Digital Signal Processing Reference
In-Depth Information
Figure 9.2
Spectrograms obtained in the case when sample values of a single-tone signal are
taken periodically with some of them pseudo-randomly skipped: (a)
N
=
2048; (b)
N
=
512
on features of this basic component of the sampling process. The goal of these
studies is to discover practical applicable methods for reduction of errors that
impair spectral analysis and waveform reconstruction of a wide class of signals.
The targeted error reduction is to be based on more extensive use of all
a priori
information. The pattern of pseudo-random skips is typically fixed, so first a
method must be found showing how this information can be used more effectively.
Aliasing for the periodic sampling pulse streams with pseudo-random skips
is well-defined, shown by the spectrograms given in Figure 9.2. It can be seen
that the aliases are located symmetrically to the sampling frequency and their
amplitudes are equal to the amplitude of the signal. However, the noise due to the
cross-interference is still present.
Broadly speaking, periodic sampling with random skipping of signal sam-
ple values belongs to the class of randomized sampling processes. However, the
features of this kind of randomized sampling differ greatly from those character-
istic of the randomized sampling processes discussed, specifically, in Chapter 3.
Indeed, the basic motivation for deliberate randomization of sampling so far has
been the avoidance of aliasing. In this particular randomization case this effect is
not achieved. Therefore there must be other reasons why such a sampling model
is considered at all.
Actually there are some good reasons. Firstly, it is important to use fault-tolerant
signal processing to discover how to reconstruct spectra and waveforms of signals
when the process of their sampling has been impaired and reduced to the process
of periodic sampling with random skips by some interference and noise. Secondly,
