Answered: An x(t) signal with X(jw) whose Fourier…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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An x(t) signal with X(jw) whose Fourier transform is given in Figure 1 is converted into a discrete-time signal by sampling using the blocks in Figure 2, and then diluted and converted back to a continuous-time signal. It is given as WL= (20). The frequency of the p(t) impulse train is 6 times the Nyquist speed; The frequency of the p[n] impulse train is 2, and the frequency of the impulse train used in the conversion from xb[n] to y_p(t) is the same as p(t). According to this;

a) Draw the graphs X(jw), X_p(jw), X(e^jw), X_p(e^jw) , X_b(e^jw), Y_p(jw), and Y(jw).

b) Are y(t) and x(t) the same signals. If x(t) and y(t) are not the same signals, what is the relationship between them?

c) Also, if x(t) and y(t) are different, what kind of change is made in the flow in Figure 2, so y(t)=x(t) is achieved?

X(jw)
-WL
WL
Figure - 1
P(t)
p[n]
Converting impulse
x(t)
x,(t) train to discrete
x[n]
(X)
Xp[n]
dilution by 2
time series
Figure - 2
Xp[n]
with Ws/2 cutoff
frequency
low pass filter
discrete time series
impulse train
y(t)
Yp(t)
conversion

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