Page 340 - Schaum's Outline of Theory and Problems of Signals and Systems

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

Thus,

Taking the inverse Fourier transform of H(R), we obtain

(c) From Eq.(6.137)

Then

Taking the inverse Fourier transform of Y(R) and using Eq. (6.1351, we get

6.33. Consider a discrete-time LTI system with impulse response

Find the output y[n] if the input x[n] is a periodic sequence with fundamental period
No = 5 as shown in Fig. 6-17.
From Eq. (6.134) we have

Since R, = 27r/NO = 2~/5 and the filter passes only frequencies in the range lRl I 7r/4, only
the dc term is passed through. From Fig. 6-17 and Eq. (6.11)