333
CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS
Fig. 6-24
Then, by Eq. (6.160)
which leads to J b+ e-]'I= 11 - ae-jnl
or or
Ib+cosn-jsinRI=Il -acosR+jasinRl 1 + b 2 + 2bcosR= 1 + a 2 - 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 ( I 2 ) = 1H ( f l ) ) 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)