Page 349 - Schaum's Outline of Theory and Problems of Signals and Systems
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FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS [CHAP. 6
By Eq. (1.90), with a = e-jR, we get
1 1 - e-i3fi 1 e-i3fi/2(ej3R/2 -, -j3R/2 1
H(R) = - = -
3 ~-~-jn e-iR/2(ejR/2-e-i~/2 )
3
where
when Hr(R) > 0
and e(n) =
when Hr(R) < 0
which are sketched in Fig. 6-26(b). We see that the system is a low-pass FIR filter with
linear phase.
6.42. Consider a causal discrete-time FIR filter described by the impulse response
h[n] = {2,2, - 2, - 2)
(a) Sketch the impulse response h[n] of the filter.
(b) Find the frequency response H(R) of the filter.
(c) Sketch the magnitude response I H(R)I and the phase response 8(R) of the filter.
(a) The impulse response h[n] is sketched in Fig. 6-27(a). Note that h[n] satisfies the
condition (6.164) with N = 4.
(b) By definition (6.27)
where
I ( 1
("z")i
IH(R)l= IHr(R)l = sln - + sin -
which are sketched in Fig. 6-27(b). We see that the system is a bandpass FIR filter with
linear phase.
