DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

30 DESIGN AND ANALYSIS OF ANALOG FILTERS:
where
and where is the unit impulse response for the ideal highpass response shown
in Figure 2.6, is for the ideal bandpass response, and is for the ideal
bandstop response. Note in (2.8), that if and then (2.8) would be
identical with (2.6), and Figure 2.8 would be identical with Figure 2.6.
A plot of (2.6) is shown in Figure 2.9, where three values of are shown:
and
A plot of (2.7) is shown in Figure 2.10,
where and A plot of (2.8) is shown
in Figure 2.11, for three values of bandwidth (BW), where BW = 200 Hz, 400 Hz,
and 800 Hz. In all three cases, and
i.e. 800, 600 Hz and
Note that the envelope of the plot shown in Figure 2.10 is the same as the plot
for 1 kHz shown in Figure 2.3 except that the vertical scale is times two. For the
values given for and comparing (2.7) to (2.2) shows that they are identical
except for the 2 and the term. This result is a direct application of the
modulation property of Fourier transforms. Note that changing the bandwidth of
Chapter 2 Analog Filter Design and Analysis Concepts