Digital Signal Processing Reference
In-Depth Information
Figure 15.11
Cumulative sums for various locations of frequencies
f
0
with respect to the
central filter frequency
f
a
in the case where the difference between them is relatively small
Some typical cumulative sums obtained under specific conditions are shown in
Figure 15.12.
The given examples show typical cumulative sums for the case of a single
tone signal. The signal structure that might be expected in reality is of course
much more complicated. Nevertheless, much can be learnt from observations of
this kind of typical cumulative sum. First of all, the cumulative sum for a signal
component at a frequency equal to the frequency to which the respective DFT
filter is tuned graphically looks like a linearly increasing function. Therefore the
presence of a linearly increasing component in a cumulative sum is evidence that
the signal contains a component at the frequency of DFT filtering. This fact has
been used before in Chapter 8 to demonstrate the alias compensation effect.
However, in general the analysis of these cumulative sums might prove not
to be so simple. Apparently it has to cover cases where signals are composed
