Speech Coding (Part I) ? Waveform Coding

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Speech Coding (Part I) ? Waveform Coding

• ???

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Content

• Overview
• Linear PCM (Pulse-Code Modulation)
• Nonlinear PCM
• Max-Lloyd Algorithm
• Differential PCM (DPCM)
• Adaptive PCM (ADPCM)
• Delta Modulation (DM)

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Speech Coding (Part I) ? Waveform Coding

• Overview

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Classification of Coding schemes

• Waveform coding
• Vocoding
• Hybrid coding

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Quality versus Bitrate of Speech Codecs
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Waveform coding

• Encode the waveform itself in an efficient way
• Signal independent
• Offer good quality speech requiring a bandwidth
  of 16 kbps or more.
• Time-domain techniques
• Linear PCM (Pulse-Code Modulation)
• Nonlinear PCM ?-law, a-law
• Differential Coding DM, DPCM, ADPCM
• Frequency-domain techniques
• SBC (Sub-band Coding) , ATC (Adaptive Transform
  Coding)
• Wavelet techniques

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Vocoding

• Voice coding .
• Encoding information about how the speech signal
  was produced by the human vocal system.
• These techniques can produce intelligible
  communication at very low bit rates, usually
  below 4.8 kbps.
• However, the reproduced speech signal often
  sounds quite synthetic and the speaker is often
  not recognisable.
• LPC-10 Codec 2400 bps American Military Standard.

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Hybrid coding

• Combining waveform and source coding methods in
  order to improve the speech quality and reduce
  the bitrate.
• Typical bandwidth requirements lie between 4.8
  and 16 kbps.
• Technique Analysis-by-synthesis
• RELP (Residual Excited Linear Prediction)
• CELP (Codebook Excited Linear Prediction)
• MPLP (Multipulse Excited Linear Prediction)
• RPE (Regular Pulse Excitation)

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Quality versus Bitrate of Speech Codecs
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Speech Coding (Part I) ? Waveform Coding

• Linear PCM
• (Pulse-Code Modulation)

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Pulse-Code Modulation (PCM)

• A method for quantizing an analog signal for the
  purpose of transmitting or storing the signal in
  digital form.

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Quantization

• A method for quantizing an analog signal for the
  purpose of transmitting or storing the signal in
  digital form.

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Linear/Uniform Quantization
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Quantization Error/Noise
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Quantization Error/Noise
overload noise
overload noise
granular noise
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Quantization Error/Noise
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Quantization Error/Noise
? Quantization Step Size
Unquantized sinewave
3-bit quantization waveform
3-bit quantization error
8-bit quantization error
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The Model of Quantization Noise
? Quantization Step Size
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Signal-to-Quatization-Noise Ratio (SQNR)

• A measurement of the effect of quantization
  errors introduced by analog-to-digital conversion
  at the ADC.

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Signal-to-Quatization-Noise Ratio (SQNR)
Assume
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Signal-to-Quatization-Noise Ratio (SQNR)
Assume
Is the assumption always appropriate?
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Signal-to-Quatization-Noise Ratio (SQNR)
Each code bit contributes 6dB.
constant
The term Xmax/?x tells how big a signal can
be accurately represented
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Signal-to-Quatization-Noise Ratio (SQNR)
Determined by A/D converter.
Depending on the distribution of signal, which,
in turn, depends on users and time.
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Signal-to-Quatization-Noise Ratio (SQNR)
In what condition, the formula is reasonable?
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Overload Distortion
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Probability of Distortion
Assume
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Probability of Distortion
Assume
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Overload and Quantization Noise withGaussian
Input pdf and b4
Assume
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Uniform Quantizer Performance
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More on Uniform Quantization

• Conceptually and implementationally simple.
• Imposes no restrictions on signal's statistics
• Maintains a constant maximum error across its
  total dynamic range.
• ?x varies so much (order of 40 dB) across sounds,
  speakers, and input conditions.
• We need a quantizing system where the SQNR is
  independent of the signals dynamic range, i.e.,
  a near-constant SQNR across its dynamic range.

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Speech Coding (Part I) ? Waveform Coding

• Nonlinear PCM

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Probability Density Functionsof Speech Signals
Counting the number of samples in each interval
provides an estimate of the pdf of the signal.
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Probability Density Functionsof Speech Signals
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Probability Density Functionsof Speech Signals

• Good approx. is a gamma distribution, of the form
• Simpler approx. is a Laplacian density, of the
  form

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Probability Density Functionsof Speech Signals

• Distribution normalized so that ?x0 and ?x1
• Gamma density more closely approximates measured
  distribution for speech than Laplacian.
• Laplacian is still a good model in analytical
  studies.
• Small amplitudes much more likely than large
  amplitudesby 1001 ratio.

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Companding

• The dynamic range of signals is compressed before
  transmission and is expanded to the original
  value at the receiver.
• Allowing signals with a large dynamic range to be
  transmitted over facilities that have a smaller
  dynamic range capability.
• Companding reduces the noise and crosstalk levels
  at the receiver.

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Companding
Compressor
Expander
Uniform Quantizer
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Companding
Compressor
Expander
Uniform Quantizer
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Companding
After compression, y is Nearly uniformly
distributed
Compressor
Expander
Uniform Quantizer
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The Quantization-Error Variance of Nonuniform
Quantizer
Compressor
Expander
Uniform Quantizer
Jayant and Noll
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The Quantization-Error Variance of Nonuniform
Quantizer
Compressor
Expander
Uniform Quantizer
Jayant and Noll
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The Optimal C(x)
Jayant and Noll
If the signals pdf is known, then the minimum
SQNR, is achievable by letting
Compressor
Expander
Uniform Quantizer
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The Optimal C(x)
Jayant and Noll
If the signals pdf is known, then the minimum
SQNR, is achievable by letting
Is the assumption realistic.
Compressor
Expander
Uniform Quantizer
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PDF-Independent Nonuniform Quantization
Assuming overload free,
We require that SQNR is independent on p(x).
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Logarithmic Companding
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?-Law A-Law Companding

• ?-Law
• A North American PCM standard
• Used by North America and Japan
• A-Law
• An ITU PCM standard
• Used by Europe

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?-Law A-Law Companding

• ?-Law
• A North American PCM standard
• Used by North America and Japan
• A-Law
• An ITU PCM standard
• Used by Europe

(?255 ? in U.S. and Canada)
(A87.56 ? in Europe)
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?-Law A-Law Companding
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?-Law Companding
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?-Law Companding
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?-Law Companding
Linear
Log
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Histogram for ?-Law Companding
x(n)
y(n)
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?-law Approximation to Log
Distribution of quantization level for a ?-law
3-bit quantizer.
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SQNR of ?-law Quantizer

• 6.02b dependence on b
• Much less dependence on Xmax/?x
• For large ? SQNR is less sensitive to the changes
  in Xmax/?x

? good
? good
? good
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Comparison of Linear and ?-law Quantizers
Linear
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A-Law Companding
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A-Law Companding
Linear
Log
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A-Law Companding
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SQNR of A-Law Companding
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Demonstration
PCM Demo
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Speech Coding (Part I) ? Waveform Coding

• Max-Lloyd Algorithm

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How to design a nonuniform quantizer?
Q(x) Quantization (Reconstruction) Level
ck
ck?1
qk
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How to design a nonuniform quantizer?
Q(x) Quantization (Reconstruction) Level
?
?
ck
ck?1
?
qk
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How to design a nonuniform quantizer?

• Major tasks
• Determine the decision thresholds xks
• Determine the reconstruction levels qks
• Related task
• Determine codewords cks

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Optimal Nonuniform Quantization

• Major tasks
• Determine the decision thresholds xks
• Determine the reconstruction levels qks

An optimal quantizer is the one that minimizes
the following quantization-error variance.
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Optimal Nonuniform Quantization
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Necessary Conditions for an Optimum
? leads to the centroid condition
? leads to the nearest neighborhood condition
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Necessary Conditions for an Optimum
? leads to the centroid condition
? leads to the nearest neighborhood condition
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Optimal Nonuniform Quantization
This suggests an iterative algorithm to reach the
optimum.
? leads to the centroid condition
? leads to the nearest neighborhood condition
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The Max-Lloyd algorithm

1. Initialize a set of decision levels xk and set
2. Calculate reconstruction levels qk by
3. Calulate mse by
4. If , exit.
5. Set and adjust decision levels xk
   by
6. Go to 2

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The Max-Lloyd algorithm
This version assumes that the pdf of signal is
availabe.

1. Initialize a set of decision levels xk and set
2. Calculate reconstruction levels qk by
3. Calulate mse by
4. If , exit.
5. Set and adjust decision levels xk
   by
6. Go to 2

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The Max-Lloyd algorithm(Practical Version)
Exercise
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Speech Coding (Part I) ? Waveform Coding

• Differential PCM (DPCM)

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Typical Audio Signals
Do you find any correlation and/or redundancy
among the samples?
A segment of audio signals
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The Basic Idea of DPCM

• Adjacent samples exhibit a high degree of
  correlation.
• Removing this adjacent redundancy before
  encoding, a more efficient coded signal can be
  resulted.
• How?
• Accompanying with prediction (e.g., linear
  prediction)
• Encoding prediction error only

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Linear Prediction
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Linear Predictor
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DPCM Codec
Channel
Quantizer
Channel
A/D converter
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DPCM Codec
The dynamic range of prediction error is much
smaller than the signals. ? Less quantization
levels needed
Channel
Quantizer

?
Predictor
Channel
A/D converter


Predictor
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Performance of DPCM

• By using a logarithmic compressor and a 4-bit
  quantizer for the error sequence e(n), DPCM
  results in high-quality speech at a rate of
  32,000 bps, which is a factor of two lower than
  logarithmic PCM

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Speech Coding (Part I) ? Waveform Coding

• Adaptive PCM (ADPCM)

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Basic Concept

• The power level in a speech signal varies slowly
  with time.
• Let the quantization step dynamically adapt to
  the slowly time-variant power level.

?(n)
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Adaptive Quantization Schemes

• Feed-forward-adaptive quantizers
• estimate ?(n) from x(n) itself
• step size must be transmitted
• Feedback-adaptive quantizers
• adapt the step size, ?, on the basis of the
  quantized signal
• step size needs not to be transmitted

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Feed Forward Adaptation
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Feed Forward Adaptation
The source signal is not available at receiver.
So, the receiver cant evaluate ?(n) by itself.
Quantizer
Encoder
Step-Size Adaptation System
?(n) has to be transmitted.
Decoder
Quantization error
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The Step-Size Adaptation System
Step-Size Adaptation System
Estimate signals short-time energy, ?2(n), and
make ?(n) ? ?(n).
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The Step-Size Adaptation System ? Low-Pass
Filter Approach
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The Step-Size Adaptation System ? Low-Pass
Filter Approach
? 0.99
? 0.9
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The Step-Size Adaptation System ? Moving Average
Approach
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Feed-Forward Quantizer

• ?(n) evaluated every M Samples
• Use M128, 1024 for estimates
• Suitable choosing of ?min and ?max

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Feed-Forward Quantizer

• ?(n) evaluated every M Samples
• Use M128, 1024 for estimates
• Suitable choosing of ?min and ?max

Too long
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Feedback Adaptation
?(n) can be evaluated at both sides using the
same alogorithm. Hence, it needs not to be
transmitted.
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The Step-Size Adaptation System
The same as feed-forward adaptation except that
the input changes.
Step-Size Adaptation System
Step-Size Adaptation System
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Alternative Approach to Adaptation

• P(n)?P1, P2, depends on c(n?1).
• Needs to impose the limits
• The ratio ?max/?min controls the dynamic range of
  the quantizer.

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Alternative Approach to Adaptation

• P(n)?P1, P2, depends on c(n?1).
• Needs to impose the limits
• The ratio ?max/?min controls the dynamic range of
  the quantizer.

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Alternative Approach to Adaptation
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Speech Coding (Part I) ? Waveform Coding

• Delta Modulation (DM)

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Delta Modulation

• Simplest form of DPCM
• The prediction of the next is simply the current
• Sampling rate chosen to be many times (e.g., 5)
  the Nyquist rate, adjacent samples are quite
  correlated, i.e., s(n)?s(n?1).
• 1-bit (2-level) quantizer is used
• Bit-rate sampling rate

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Review DPCM
Quantizer
Channel
Channel
A/D converter
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DM Codec
Quantizer
Channel
z?1
Channel
A/D converter
z?1
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Distortions of DM
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
code words
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Distortions of DM
slope overload condition
granular noise
code words
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Choosing of Step Size
Needs large step size
Needs small step size
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Adaptive DM (ADM)
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Adaptive DM (ADM)