Frequency Domain Coding of Speech 主講人：虞台文

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

Frequency Domain Coding of Speech Introduction

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

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

Classification of Speech Coders

Frequency Domain Coding of Speech The Short-Time Fourier Transform

Definition of STFT Interpretations: Filter Bank Interpretation Block Transform Interpretation

Filter Bank Interpretation  is fixed at  0. f ( m ) Analysis Filter

Filter Bank Interpretation h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) x(n)x(n)

Modulation   00

Filter Bank Interpretation   00 Lowpass Filter Modulation

Filter Bank Interpretation h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) x(n)x(n) Modulated Subband signals

Block Transform Interpretation n is fixed at n 0. Windowed Data Analysis Window FT of Windowed Data

Block Transform Interpretation n is fixed at n 0. n1n1 n2n2 n3n nrnr

Analysis/Synthesis Equations Analysis Synthesis In what condition we will have

Analysis/Synthesis Equations Analysis Synthesis Replace r with n+r

Analysis/Synthesis Equations Analysis Synthesis Therefore, if

Analysis/Synthesis Equations More general, Analysis Synthesis Therefore, if

Examples

h (0) x ( n )

Examples

Frequency Domain Coding of Speech The Short-Time Discrete Fourier Transform

Definition of STDFT Analysis: Synthesis: In what condition we will have

Synthesis 1

We need only one period. Therefore, the condition is respecified as:

Implementation Consideration n Frequency k 0 Spectrogram

Sampling n Frequency k 0 Spectrogram R2R2R3R3R4R4R

Sampled STDFT Analysis: Synthesis: In what condition we will have

Sampled STDFT Analysis: Synthesis: In what condition we will have

Frequency Domain Coding of Speech Wide-Band Analysis/Synthesis

Short-Time Synthesis --- Filter Bank Summation STFT h(n)h(n) h(n)h(n) x(n)x(n) Lowpass Filter

Short-Time Synthesis --- Filter Bank Summation STFT

Short-Time Synthesis --- Filter Bank Summation  |H(e j  )|  |H k (e j  )| kk Lowpass filterBandpass filter

Short-Time Synthesis --- Filter Bank Summation hk(n)hk(n) hk(n)hk(n) x(n)x(n) Bandpass Filter h(n)h(n) h(n)h(n) x(n)x(n) Lowpass Filter Lowpass representation of for the signal in a band centered at  k.

Short-Time Synthesis --- Filter Bank Summation hk(n)hk(n) hk(n)hk(n) x(n)x(n) Bandpass Filter h(n)h(n) h(n)h(n) x(n)x(n) Lowpass Filter Encoding one bandDecoding one band

Short-Time Synthesis --- Filter Bank Summation h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n) Analysis Synthesis

Short-Time Synthesis --- Filter Bank Summation h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n) Analysis Synthesis

Short-Time Synthesis --- Filter Bank Summation h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n) Analysis Synthesis

Equal Spaced Ideal Filters 11 22 33 44 55 22  1 0 N = 6

Equal Spaced Ideal Filters h1(n)h1(n) x(n)x(n) h0(n)h0(n) hN1(n)hN1(n) What condition should be satisfied so that y(n)=x(n)?

Equal Spaced Ideal Filters Equal spaced sampling of H ( e j  ) Inverse discrete FT of H ( e j  ) Time-Aliased version of h ( n )

Equal Spaced Ideal Filters Consider FIR, i.e., h(n) is of duration of L samples. 0 L1L1 n h(n)h(n) In case that N  L,

Equal Spaced Ideal Filters

h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n) L1L1 n h(n)h(n) x(n) can always be Reconstructed if N  L,

Equal Spaced Ideal Filters h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n) L1L1 n h(n)h(n) x(n) can always be Reconstructed if N  L, Does x(n) can still be reconstructed if N<L? If affirmative, what condition should be satisfied?

Equal Spaced Ideal Filters h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n) p(n)p(n)

p(n)p(n) Signal can be reconstructed If it equals to  ( n  m ).

Typical Sequences of h (n) Ideal lowpass filter with cutoff at  /N. 0 NN 2N2N N2N2N3N3N4N4N p(n)p(n) N 0 NN 2N2N N2N2N3N3N4N4N h(n)h(n) 1/N

Typical Sequences of h (n) 0 NN 2N2N N2N2N3N3N4N4N p(n)p(n) N 0 NN 2N2N N2N2N3N3N4N4N h(n)h(n) h(0) LL 2L2L L2L2L3L3L4L4L N  LN  L

Typical Sequences of h (n) 0 NN 2N2N N2N2N3N3N4N4N p(n)p(n) N 0 NN 2N2N N2N2N3N3N4N4N h(n)h(n) h(0) 1/N A causal FIR lowpass filter

Typical Sequences of h (n) 0 NN 2N2N N2N2N3N3N4N4N p(n)p(n) N 0 NN 2N2N N2N2N3N3N4N4N h(n)h(n) h(0) 1/N A causal IIR lowpass filter

Filter Back Implementation for a Single Channel hk(n)hk(n) x(n)x(n) h(n)h(n) x(n)x(n) Analysis Synthesis

hk(n)hk(n) x(n)x(n) h(n)h(n) x(n)x(n) Filter Back Implementation for a Single Channel R:1 1:R Analysis Synthesis Decimator Interpolator

hk(n)hk(n) x(n)x(n) h(n)h(n) x(n)x(n) Filter Back Implementation for a Single Channel R:1 1:R Analysis Synthesis Decimator Interpolator Depends on the bandwidth of h(n). R=?

Frequency Domain Coding of Speech Sub-Band Coding

Analysis Synthesis Filter Bank Implementation (Direct Implementation) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) x(n)x(n) R:1 1:R f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) x(n)x(n) Complex Channels R=2  B Bandwidth B/2

Filter Bank Implementation (Practical Implementation) 0 B kk 0 B  k 0 B/2  B/2 0 B/2  B/2 0 BB 0 B 0 BB B

Filter Bank Implementation (Practical Implementation) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) x(n)x(n)......

h(n)h(n) h(n)h(n) x(n)x(n) h(n)h(n) h(n)h(n)

h(n)h(n) h(n)h(n) x(n)x(n) h(n)h(n) h(n)h(n) D:1 Why?

Filter Bank Implementation (Practical Implementation) h(n)h(n) h(n)h(n) x(n)x(n) h(n)h(n) h(n)h(n) D:1

h(n)h(n) h(n)h(n) x(n)x(n) h(n)h(n) h(n)h(n) Filter Bank Implementation (Practical Implementation)

x(n)x(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) D:1 2D:1

Filter Bank Implementation (Practical Implementation) ADPCM CODEC h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) 2D:1 f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) Filter Bank Analysis Filter Bank Analysis Sub-Band Coder Modification Sub-Band Coder Modification Filter Bank Synthesis Filter Bank Synthesis