Question: We are interested in implementing a continuous-time LTI lowpass filter H(j?) using the system shown in Fig. when the discrete-time system has frequency response H

We are interested in implementing a continuous-time LTI lowpass filter H(j?) using the system shown in Fig. when the discrete-time system has frequency response H_d(e^j?). The sampling time T = 10^?4 second and the input signal x_c(t) is appropriately bandlimited with X_c(j?) = 0 for |?| ? 2?(5000).

?Let the specifications on |H(j?)| be?

0.99 ? |H_e(j?)| ? 1.01, ? ? ? ? ? ??|?| ? 2?(1000),

|H_e(j?)| ? 0.01, ? ? ? ? ? ? ? ? ? ? ? ?|?| ? 2?(1100).

Determine the corresponding specifications on the discrete-time frequency response H_d(e^j?).

C/D x{n] = x, (n1) *(1)

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