Answered: The input-output relationship of a…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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The input-output relationship of a discrete-time LTI system is given as follows
?[n] = 2x[n − 4] − 3x[n − 6].
a) Determine the impulse response of the system, h[n].
b) Using h[n], show that the system is causal.
c) Using h[n], show that whether the system is BIBO stable or not.
d) Determine the transfer function H(z). Plot pole-zero diagram. Indicate ROC.
e) Using H(z), show that whether the system is stable or not.
f) Determine the frequency response of the system, if exists. Why?
g) Determine the impulse response of the inverse system calculated in f).

An analog signal is given as
x(t) = 5 + 2 cos(20tt) + 3cos(400nt)
a) What is the bandwidth of x (t)? Determine the Nyquist sampling frequency for x(t), both in
radian/sec (@s), and in Hz (F;).
b) Formulate X,(jw), the signal sampled with the Nyquist frequency.
c) Plot frequency spectrum of the sampled signal, X,(jw).
d) Determine the filter to reconstruct the signal x(t).
e) Is it possible to reconstruct the signal x(t) for T; = 0.004 [s]? State that if aliasing error occurs or
not.

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