Question 3-) Consider two discrete signals r1[k] and x2[k]. Let 11[k], 12[k] be periodic signals with periods N,M respectively. Define y[k] = x1[k] + x2[k] . (a) Show that y[k] is periodic with NM. (b) Let Fourier coefficients of x1[k] and r2[k] be ak, bɛ respectively. Find Fourier coeffi- cients ck of y[k] in terms of a and b.
Question 3-) Consider two discrete signals r1[k] and x2[k]. Let 11[k], 12[k] be periodic signals with periods N,M respectively. Define y[k] = x1[k] + x2[k] . (a) Show that y[k] is periodic with NM. (b) Let Fourier coefficients of x1[k] and r2[k] be ak, bɛ respectively. Find Fourier coeffi- cients ck of y[k] in terms of a and b.
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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Consider two discrete signals x1[k] and x2[k]. Let x1[k]; x2[k] be periodic signals with periods N,M respectively. Define y[k] = x1[k] + x2[k].
a) Show that y[k] is periodic with N M.
b) Let Fourier coefficients of x1[k] and x2[k] be ak, bk respectively. Find Fourier coefficients ck of y[k] in terms of ak and bk.
![Question 3-) Consider two discrete signals r1[k] and r2[k]. Let r1[k], x2[k] be periodic
signals with periods N,M respectively. Define y[k] = x1[k] + x2[k] .
(a) Show that y[k] is periodic with NM.
(b) Let Fourier coefficients of x1[k] and r2[k] be ak, bɛ respectively. Find Fourier coeffi-
cients ck of y[k] in terms of a and b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bfa86dd-a2d9-4371-9264-3cbf319a8f92%2F00f2e5d7-902d-4870-b05e-4d6f24c0a96f%2Fquvav6k_processed.png&w=3840&q=75)
Transcribed Image Text:Question 3-) Consider two discrete signals r1[k] and r2[k]. Let r1[k], x2[k] be periodic
signals with periods N,M respectively. Define y[k] = x1[k] + x2[k] .
(a) Show that y[k] is periodic with NM.
(b) Let Fourier coefficients of x1[k] and r2[k] be ak, bɛ respectively. Find Fourier coeffi-
cients ck of y[k] in terms of a and b.
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