Frequency Domain Coding of Speech

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Frequency Domain Coding of Speech

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Content

• Introduction
• The Short-Time Fourier Transform
• The Short-Time Discrete Fourier Transform
• Wide-Band Analysis/Synthesis
• Sub-Band Coding

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Frequency Domain Coding of Speech

• Introduction

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Speech Coders

• Waveform Coders
• Attempt to reproducing the original waveform
  according to some fidelity criteria
• Performance successful at producing good
  quality, robust speech.
• Vocoders
• Correlated with speech production model.
• Performance more fragile and more model
  dependent.
• Lower bit rate

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Frequency-Domain Coders

• Sub-band coder (SCB).
• Adaptive Transform Coding (ATC).
• Multi-band Excited Vocoder (MBEV).
• Noise Shaping in Speech Coders.

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Classification of Speech Coders
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Frequency Domain Coding of Speech

• The Short-Time Fourier Transform

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Definition of STFT
Interpretations

• Filter Bank Interpretation
• Block Transform Interpretation

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Filter Bank Interpretation
f (m)
Analysis Filter
? is fixed at ?0.
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Filter Bank Interpretation
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Filter Bank Interpretation
Modulation
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Filter Bank Interpretation
Modulation
Lowpass Filter
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Filter Bank Interpretation
Modulated Subband signals
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Block Transform Interpretation
n is fixed at n0.
Analysis Window
FT of Windowed Data
Windowed Data
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Block Transform Interpretation
n is fixed at n0.
. . .
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Analysis/Synthesis Equations
Analysis
Synthesis
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Analysis/Synthesis Equations
Analysis
Synthesis
Replace r with nr
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Analysis/Synthesis Equations
Analysis
Synthesis
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Analysis/Synthesis Equations
Analysis
Synthesis
More general,
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Examples
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Examples
h(0)x(n)
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Examples
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Frequency Domain Coding of Speech

• The Short-Time Discrete Fourier Transform

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Definition of STDFT
Analysis
Synthesis
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Synthesis
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Synthesis
We need only one period.
Therefore, the condition is respecified as
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Implementation Consideration
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Sampling
R
2R
3R
4R
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Sampled STDFT
Analysis
Synthesis
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Sampled STDFT
Analysis
Synthesis
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Frequency Domain Coding of Speech

• Wide-Band
• Analysis/Synthesis

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Short-Time Synthesis --- Filter Bank Summation
STFT
Lowpass Filter
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Short-Time Synthesis --- Filter Bank Summation
STFT
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Short-Time Synthesis --- Filter Bank Summation
Lowpass filter
Bandpass filter
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Short-Time Synthesis --- Filter Bank Summation
Lowpass representation of for the signal
in a band centered at ?k.
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Short-Time Synthesis --- Filter Bank Summation
Encoding one band
Decoding one band
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Short-Time Synthesis --- Filter Bank Summation
. . .
Analysis
Synthesis
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Short-Time Synthesis --- Filter Bank Summation
. . .
Analysis
Synthesis
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Short-Time Synthesis --- Filter Bank Summation
h1(n)
. . .
Analysis
Synthesis
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Equal Spaced Ideal Filters
N 6
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Equal Spaced Ideal Filters
What condition should be satisfied so that
y(n)x(n)?
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Equal Spaced Ideal Filters
Time-Aliased version of h(n)
Equal spaced sampling of H(ej?)
Inverse discrete FT of H(ej?)
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Equal Spaced Ideal Filters
In case that N ? L,
Consider FIR, i.e., h(n) is of duration of L
samples.
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Equal Spaced Ideal Filters
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Equal Spaced Ideal Filters
x(n) can always be Reconstructed if N ? L,
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Equal Spaced Ideal Filters
Does x(n) can still be reconstructed if NltL?
If affirmative, what condition should be
satisfied?
x(n) can always be Reconstructed if N ? L,
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Equal Spaced Ideal Filters
p(n)
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Equal Spaced Ideal Filters
Signal can be reconstructed If it equals to
?(n?m).
p(n)
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Typical Sequences of h(n)
Ideal lowpass filter with cutoff at ?/N.
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Typical Sequences of h(n)
N ? L
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Typical Sequences of h(n)
A causal FIR lowpass filter
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Typical Sequences of h(n)
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Filter Back Implementation for a Single Channel
Analysis
Synthesis
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Filter Back Implementation for a Single Channel
Decimator
Interpolator
Analysis
Synthesis
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Filter Back Implementation for a Single Channel
Depends on the bandwidth of h(n).
Decimator
Interpolator
R?
Analysis
Synthesis
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Frequency Domain Coding of Speech

• Sub-Band Coding

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Filter Bank Implementation(Direct Implementation)
Complex Channels
R2??B
Bandwidth B/2
Analysis
Synthesis
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Filter Bank Implementation(Practical
Implementation)
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Filter Bank Implementation(Practical
Implementation)
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Filter Bank Implementation(Practical
Implementation)
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Filter Bank Implementation(Practical
Implementation)
Why?
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Filter Bank Implementation(Practical
Implementation)
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Filter Bank Implementation(Practical
Implementation)
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Filter Bank Implementation(Practical
Implementation)
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Filter Bank Implementation(Practical
Implementation)
ADPCM CODEC
Filter Bank Analysis
Sub-Band Coder Modification
Filter Bank Synthesis