Answered: Problem 4 Consider a continuous-time…

Problem 4 Consider a continuous-time LTI system whose frequency response H(jw) is shown graphically below. H(jw) 1 4 4 4 If the input to this system is the periodic signal given by 0, -4

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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Question

Problem 4
Consider a continuous-time LTI system whose frequency response H(jw) is shown
graphically below.
H(jw)
1
4
|
4
If the input to this system is the periodic signal given by
0, -4 <t < -1
r(t) = {1, -1<t<1
1<t<4
with period T = 8,
(a) sketch r(t) for -4 <t< 4,
(b) determine the Fourier series coefficients ap of r(t),
(c) determine the Fourier series coefficients b, of the corresponding output y(t). A finite
number of them are not zero. What are they? You are asked to find the non zero
exponential Fourier series coefficients of y(t)
(d) Since the non-zero Fourier series coefficients of y(t) are finite, y(t) is a sum of finite
number of sinusoids. Express y(t) as sum of cosine functions.
3.

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