Consider the system shown in Figure. The input to this system is the bandlimited signal whose Fourier transform is shown in Figure with ?_0?= ? / T. The discrete-time LTI system in Figure has the frequency response shown in Figure.

(a) Sketch the Fourier transforms X(e^j?), X_e(e^j?), y_e(e ^j?), and y_c(j?).

(b) For the general case when X_c(j?). = 0 for |?| ? ? / T, express y_c(j?) in terms of X_c(j?). Also, give a general expression for y_c(t) in terms of x_c(t) when x_c(t) is bandlimited in this manner.

Transcribed Image Text:

Ideal C/D Ideal 1 4 *In] H(e) D/C *, (1) x n] yIn] y(t) T = T/4 H(e") 3т Зт TT 4