Digital Signal Processing Reference
In-Depth Information
Fourier, and similar, coefficients estimated in the course of spectral transforms,
which are performed on an exponential and other orthogonal function basis. Their
estimation is considered in the following chapters. As shown there, optimizing is
carried out by taking into account some additional factors, for instance, whether
or not the signal is noisy. Both fine and rough quantizing modes are applicable
for estimating these parameters.
12.3
Specifics Related to Pseudo-randomized Quantizing
The previous sections have clearly shown that when signal average parameters
have to be estimated, it is advantageous to quantize signals pseudo-randomly.
However, as most of the existing algorithms for digital estimation of such param-
eters have been developed for processing deterministically quantized signals, the
application of pseudo-randomized quantizing is possible only if the processing
algorithms are appropriately modified.
Attempts to replace deterministic by pseudo-randomized quantizers without
adapting the processing algorithms and hardware to the specifics of such quantiz-
ing may well be unsuccessful. Although the digital signals obtained by pseudo-
randomized quantizers have considerably superior properties, the price for this
improvement is an increased bit rate and corresponding hardware complications.
Recall that pseudo-randomly quantized signals are defined as
=
ξ
2
q
1
x
k
−
+
n
k
q
.
(12.32)
k
The first term of this equation indicates the positions that the threshold levels
occupy at the quantization time instants
t
k
when the rounding-off results
n
k
q
are
obtained. In the case of deterministic quantizing, the thresholds are fixed and it is
not necessary to add this information to the descriptions of the quantized signals.
Pseudo-randomized quantizer outputs therefore have more bits in principle, and
for this reason their straightforward applications may sometimes be question-
able. Overall good results from the application of such quantizers may only be
expected if their output signals are processed in a way best suited to the given
conditions.
However, as the conditions of signal processing can differ considerably, it is not
possible to give precise recipes for every particular case; for success the general
technical principles must be understood. The material in this chapter may be
found to be helpful in this.
It is first recommended that the digital signal processing be organized in such
a way that the sequences (
1
2
)
q
and
n
k
q
are processed separately. Next, it
should be taken into account that the process (
ξ
−
k
1
ξ
−
2
)
q
is predetermined and can
k
