The overall system of Figure is a discrete-time linear time-invariant system with frequency response H(ej?) and impulse response h[n].

(a) H(e^j?) can be expressed in the form?

H(e^j?) = A(e^j?)e^j?(?),

with A(e^j?) real. Determine and sketch A(e^j?) and ?(?) for |?|

(b) Sketch h[n] for the following:

(i) ? = 3

(ii) ? = 3 ??

(iii) ? = 3 ?

(c) Consider a discrete-time linear time-invariant system for which?

H(e^j?) = A(e^j?)e^ja?, ? ? ?|?|

?with A(e^j?) real. What can be said about the symmetry of h[n] for the following?

(i) ? = integer?

(ii) ? = M/2, where M is an odd integer?

(iii) General ? ??

Transcribed Image Text:

x(()Delay C/D D/C y[n] y(() = x,(t-aT) aT (n]