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Unformatted text preview: ct that uniform quantizer is optimal for a uniform pdf. Thus if a nonlinearity is applied to the waveform x[n] to form a new sequence g[n] whose pdf is uniform then Uniform quantizer can be applied to g[n] to obtain g[n], as depicted in the Figure 12.10 in the next slide. ^ February 11, 2012 Veton Kpuska 52 Companding February 11, 2012 Veton Kpuska 53 Companding A number of other nonlinear approximations nonlinear transformation that achieves uniform density are used in practice which do not require pdf measurement. Specifically and Alaw and law companding. law coding is give by: T ( x[n]) = xmax x[ n ] log1 + xmax log(1 + ) sign( x[n]) CCITT international standard coder at 64 kbps is an example application of law coding. law transformation followed by 7bit uniform quantization giving toll quality speech. Equivalent quality of straight uniform quantization achieved by 11 bits. Veton Kpuska 54 February 11, 2012 Adaptive Coding Adaptive Coding Nonuniform quantizers are optimal for a long term pdf of speech signal. However, considering that speech is a highlytimevarying signal, one has to question if a single pdf derived from a longtime speech waveform is a reasonable assumption. Changes in the speech waveform: Approach: Temporal and spectral variations due to transitions from unvoiced to voiced speech, Rapid volume changes. Estimate a shorttime pdf derived over 2040 msec intervals. Shorttime pdf estimates are more accurately described by a Gaussian pdf regardless of the speech class. February 11, 2012 Veton Kpuska 56 Adaptive Coding A pdf derived from a shorttime speech segment more accurately represents the speech nonstationarity. One approach is to assume a pdf of a specific shape in particular a Gaussian with unknown variance 2. For a Gaussian we have: Measure the local variance then adapt a nonuniform quantizer to the resulting local pdf. This approach is referred to as adaptive quantization. p x ( x) =
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2 2 x e x2 - 2 2 x Veton Kpuska 57 Adaptive Coding Measure the variance x2 of a sequence x[n] and use resulting pdf to design optimal max quantizer. Note that a change in the variance simply scales the time signal: 1. If E(x2[n]) = x2 then E[(x [n])2] = 2x2 2. Need to design only one nonuniform quantizer with unity variance and scale decision and reconstruction levels according to a particular variance. Fix the quantizer and apply a timevarying gain to the signal according to the estimated variance (scale the signal to match the quantizer). February 11, 2012 Veton Kpuska 58 Adaptive Coding February 11, 2012 Veton Kpuska 59 Adaptive Coding There are two possible approaches for estimation of a time varying variance 2[n]: Feedforward method (shown in Figure 12.11) where the variance (or gain) estimate is obtained from the input Feedback method where the estimate is obtained from a quantizer output. Adaptive quantizers can achieve higher SNR than the use of law companding. law companding is generally preferred for highrate waveform coding because of its lower background noise when transmission channel is idle. Adaptiv...
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