=0;xj<_window_sz;xj++)
s[xj]=OPUS_SINF((2*OPUS_PI/_window_sz)*xj);
for(xi=0;xi<_nframes;xi++){
int ci;
int xk;
int bi;
for(ci=0;ci<_nchannels;ci++){
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for(xk=0;xk<_window_sz;xk++){
x[ci*_window_sz+xk]=window[xk]
*_in[(xi*_step+xk)*_nchannels+ci];
}
}
for(bi=xj=0;bi<_nbands;bi++){
float e2;
e2=0;
for(;xj<_bands[bi+1];xj++){
float p;
p=0;
for(ci=0;ci<_nchannels;ci++){
float re;
float im;
int ti;
ti=0;
re=im=0;
for(xk=0;xk<_window_sz;xk++){
re+=c[ti]*x[ci*_window_sz+xk];
im-=s[ti]*x[ci*_window_sz+xk];
ti+=xj;
if(ti>=_window_sz)ti-=_window_sz;
}
p+=OPUS_SQRTF(re*re+im*im);
}
p*=(1.0F/_nchannels);
e2+=p*p;
}
_out[xi*_nbands+bi]=e2/(_bands[bi+1]-_bands[bi])+1;
}
}
free(window);
}
static int cmp_float(const void *_a,const void *_b){
float a;
float b;
a=*(const float *)_a;
b=*(const float *)_b;
return (a>b)-(a<b);
}
#define NBANDS (21)
/*Bands on which we compute the pseudo-NMR (Bark-derived
CELT bands).*/
static const int BANDS[NBANDS+1]={
0,2,4,6,8,10,12,14,16,20,24,28,32,40,48,56,68,80,96,120,156,200
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};
/*Per-band NMR threshold.*/
static const float NMR_THRESH[NBANDS]={
85113.804F,72443.596F,61659.5F, 52480.746F,44668.359F,38018.940F,
32359.366F,27542.287F,23442.288F,19952.623F,16982.437F,14454.398F,
12302.688F,10471.285F, 8912.5094F,7585.7758F,6456.5423F,5495.4087F,
4677.3514F,3981.0717F,3388.4416F
};
/*Noise floor.*/
static const float NOISE_FLOOR[NBANDS]={
8.7096359F,7.5857758F,6.6069345F,5.7543994F,5.0118723F,4.3651583F,
3.8018940F,3.3113112F,2.8840315F,2.5118864F,2.1877616F,1.9054607F,
1.6595869F,1.4454398F,1.2589254F,1.0964782F,0.95499259F,0.83176377F,
0.72443596F,0.63095734F,0.54954087F
};
#define TEST_WIN_SIZE (480)
#define TEST_WIN_STEP (TEST_WIN_SIZE>>1)
int main(int _argc,const char **_argv){
FILE *fin1;
FILE *fin2;
float *x;
float *y;
float *xb;
float *eb;
float *nmr;
float thresh;
float mismatch;
float err;
float nmr_sum;
size_t weight;
size_t xlength;
size_t ylength;
size_t nframes;
size_t xi;
int bi;
int nchannels;
if(_argc<3||_argc>4){
fprintf(stderr,"Usage: %s [-s] <file1.sw> <file2.sw>\n",
_argv[0]);
return EXIT_FAILURE;
}
nchannels=1;
if(strcmp(_argv[1],"-s")==0)nchannels=2;
fin1=fopen(_argv[nchannels],"rb");
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if(fin1==NULL){
fprintf(stderr,"Error opening '%s'.\n",_argv[nchannels]);
return EXIT_FAILURE;
}
fin2=fopen(_argv[nchannels+1],"rb");
if(fin2==NULL){
fprintf(stderr,"Error opening '%s'.\n",_argv[nchannels+1]);
fclose(fin1);
return EXIT_FAILURE;
}
/*Read in the data and allocate scratch space.*/
xlength=read_pcm16(&x,fin1,nchannels);
fclose(fin1);
ylength=read_pcm16(&y,fin2,nchannels);
fclose(fin2);
if(xlength!=ylength){
fprintf(stderr,"Sample counts do not match (%lu!=%lu).\n",
(unsigned long)xlength,(unsigned long)ylength);
return EXIT_FAILURE;
}
if(xlength<TEST_WIN_SIZE){
fprintf(stderr,"Insufficient sample data (%lu<%i).\n",
(unsigned long)xlength,TEST_WIN_SIZE);
return EXIT_FAILURE;
}
nframes=(xlength-TEST_WIN_SIZE+TEST_WIN_STEP)/TEST_WIN_STEP;
xb=(float *)opus_malloc(nframes*NBANDS*sizeof(*xb));
eb=(float *)opus_malloc(nframes*NBANDS*sizeof(*eb));
nmr=(float *)opus_malloc(nframes*NBANDS*sizeof(*nmr));
/*Compute the error signal.*/
for(xi=0;xi<xlength*nchannels;xi++){
err=x[xi]-y[xi];
y[xi]=err-OPUS_CLAMP(-1,err,1);
}
/*Compute the per-band spectral energy of the original signal
and the error.*/
band_energy(xb,BANDS,NBANDS,x,nchannels,nframes,
TEST_WIN_SIZE,TEST_WIN_STEP);
free(x);
band_energy(eb,BANDS,NBANDS,y,nchannels,nframes,
TEST_WIN_SIZE,TEST_WIN_STEP);
free(y);
nmr_sum=0;
for(xi=0;xi<nframes;xi++){
/*Frequency masking (low to high): 10 dB/Bark slope.*/
for(bi=1;bi<NBANDS;bi++)
xb[xi*NBANDS+bi]+=0.1F*xb[xi*NBANDS+bi-1];
/*Frequency masking (high to low): 15 dB/Bark slope.*/
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for(bi=NBANDS-1;bi-->0;)
xb[xi*NBANDS+bi]+=0.03F*xb[xi*NBANDS+bi+1];
if(xi>0){
/*Temporal masking: 5 dB/5ms slope.*/
for(bi=0;bi<NBANDS;bi++)
xb[xi*NBANDS+bi]+=0.3F*xb[(xi-1)*NBANDS+bi];
}
/*Compute NMR.*/
for(bi=0;bi<NBANDS;bi++){
nmr[xi*NBANDS+bi]=xb[xi*NBANDS+bi]/eb[xi*NBANDS+bi];
nmr_sum+=10*OPUS_LOG10F(nmr[xi*NBANDS+bi]);
}
}
/*Find the 90th percentile of the errors.*/
memcpy(xb,eb,nframes*NBANDS*sizeof(*xb));
qsort(xb,nframes*NBANDS,sizeof(*xb),cmp_float);
thresh=xb[(9*nframes*NBANDS+5)/10];
free(xb);
/*Compute the mismatch.*/
mismatch=0;
weight=0;
for(xi=0;xi<nframes;xi++){
for(bi=0;bi<NBANDS;bi++){
if(eb[xi*NBANDS+bi]>thresh){
mismatch+=NMR_THRESH[bi]/nmr[xi*NBANDS+bi];
weight++;
}
}
}
free(nmr);
free(eb);
printf("Average pseudo-NMR: %3.2f dB\n",nmr_sum/(nframes*NBANDS));
if(weight<=0){
err=-100;
printf("Mismatch level: below noise floor\n");
}
else{
err=10*OPUS_LOG10F(mismatch/weight);
printf("Weighted mismatch: %3.2f dB\n",err);
}
printf("\n");
if(err<0){
printf("**Decoder PASSES test (mismatch < 0 dB)\n");
return EXIT_SUCCESS;
}
printf("**Decoder FAILS test (mismatch >= 0 dB)\n");
return EXIT_FAILURE;
}
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Authors' Addresses
Jean-Marc Valin
Octasic Inc.
4101, Molson Street
Montreal, Quebec
Canada
Phone: +1 514 282-8858
Email: jmvalin@jmvalin.ca
Koen Vos
Skype Technologies S.A.
Stadsgarden 6
Stockholm, 11645
SE
Phone: +46 855 921 989
Email: koen.vos@skype.net
Timothy Terriberry
Mozilla Corporation
Phone:
Email: tterriberry@mozilla.com
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