Digital Signal Processing Reference
In-Depth Information
Use of periodic sampling under the same conditions would result in taking many
more sample values at a sampling rate about 30 times higher. Apparently the
excessive sample values would not add information in this particular case. They
would serve only to resolve the uncertainty caused by overlapping signal spectral
components. The additional sample values would also help to reduce the impact
of noise present in the signal.
This leads to the conclusion that using nonuniform sampling based anti-aliasing
techniques is quite beneficial under the given conditions. Nonuniform sampling
makes it possible to compress data significantly, so much simpler electronic cir-
cuitry is needed to complete the task. Just imagine how much more complicated
the hardware would need to be in order to execute the periodic sampling operation
at the required frequency of 2.370 GHz and to perform vector spectrum analysis
of the extremely wideband digital signal.
Therefore, as the example suggests, avoiding aliasing in some other way not
based on the use of high-frequency sampling should lead to a reduction in the
requirements for the mean sampling rate and to other related benefits. In other
words, the introduction of such sparse sampling should result in lifting the fre-
quency limit to some higher level and in widening the digital domain in the
direction of higher frequencies. In addition, the application of sparse sampling
might also be good from other points of view. For instance, if a particular task for
signal processing could be resolved by processing fewer signal sample values,
data compression would take place, and that is always beneficial.
Application of sparse sampling (or undersampling) makes sense if the condi-
tions are right. However, it has to be kept in mind that this sparse sampling is also
necessarily nonuniform as only this kind of sampling would lead to suppression
of aliasing. Consequently, processing digital signals obtained as a result of this
kind of sampling has to be carried out in a special way that is suitable for handling
nonuniformly sampled signals, which is a significantly more difficult task than
processing periodically sampled signals.
Of course, there are also application limitations for nonuniform sparse sam-
pling, but they differ from the limitations characterizing application conditions
for periodic sampling. In the case of nonuniform sampling, the limitations on the
lowest sampling rate are imposed by signal parameter variation dynamics rather
than by the upper frequency of their spectra. This changes the attitude to establish-
ing the required parameters for used sampling drivers. The signal nonstationarity
issue becomes the primary consideration and analysis of the expected signal be-
haviour has to be carried out to determine the requirements for the designs of the
sampling driver including the required mean sampling rate.
