Consider the discrete-time system shown in Figure P4.40-1. (a) Assu...

Consider the discrete-time system shown in Figure P4.40-1.

(a) Assume that M = 2 and that X(e^jω), the DTFT of x[n], is real and is as shown in Figure P4.40-2. Make an appropriately labeled sketch of Xe(e^jω), Ye(e^jω), and Y(e^jω), the DTFTs of x_e[n], y_e[n], and y[n], respectively. Be sure to clearly label salient amplitudes and frequencies.

(b) For M = 2 and X(e^jω) as given in Figure P4.40-2, find the value of

(c) For M = 2, the overall system is LTI. Determine and sketch the magnitude of the frequency response of the overall system |H_eff(e^jω)|.

(d) For M = 6, the overall system is still LTI. Determine and sketch the magnitude of the overall system’s frequency response |H_eff(e^jω)|.