3. Consider a continuous-time system represented by a delayed low- pass filter defined by the Laplace transform of the unit impulse response He(s) The input signal x (t) is sampled in

discrete time and then processed by a discrete-time system represented by the frequency response H (e) as shown in the following figure. x(1) (e) (a) (c) C/D system. T Sice #d s+ Sc Discrete-time system y[n] Compute the unit impulse response he (t) of the continuous-time (b) Compute the unit impulse response h[n] of the discrete-time system by the impulse variance method for ta = 27. D/C ↑ T y, (t) Compute the Fourier transform H (e) for h[n]. Obtain the magnitude and phase expressions. (d) Suppose xc (t) = 2 cos 15t +0.2 sin 30t. The signal is sam- pled with a sampling period T = 100 sec. Determine the discrete-time sampled signal x[n]. Justify your answer. The cutoff frequency of the low-pass filter is 2 = 207 rad/sec. Compute the output signal y [n].