schaum's outlines of signals and systems

Page 344

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)


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