Page 239 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS [CHAP. 5

(c) (4
Fig. 5-5 Magnitude responses of ideal frequency-selective filters.

3. Ideal Bandpass Filter:
An ideal bandpass filter (BPF) is specified by

0, < lwl < 02
IH(w)l=
otherwise
which is shown in Fig. 5-5(c).

4. Ideal Bandstop Filter:
An ideal bandstop filter (BSF) is specified by

0 0, < 101 < w2
H(w)1=
otherwise

which is shown in Fig. 5-5(d).
In the above discussion, we said nothing regarding the phase response of the filters. To
avoid phase distortion in the filtering process, a filter should have a linear phase
characteristic over the pass band of the filter, that is [Eq. (5.82b11,

where t, is a constant.
Note that all ideal frequency-selective filters are noncausal systems.