A system that processes analog signals digitally (as in Fig. 6.21a) is designed to act as an ideal lowpass filter with 20-kHz cutoff frequency. Assuming the input is bandlimited to 60 kHz and no...

A system that processes analog signals digitally (as in Fig. 6.21a) is designed to act as an ideal lowpass filter with 20-kHz cutoff frequency. Assuming the input is bandlimited to 60 kHz and no anti-aliasing filter is used at the input, find the smallest sampling frequency that allows this system to function properly as a 20-kHz lowpass filter.

Designating the system sampling interval as T , consider two inputs x1(t) = u(t) − u(t−T /2) and x2(t) = x₁(t−T /4). Sketch signals and the corresponding spectra at (a) the input of the C/D converter, (b) the input of H(Ω), (c) the output of H(Ω), and (d) the output of the D/C converter. Because the input x2(t) is just a delayed version of signal x₁(t), is the system response to x₂(t) just a delayed version of the response to x₁(t)? Explain your answer with reasons.