Consider the discrete-time system shown in Figure P4.32-1 where (i) L and M are...

Consider the discrete-time system shown in Figure P4.32-1

where (i) L and M are positive integers.

(a) Assume that L = 2 and M = 4, and that X(e^jω), the DTFT of x[n], is real and is as shown in Figure P4.32-2. Make an appropriately labeled sketch of Xe(e^jω), Ye(e^jω), and Y(e^jω), the DTFTs of xe[n], ye[n], and y[n], respectively. Be sure to clearly label salient amplitudes and frequencies.

(b) Now assume L = 2 and M = 8. Determine y[n] in this case. Hint: See which diagrams in your answer to part (a) change.