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d) Find the y(n) that corresponds to Y(w). Is y(n) periodic? Is y(n) causal? e) What is the convolution of w(n) = x(n)*y(n)? (Hint: work with DTFTs)

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
Given is one period of DTFT function X(w) and Y(w) for lw|≤ π
X(w) =
1,
(0,
TL
|w|≤:
32
elsewhere between-,
72 T
1/2, Slwls +64
r(w) = {1/2,
0,
7
TL
2 64
elsewhere between-,

d) Find the y(n) that corresponds to Y(w). Is y(n) periodic? Is y(n) causal?
e) What is the convolution of w(n) = x(n)*y(n) ? (Hint: work with DTFTs)
Hint: using the modulation property of the DTFT for evaluating y(n) and Y(w) may be much simpler.

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circuits 35 36