Page 346 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS 333

Fig. 6-24

Then, by Eq. (6.160)

which leads to

Jb + e-]'I= 11 - ae-jnl
or Ib+cosn-jsinRI=Il -acosR+jasinRl
or 1 +b2+ 2bcosR= 1 +a2- 2acosO (6.162)
and we see that if b = -a, Eq. (6.162) holds for all R and Eq. (6.160) is satisfied.

6.40. Let h[n] be the impulse response of an FIR filter so that

h[n] = 0 n<O,nrN
Assume that h[n] is real and let the frequency response H(R) be expressed as

H(I2) = 1 H(fl))e~~(~)

(a) Find the phase response 8(R) when h[n] satisfies the condition [Fig. 6-25(a)]
h[n] =h[N- 1 -n] (6.163)

(b) Find the phase response B(R) when h[n] satisfies the condition [Fig. 6-25(b)]

h[n] = -h[N-1 -n] (6.164)