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].