Two discrete-time systems are proposed for implementing an ideal low-pass filter with cu...

Two discrete-time systems are proposed for implementing an ideal low-pass filter with cutoff frequency π/4. System is depicted in Figure P7.20(a). System is depicted in Figure P7.20(b). In these figures, corresponds to a zero-insertion system that inserts one zero after every input sample, while corresponds to a decimation system that extracts every second sample of its input.

(a) Does the proposed system correspond to the desired ideal lowpass filter?

(b) Does the proposed system correspond to the desired ideal lowpass filter?