Consider the system shown in Figure for discrete-time processing of the continuous-time input signal g_c(t). The input signal g_c(t) is of the form g_c(t) = f_c(t) + e_c(t).where the Fourier transforms of f_c(t) and e_c(t) are shown in Figure. Since the input signal is not bandlimited, a continuous-time anti aliasing filter H_aa(j?) is used. The magnitude of the frequency response for H_aa(j?) is shown in Figure, and the phase resonse of the anti aliasing filter is aa(j?) = ??³.

(a) If the sampling rate is 2? / T 1600?, determine the magnitude and phase of H(e^j?), the frequency response of the discrete-time system, so that the output is y_c(t) = f_c(t).

(b) Is it possible that yc(t) = f_c(t) if 2? / T j?) for this choice of 2? / T.

-=-Q-8-Q- D-T LTI C-T LTI D/C system Haa (jn) C/D system H(e) g, () x, (1) x(n] y. (1) E, (j1) F,(0) B 400 -4007 4007 400T |. u2)| -800m -400T 400T 8007