DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

32 DESIGN AND ANALYSIS OF ANALOG FILTERS:
bandpass filter, and illustrates the long, modulated-ringing that can appear in the
impulse response. A realizable filter would be, of course, causal, and would therefore
differ from that illustrated in Figure 2.12, but the plot is representative of what might
be expected.
Such ringing can have very negative effects on the processing of analog
signals. For the example illustrated in Figure 2.12, the only steady-state sine waves
on the filter input that would appear in the filter output would be those with
frequencies between 24,500 Hz and 25,500 Hz . The impulse response of the filter
is a modulated sine wave with a frequency of 25,000 Hz . Any transient on the filter
input, with an appropriate spectral content, could excite the filter to produce some
output at about 25,000 Hz . The question is, how could the remaining processing,
or an engineer by observing the filter output only, distinguish between a sine wave on
the filter input at a frequency at or near 25,000 Hz , and the ringing of the filter?
Or, as a corollary, if a tone burst at 25,000 Hz was applied to the filter, say from a
radar or sonar receiver, how could the end of the tone burst be accurately detected by
observing only the filter output? This example serves to illustrate that the timedomain
response of a filter is an important characteristic that must be considered when
evaluating the appropriateness of a filter design to a particular filter application.
An application where the time-domain response of a filter is of considerable
importance is in the pulse shaping that is applied to digital communications signals
prior to modulating the carrier (Stremler, 1990). The goal is to reduce the bandwidth
as much as possible while not introducing intersymbol interference in the time domain.
A class of such pulse shaping is known as raised-cosine pulse shaping. This class of
filters is studied here to illustrate the trade-off between the sharpness of a filter
Chapter 2 Analog Filter Design and Analysis Concepts