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Adaptive PCM and DPCM (ADPCM) 615
and performance of these encoders can be improved by having them adapt
to the slowly time-variant power level of the speech signal.
In both PCM and DPCM the quantization error q(n) resulting from a
uniform quantizer operating on a slowly varying power level input signal
will have a time-variant variance (quantization noise power). One improvement
that reduces the dynamic range of the quantization noise is
the use of an adaptive quantizer.
Adaptive quantizers can be classified as feedforward or feedback. A
feedforward adaptive quantizer adjusts its step size for each signal sample,
based on a measurement of the input speech signal variance (power). For
example, the estimated variance, based as a sliding window estimator, is
ˆσ 2 n+1 = 1 M
Then the step size for the quantizer is
n+1
∑
k=n+1−M
s 2 (k) (12.18)
∆(n +1)=∆(n)ˆσ n+1 (12.19)
In this case it is necessary to transmit ∆ (n +1)tothe decoder in order
for it to reconstruct the signal.
A feedback adaptive quantizer employs the output of the quantizer
in the adjustment of the step size. In particular, we may set the step size
as
∆(n +1)=α(n)∆(n) (12.20)
where the scale factor α(n) depends on the previous quantizer output.
For example, if the previous quantizer output is small, we may select
α(n) < 1inorder to provide for finer quantization. On the other hand,
if the quantizer output is large, then the step size should be increased
to reduce the possibility of signal clipping. Such an algorithm has been
successfully used in the encoding of speech signals. Figure 12.5 illustrates
such a (3-bit) quantizer in which the step size is adjusted recursively
according to the relation
∆(n +1)=∆(n) · M(n)
where M(n) isamultiplication factor whose value depends on the quantizer
level for the sample s(n), and ∆(n)isthe step size of the quantizer for
processing s(n). Values of the multiplication factors optimized for speech
encoding have been given by [14]. These values are displayed in Table 12.1
for 2-, 3-, and 4-bit quantization for PCM and DPCM.
In DPCM the predictor can also be made adaptive. Thus in ADPCM
the coefficients of the predictor are changed periodically to reflect the
changing signal statistics of the speech. The linear equations given by
(12.11) still apply, but the short-term autocorrelation function of s(n),
r ss (m) changes with time.
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