Digital Signal Processing Reference
In-Depth Information
Figure 1.2
Overlapping of a periodically sampled signal component and its possible aliases
To ensure that a digital signal can provide the correct original analog signal,
the bandwidth of the signal should not exceed half of the sampling frequency.
If all spectral components outside the limited frequency band are filtered off
the original signal or more signal sample values are taken within the same time
interval, there would be no uncertainty. Either one of these possible actions impose
limitations on the bandwidth of the signal, which could be sampled at the given
sampling frequency without corruptions due to aliasing. Apparently, if some other
way could be found to avoid aliasing, a special application of oriented digital
processing of signals would be possible in a much broader frequency range.
That would open up a broad area of new beneficial digital signal processing
applications.
However, it is not clear whether sampling that is not corrupted by aliasing is
feasible at all. In an attempt to find an alternative approach to realization of this
operation, look at the diagrams of Figure 1.2 again. Notice that the time intervals
between the taken signal sample values are of equal length. Now try to vary these
intervals. The sample values of all indicated sinusoidal curves become different,
even at small changes in distances between them. That clearly is interesting as
it means that taking signal sample values irregularly disturbs the aliasing phe-
nomenon.
To see, in a more detailed way, the consequences of this fact look at
Figure 1.3. The signal shown (solid line) is the same one as given in Figure 1.2. The
lower frequency sine function is again sampled and the corresponding data set is
