Page 347 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS [CHAP. 6

N even

N- I
n

I
I N odd
I a
I
I
- I -
w b
0 N n

t

Fig. 6-25

(a) Taking the Fourier transform of Eq. (6.163) and using Eqs. (6.431, (6.461, and (6.62). we
obtain
H(R) = H*(R) e-j(N-')R

or IH(f))le1flfl) = )H(n)(e-io(~~e-~(N-I)n
Thus,
e(n) = -e(n) - (N- i)n
and e(n) = - +(N - 1 ) ~
which indicates that the phase response is linear.
(b) Similarly, taking the Fourier transform of Eq. (6.164, we get
=
~(n) -H*(R) e-~("-')fl
or IH(fl)lei0(n), IH(n)(e~ne-l@(fl)e-~(N-l)fl
Thus,
e(n) =T-qn) -(N-ip

and

which indicates that the phase response is also linear.