Speech Compression

1
SpeechCompression
2
Quick Overview
Spch Comp

• Simple coders
• G.711 A-law m-law
• Delta
• ADPCM
• CELP coders
• LPC-10
• RELP/GSM
• CELP

• Other methods
• MBE
• MELP
• STC
• Waveform Interpolation

3
Encoder Criteria
Spch Comp

• Encoders can be compared in many ways
• the most important are
• Bit rate (Kbps)
• Speech quality (MOS)
• Delay (algorithmic framelookahead
  computational propagation)
• Computational Complexity
• Often less important
• Bit exactness (interoperability)
• Transcoding robustness
• Behavior on non-speech (babble noise, tones,
  music)
• Bit error robustness

4
PSTN Quality Coders
Spch Comp

• Rate ITU-T encoder
• 128 Kbps 16bit linear
  sampling
• 64 Kbps G.711 A-law/m-law 8bit
  log sampling
• 32 Kbps G.726 ADPCM
• 16 Kbps G.728 LDCELP
• 8 Kbps G.729 CS-ACELP
• 4 Kbps SG16Q21 ???
• toll quality MOS rating, but higher delay

5
Digital Cellular Standards
Spch Comp
6
Military / Satellite Standards
Spch Comp
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• Simple
• coders

8
G.711
Spch Comp

• 16 bit linear sampling at 8 KHz means 128 Kbps
• Minimal toll quality linear sampling is 12 bit
  (96 Kbps)
• 8 bit linear sampling (256 levels) is noticeably
  noisy
• Due to
• prevalence of low amplitudes
• logarithmic response of ear
• we can use logarithmic sampling
• Different standards for different places

9
G.711 - cont.
Spch Comp
North America m 255

• m-law
• A-law
• Although very different looking they are nearly
  identical
• G.711 approximates these expressions by 16
  staircase straight-line segments
• (8 negative and 8 positive)
• m-law horizontal segment through origin, A-law
  vertical segment

Rest Of World A 87.56
10
DPCM
Spch Comp

• Due to low-pass character of speech
• differences are usually smaller than signal
  values
• and hence require fewer bits to quantize
• Simplest Delta-PCM (DPCM) quantize first
  difference signal D
• Delta-PCM quantize difference between signal
  and prediction
• sn p ( sn-1 , sn-2 , , sn-N ) S pi sn-i
• If predict using linear combination (FIR filter),
  this is linear prediction
• Delta-modulation (DM) use only sign of
  difference (1bit DPCM)
• Sigma-delta (1bit) oversample, DM, trade-off
  rate for bits

i
11
DPCM with prediction
Spch Comp

• If the linear prediction works well, then the
  prediction error
• en sn - sn
• will be lower in energy and whiter than sn
  itself !
• Only the error is needed for reconstruction,
• since the predictable portion can be predicted sn
  sn en!

sn
prediction filter
12
DPCM - post-filtering
Spch Comp

• Simplest case
• if highly oversampled
• then previous sample sn-1 predicts sn well,
• so we can use DM,
• if sgn(en) lt 0 then -D else D
• For DM there is no way to encode zero prediction
  error
• so decoded signal oscillates wildly
• Standard remedy is a post-filter that low-pass
  filters this noise
• But there is a b i g g e r problem!

13
Open-loop Prediction
Spch Comp

• The encoder (linear predictor) is present in the
  decoder
• but there runs as feedback
• The decoders predictions are accurate with the
  precise error en
• but it gets the quantized error en and the models
  diverge!

14
Side Information
Spch Comp

• There are two ways to solve the problem ...
• The first way is to send the prediction
  coefficients
• from the encoder to the decoder
• and not to let the decoder derive them
• The coefficients sent are called side-information
• Using side-information means higher bit-rate
• (since both en and coefficients must be sent)
• The second way does not require increasing bit
  rate

15
Closed-loop Prediction
Spch Comp

• To ensure that the encoder and decoder stay
  in-sync
• we put the decoder into the encoder
• Thus the encoders predictions are identical to
  the decoders
• and no model difference accumulates

en
sn
en
sn
Q
IQ
IQ
PF
PF
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Two types of error
Spch Comp

• For DM there are two types of error (depending on
  step size)

D too small
D OK
D too large
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Adaptive Step Size
Spch Comp

• Speech signals are very nonstationary
• We need to adapt the step size to match signal
  behavior
• Increase D when signal changes rapidly
• Decrease D when signal is relatively constant
• Simplest method (for DM only)
• If present bit is the same as previous multiply D
  by K (K1.5)
• If present bit is different, divide D by K
• Constrain D to a predefined range
• More general method
• Collect N samples in buffer (N 128 512)
• Compute standard deviation in buffer
• Set D to a fraction of standard deviation
• Send D to decoder as side-information or
• Use backward adaptation (closed-loop D
  computation)

18
ADPCM
Spch Comp

• G.726 has
• Adaptive predictor
• Adaptive quantizer and inverse quantizer
• Adaptation speed control
• Tone and transition detector
• Mechanism to prevent loss from tandeming
• Computational complexity relatively high (10
  MIPS)
• 24 and 16 Kbps modes defined, but not toll
  quality
• G.727 same rates but embedded for packetize
  networks
• ADPCM only used general low-pass characteristic
  of speech
• What is the next step?

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Scalar Quantization
Spch Comp

• Standard A/D has preset, evenly distributed
  levels
• G.711 has preset, non-evenly distributed levels
• With a criterion we can make an adaptive
  quantizer
• Simplest criterion minimum squared quantization
  error
• en sn - sn E lt en2 gt
• Need algorithm to find optimal placement of
  levels EM-type algorithms

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Vector Quantization
Spch Comp

• We can do the same thing in higher dimensions
• Here we wish to match input data xi i 1
  .. N
• to a codebook of codewords Cj j 1 .. M
• with Minimal Mean Squared Error
• E Si1..N xi - C 2
• where C is the codeword closest to xi in the
  codebook

xi
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LBG Algorithm for VQ
Spch Comp

• Input xi i 1 .. N clustering, unsupervised
  learning
• Randomly initialize codebook Cj j 1 .. M
• Loop until converge
• Classification Step
• for i 1 .. N
• for j 1 .. M
• compute Dij2 xi - Cj 2
• classify xi to Cj with minimal Dij2
• Expectation Step
• for j 1 .. M correct center Cj S
  i e Cj xi

1
Nj
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Speech Application of VQ
Spch Comp

• OK, I understand what to do with scalar
  quantization
• what is VQ good for ?
• We could try to simply VQ frames of speech
  samples
• but this doesnt work well !
• We can VQ spectra or sub-band components
• We often VQ parameter sets (e.g. LPC
  coefficients)
• We also VQ model error signals

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• CELP
• coders

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LPC-10
Spch Comp

• Based on 10th order LPC (obviously) Bishnu
  Atal
• 180 sample blocks are encoded into 54 bits
• Pitch U/V (found using AMDF) 7 bits
• Gain
  5 bits
• 10 reflection coefficients found by covariance
  method
• first two coefficients converted to log area
  ratios
• L1, L2, a3, a4 5 bits each
• a5, a6, a7, a8 4 bits each
• a9 3 bits a10 2 bits 41 bits
• 1 sync bit 1
  bit
• 54 bits 44.44 times per second results in 2400
  bps
• By using VQ could reduce bit rate to under 1
  Kbps!
• LPC-10 speech is intelligible, but synthetic
  sounding
• and much of the speaker identity is lost !

25
The Residual
Spch Comp

• Recover sn by adding back the residual error
  signal
• sn sn en
• So if we send en as side-information we can
  recover sn
• en is smaller than sn so may require fewer bits
  !
• But en is whiter than sn so may require many
  bits!
• The question has now become
• How can we compress the residual?

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Encoding the Residual
Spch Comp

• RELP (6-9.6 Kbps)
• Low-pass filter and downsample residual to 1 KHz
• Encode using ADPCM
• VQ-RELP (4.8 Kbps)
• VQ coding of residual
• RELP (4.8 Kbps)
• Perform FFT on residual
• Baseband coding
• RPE-LTP (GSM-FR at 13 Kbps)
• Residual Pulse Excitation - Long Term Predictor
• Perform Long Term Prediction (pitch recovery)
• Subtract to obtain new residual
• Decimate by 3, use phase with maximum energy
• Extract 6-bit overall gain
• Encode remainder with 3 bits/sample

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Residual and Excitation
Spch Comp

• Synthesis filter sn
  en S am sn-m
• Analysis filter rn
  sn - S am sn-m
• So rn en !

excitation
residual
Note all-zero filter is the inverse of the
all-pole filter
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CELP
Spch Comp

• Atals idea
• Find a way to efficiently encode the excitation !
• Questions
• How can we find the excitation?
• Theoretically, by algebra (invert the filter!)
• How can we efficiently encode the residual?
• VQ - Code Excited Linear Prediction
• How can we efficiently find the best codeword?
• Exhaustive search

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CELP - cont.
Spch Comp

• Atal and friends (Schroeder, Remde, Singhal,
  etc.) discoveries
• Even random codebooks work well Gaussian,
  uniform
• Dont need large codebooks e.g. 1024 codewords
  for 40 samples
• Can center-clip with little loss
• Codebook with constant amplitude almost as good
• So we can use codebooks with structure (and save
  storage/search/bits)
• Multipulse (MP)
• Constant Amplitude Pulse

Regular Pulse (RP)
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Special Excitations
Spch Comp

• Shift technique reduces random CB operations from
  O(N2) to O(N)
• a b c d e f c d e f g h e f g h I j ...
• Using a small number of 1 amplitude pulses
  leads to MIPS reduction
• Since most values are zero, there are few
  operations
• Since amplitudes 1 no true multiplications
• In a CB containing CW and -CW we can save half
• Algebraic codebooks exploit algebraic structure
• Example choose pulses according to Hadamard
  matrix
• Using FHT reduces computation
• Conjugate structure codebooks
• Excitation is sum of codewords from two related
  CBs

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Analysis by Synthesis
Spch Comp

• Finding the best codeword by exhaustive search

sn
Compute energy
-
LPC
find minimum
32
Perceptual Weighting
Spch Comp

• The criterion for selecting the best codeword
  should be perceptual
• not simply the energy of the difference signal!
• We perceptually weight the signal and the
  synthesized signal

sn
PW
-
Since PW is a filter we need use it only once
CB
LPC
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Perceptual Weighting - cont.
Spch Comp

• The most important PW effect is masking
• Coding error energy near formants is not heard
  anyway
• so we allow higher error near formants
• but demand lower perceivable error energy
• To do this we de-emphasize according to the LPC
  spectrum!
• Simplest filter is 1 - S ai z-I where ai are
  the LPC coefficients
• How do we take the critical bandwidth into
  account?
• We perform bandwidth expansion Denominator
  expansion gt numerator 1 - S g1i ai z-I
• 1 - S g2i ai z-I

BW - ln(g) Fs p
1 gt g1 gt g2 gt 0
Typical values g1 0.9 g2 0.6
34
Post-filter
Spch Comp

• Not related to the subject, but if we are already
  here
• In order to increase the subjective quality of
  many coders
• post-filters are often used to emphasize the
  formant structure
• These have the same form as the perceptual
  weighting filter
• but 1 gt g2 gt g1 gt 0 with typical values g1 0.5
  g2 0.75
• Denominator expansion lt numerator!
• the post-filter also reinforces tilt
• which should then be compensated by an IIR filter
• since the spectral valleys are de-emphasized
• we should change the PW filter parameters g1 and
  g2
• Originally proposed for ADPCM !

35
Subframes
Spch Comp

• Coders with large frames (gt 10 ms) need a long
  excitation signal
• and hence a lot of bits to encode
• An alternative is to divide the frame into (2-4)
  subframes
• each of which has its own codeword excitation

frame n-1
frame n1
frame n
We really should recompute LPC per subframe but
we can get away with interpolating !
36
Lookahead
Spch Comp

• If we are already dividing up the frame
• we can compute the LPC based on a shifted frame
• This is called lookahead, and it adds processing
  delay !
• To decrease delay we can use backward looking IIR
  filter
• and then we neednt send/store the LPC
  coefficients at all!

------- LPC -------
------- LPC -------
CW
CW
CW
CW
CW
CW
CW
CW
37
What happened to the pitch?
Spch Comp

• Unlike LPC, the ABS CELP coder is excited by
  codebook
• Where does the pitch come from?
• Random CB minimi zation will prefer good
  excitation
• Regular/Multi pulse pulse spacing (not enough
  pulses for high pitch)
• But this is usually not enough (residual has
  pitch periodicity)
• Two solutions
• Adaptive codebook (Klejn, etal)
• Long term prediction (Atal Singhal)
• Both of these reinforce the pitch component

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Adaptive CB
Spch Comp

• Adaptive codebook is repetitions of previous
  excitations
• Total excitation is weighted sum of stochastic CB
  (random, MP, RP, etc)
• and adaptive CB

Adaptive CB
Ga
LPC
Gs
Fixed CB
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Long Term Prediction
Spch Comp

• Using long-term (pitch predictor) and short-term
  (LPC) prediction
• Long term predictor may have only
• one delay, but then non-integer
• 1
• 1 - b z - d

sn
pitch predictor
gain
-
codebook
LPC
perceptual weighting
error computation
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Federal Standard CELP
Spch Comp

• FS 1016 at 4.8 Kbps has MOS 3.2
• Developed by ATT Bell Labs for DOD 144 bits /
  30 ms frame
• 10th order LPC on 30 ms Hamming window
• no pre-emphasis, additional 15 Hz BW expansion
  (quality and LSP robustness)
• Conversion to LSP and nonuniform scalar
  quantization to 34 bits
• 4 subframes (7.5 ms) LSP interpolation
• 512 entry fixed CB - static -1,0,1 from
  center-clipped Gaussian
• 5 bit nonuniform quantized gain 56 bits
• 256 entry adaptive CB - 8 bits 5 bit nonuniform
  quantized gain 48 bits
• optional noninteger delays, optional
• Perceptual weighting
• Postfilter spectral tilt compensation,
  removable for noise or tandeming
• FEC 4 bits SYNC 1 bit reserved 1 bit

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G.728
Spch Comp

• 16 Kbps with MOS similar to G.726 at 32 Kbps
• Low 5 sample (0.625 msec) delay
• High computational complexity (about 30 MIPS)
• CELP with Backward LPC
• LPC order 50 (why not? - we dont transmit
  side-information!)
• Frame of 2.5 ms (20 samples)
• 4 subframes of 0.625 ms (5 samples)
• Perceptual weighting
• Only 10 bit index to fixed CB is transmitted
• 10 bits per 0.625 ms is 16 Kbps !

42
G.729
Spch Comp

• 8 Kbps toll-quality coder for DSVD and VoIP
• Computational complexity 20 MIPS, but G.729a is
  about 10 MIPS
• frame 10 ms (80 samples) lookahead 5 ms (1
  subframe)
• LPC, LSP, VQ, LSP interpolation
• CS-ACELP CB (Interleaved single pulse
  permutation) 4 1 pulses / subframe
• closed loop pitch prediction and adaptive CB
  (delaygain)
• 2 (40 sample) subframes per frame
• For each frame the encoder outputs 80 bits
• LSF coefficients 18 bits pitch
  8 bits gain CB 14 bits
• adaptive CB 5 bits parity check 1
  bit
• pulse positions 26 bits pulse signs 8
  bits

43
G.729 annexes
Spch Comp

• A Compatible reduced complexity encoder with
  minimal MOS reduction
• B VAD and CNG
• C Floating point implementation
• D 6.4 Kbps version
• similar to G.729 but 64 output bits per frame,
  quality better than G.726 at 24Kbps
• LSF coefficients 18b pitchadaptive CB 84b
  gain CB 12b fixed CB 22b
• E 11.8 Kbps coder for high quality and music

44
G.723.1
Spch Comp

• 6.4 (MP-MLQ) and 5.4 (ACELP) Kbps rates
• About 18 MIPS on DSP
• frame 30 ms (240 samples) lookahead 15 ms.
• LPC on 30 ms (240 sample) frames, LSP and VQ
• open-loop pitch computation on half-frames (120
  sample)
• excitation on 4 subframes (60 samples) per frame
• perceptual weighting and harmonic noise weighting
• fifth-order closed loop pitch predictor
• MP-MLQ 5 or 6 1 pulses / subframe, positions
  all even or all odd
• ACELP 4 1 pulses / subframe, positions differ
  by 8
• Annex A VAD-CNG Annex B floating point
  implementation

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• Other
• Coders

46
MBE coder
Spch Comp

• LPC10 makes hard U/V decision - no mixed voicing
• Multi Band Excitation uses a different excitation
• harmonics of pitch frequency
• frequency-dependent binary U/V decision
• large number of sub-bands (gt16)
• Simultaneous ABS estimation of pitch and spectral
  envelope
• Then U/V decision made based on spectral fit
• Use of dynamic programming for pitch tracking

47
MBE coder - cont.
Spch Comp

• DVSI made various MBE, AMBE and IMBE for
  satellite (INMARSAT)
• Bit rates 2.4 - 9.6 Kbps (toll quality at 3.6
  Kbps)
• Integral FEC for bit-error robustness
• As an example
• 128 bits for each 20 ms frame
• pitch 8 bits
• U/V decisions K bits (K lt 12)
• spectral amplitudes (DCT) 75-K bits
• FEC (Golay codes) 45 bits

48
MELP
Spch Comp

• DOD wanted a new 2.4 Kbps coder with MOS similar
  to FS1016
• Main problems with LPC10
• voicing determination errors
• no handling of partially voiced speech
• Unlike MBE MELP uses standard LPC model
• MELP excitation is pulse train plus random noise
• Soft decision in small number (5) of sub-bands
• Frame 22.5 ms (180 samples)
• 10th order LPC, 15 Hz BW expansion, LSF,
  interpolation, VQ
• pitch refinement
• 5 sub-bands (0-500-1000-2000-3000-4000Hz) pitch
  and noise excitation
• FEC

49
Sinusoidal Transform Coder
Spch Comp

• McAulay and Quatieri model
• instead of LPC use sum of sine waves
• sn Si 1 .. N Ai cos ( wi n fi )
• For each analysis frame (10 - 20 ms) need to
  extract N Ai fi s
• Voiced speech
• Use pitch and important harmonics from
  pitch-synchronized STFT
• Unvoiced speech
• Use peaks of STFT points where slope changes
  from to -
• At high bit-rates keep magnitudes, frequencies
  and phases
• At low bit-rates frequencies constrained and
  phases modeled

50
STC - cont.
Spch Comp

• Sparse spectrum is updated at regularly spaced
  times
• Amplitude linearly interpolated between updates
• Interpolated phase must obey 4 conditions (w f
  w f)

overlapped windowing
sn
FFT
sum of sinusoids
sn
peak picker
spectrum encoder
spectrum decoder
e.g. all-pole model
51
STC - cont.
Spch Comp

• Tracking the sinusoidal components

birth
frequency
death
time
52
Waveform Interpolation
Spch Comp

• Voiced speech is a sequence of pitch-cycle
  waveforms
• The characteristic waveform usually changes
  slowly with time

Useful to think of waveform in 2d
time
Phase in pitch period
This waveform can be the speech signal or the LPC
residual
53
WI - cont.
Spch Comp

• Per frame LPC and pitch are extracted
• Represent CW by features (e.g. DFT coefficients)
• Alignment by circular shift until maximum
  correlation
• Separate treatment for voice and unvoiced
  segments

LPC pitch tracking
sn
Characteristic waveform extraction
conversion to 1d
sn
2d CW alignment
waveform interpolation
quantization
decoding
54
We can go even lower
Spch Comp

• The Shannon entropy of speech is 200-500 bps
• So even deeper compression should be possible
• There are even lower rate speech coders (300-600
  bps)
• but they are not practical at this point
• extremely high MIPS and memory
• very long latency
• very sensitive to background noise