Page 348 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS 335

6.41. Consider a three-point moving-average discrete-time filter described by the difference
equation

(a) Find and sketch the impulse response h[n] of the filter.
(b) Find the frequency response H(IR) of the filter.

(c) Sketch the magnitude response IH(IR)I and the phase response 8(IR) of the filter.
(a) By the definition of h[n] [Eq. (2.30)] we have

Osns2
h[n] =
otherwise
which is sketched in Fig. 6-26(a). Note that h[n] satisfies the condition (6.163) with
N=3.
(b) Taking the Fourier transform of Eq. (6.168), we have

Fig. 6-26