Lecture 16_winter_2012_6tp

Lecture 16_winter_2012_6tp - Speech Waveform Coding-Summary...

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1 1 Digital Speech Processing— Lecture 16 Speech Coding Methods Based on Speech Waveform Representations and Speech Models—Adaptive and Differential Coding Speech Waveform Coding-Summary of Part 1 12 3 2 3 0 8 / () || σ πσ ⎡⎤ = =∞ ⎢⎥ ⎣⎦ x x x px e p x 2 11 0 22 == x x xx e p 1. Probability density function for speech samples Gamma Laplacian 2. Coding paradigms uniform -- divide interval from +X max to –X max into 2 B intervals of length =(2X max /2 B ) for a B -bit quantizer ∆∆ -X max =4 x +X Speech Waveform Coding-Summary of Part 1 6 4 77 20 10 20 10 26 0 2 4 6 max max max max ˆ [] [] [] .l o g sensitivity to / ( varies a lot!!!) not great use of bits for actual speech densities! log (uniform) (B=8) .. x xn xn en X SNR B X XX SNR σσ =+ =+ − ± ± 75 4 1204 4073 8 1806 3471 16 24 08 28 69 32 30 10 22 67 64 36 12 16 65 max max (or equivalently ) varies a lot across sounds, speakers, environments need to adapt coder ( [ ]) to time varying or key x x X nX Δ ± ± ± question is how to adapt - /2 /2 1/ p(e) 30 dB loss as X max / σ x varies over a 32:1 range 4 Speech Waveform Coding-Summary of Part 1 [ ] 1 1 max max [ ] [ ] |[] | log [ ] log( ) yn F xn X X sign x n μ = + =⋅ + pseudo-logarithmic (constant percentage error) - compress x [ n ] by pseudo-logarithmic compander - quantize the companded x [ n ] uniformly - expand the quantized signal max max large | [ ] | | | [ ] | log log X yn X ≈⋅ 5 Speech Waveform Coding-Summary of Part 1 2 10 10 6 4 77 20 1 10 1 2 max max max ( ) . log ln( ) log insensitive to / over a wide range for large μσ σμ ⎛⎞ +− + + ⎜⎟ ⎝⎠ ± x SNR dB B X maximum SNR coding — match signal quantization intervals to model probability distribution (Gamma, Laplacian) • interesting—at least theoretically 6 Adaptive Quantization • linear quantization => SNR depends on σ x being constant (this is clearly not the case) • instantaneous companding => SNR only weakly dependent on X max / σ x for large μ -law compression (100- 500) • optimum SNR => minimize σ e 2 when σ x 2 is known, non- uniform distribution of quantization levels Quantization dilemma : want to choose quantization step size large enough to accomodate maximum peak-to- peak range of x [ n ]; at the same time need to make the quantization step size small so as to minimize the quantization error – the non-stationary nature of speech (variability across sounds, speakers, backgrounds) compounds this problem greatly
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2 7 Solutions to Quantization Dilemna Solution 1 -le t vary to match the variance of the input signal => [ n ] Solution 2 -use ±a ± variable gain, G [ n ] , followed by a fixed quantizer step size, => keep signal variance of y [ n ] =G [ n ] x [ n ] constant Case 1 : [ n ] proportional to σ x => quantization levels and ranges would be linearly scaled to match σ x 2 => need to reliably estimate σ x 2 Case 2 : G[ n ] proportional to 1/ σ x to give σ y 2 constant need reliable estimate of σ x 2 for both types of adaptive quantization Adaptive Quantization : 8 Types of Adaptive Quantization • instantaneous-amplitude changes reflect sample-
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Lecture 16_winter_2012_6tp - Speech Waveform Coding-Summary...

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