Digital Signal Processing Reference
In-Depth Information
all other times it is only known that the signal is somewhere within the limits of
these two threshold levels, some information is lost.
A method for recovering this information, at least partly, has been developed.
This involves adding some auxiliary process to the signal, either periodic or
random. The resulting mixture crosses the threshold levels much more often,
as shown in Figure 2.5(b), which makes it possible to increase the quantization
accuracy by applying short-time averaging or interpolation procedures.
It can be seen that the addition of random noise to the signal results in a
marked change in the pattern of the quantizer output signal. Instead of more or
less long series of one and the same digital sample value, larger and smaller
sample values are obtained. The pattern of the sequence is random, because it
is formed according to probabilistic rules. A larger number appears at any given
sampling instant with a probability proportional to the closeness of the signal to
the nearest upper threshold.
When this approach is used, the output signals of the ADCs are formed in such
a way that each digital number at the output is calculated by taking into account
some quantity of the quantized samples. Averaging of these samples is usually
carried out to achieve that. In this way, refined results of quantization are obtained,
which are represented by a sequence of digital numbers that may have fractional
parts. These fractional parts can assume any value between 0 and
q
However,
this digital sequence can be regarded as the output of a more precise quantizer,
so the least significant bit of each digital number obtained is equal to a step-size
of quantization that is several times smaller. In other words, this approach allows
the number of bits per sample to be increased or the signal-to-noise ratio (SNR)
to be improved, since the power of quantization noise is directly related to the
step-size of the quantizer.
The positive effect just described is obtained as a result of applying two proce-
dures: dithering and averaging. The latter can also be used in cases of conventional
quantization without any random noise being added to the signal. It is therefore
of some interest to evaluate the effect due to dithering itself. The results of the
analysis show that averaging by itself does little to improve the accuracy of quan-
tization, as it might lead to considerable signal-dependent errors. Consequently,
it is not of much use to apply this procedure to increase the number of bits per
sample value without doing something to prevent these bias errors. Amazingly,
this can be accomplished by adding noise to the signal.
Of course, averaging itself does not lead to these signal-dependent errors,
which are caused by the mode of quantization used. In addition, the results of
fixed-threshold deterministic quantization are more or less distorted by bias errors.
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