Digital Signal Processing Reference
In-Depth Information
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Figure 17.10. Zoomed in raised cosine impulse response.
Table 17.3
summarizes the raised cosine response shown in
Figure 17.8
for different roll off factors. These labels are also used
in
Figures 17.9 and 17.10
.
In
Figure 17.8
the frequency response of the raised cosine filter
is shown. To better see the passband shape, it is plotted linearly,
rather than logarithmically (dB). It has a cutoff frequency of
500 kHz, the same as our ideal low-pass filter. A raised cosine
filter response is wider than the ideal low-pass filter, due to the
transition band. This excess frequency bandwidth is controlled by
a parameter called the “roll off” factor. The frequency response is
plotted for several different roll off factors. As the roll off factor
gets closer to zero, the transition becomes steeper, and the filter
approaches the ideal low-pass filter.
The impulse response of the raised cosine filter is portrayed
in
Figure 17.9
, which shows the filter impulse response, and
Figure 17.10
zooms in to better show the lobes of the filter
impulse. Again, it is plotted for several different roll off factors. It
is similar to the sinc impulse response in that it has zero
crossings at time intervals of T (as this is shown in sample
domain, rather than time domain, it is not readily apparent from
the diagram).
