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1. Consider the following signal with length N = 4: 1, n = 1,3, x[n]=2, n=2 |0, n = 0. (a) Let xp[n] be a periodic signal whose one period is x[n]. Plot x[n], xp[n]. Notation difference: in Lecture 16, ro[n] represents one period, and x[n] repre- sents the periodic signal. In Lecture 17 and this problem, x[n] represents one period, and xp[n] represents the periodic signal. (b) Let W = e. Find W" for n = 0,1,...,9 and plot them on the complex plane. (c) Use the DTFT formula for periodic sequences, find X(N) = DTFT[x[n]] and Xp() = DTFT[xp[n]]. (d) Use the DFT formula or the matrix representation to find X[k] = DTF[x[n]], k = 0, 1,2,3. (e) How do you compare X(2), X(N), X[k]?

1. Consider the following signal with length N = 4: 1, n = 1,3, x[n]=2, n=2 |0, n = 0. (a) Let xp[n] be a periodic signal whose one period is x[n]. Plot x[n], xp[n]. Notation difference: in Lecture 16, ro[n] represents one period, and x[n] repre- sents the periodic signal. In Lecture 17 and this problem, x[n] represents one period, and xp[n] represents the periodic signal. (b) Let W = e. Find W" for n = 0,1,...,9 and plot them on the complex plane. (c) Use the DTFT formula for periodic sequences, find X(N) = DTFT[x[n]] and Xp() = DTFT[xp[n]]. (d) Use the DFT formula or the matrix representation to find X[k] = DTF[x[n]], k = 0, 1,2,3. (e) How do you compare X(2), X(N), X[k]?

Introductory Circuit Analysis (13th Edition)
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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1. Consider the following signal with length N = 4: 1, n = 1,3, x[n]=2, n=2 |0, n = 0. (a) Let xp[n] be a periodic signal whose one period is x[n]. Plot x[n], xp[n]. Notation difference: in Lecture 16, ro[n] represents one period, and x[n] repre- sents the periodic signal. In Lecture 17 and this problem, x[n] represents one period, and xp[n] represents the periodic signal. (b) Let W = e. Find W" for n = 0,1,...,9 and plot them on the complex plane. (c) Use the DTFT formula for periodic sequences, find X(N) = DTFT[x[n]] and Xp() = DTFT[xp[n]]. (d) Use the DFT formula or the matrix representation to find X[k] = DTF[x[n]], k = 0, 1,2,3. (e) How do you compare X(2), X(N), X[k]?
Transcribed Image Text:1. Consider the following signal with length N = 4: 1, n = 1,3, x[n]=2, n=2 |0, n = 0. (a) Let xp[n] be a periodic signal whose one period is x[n]. Plot x[n], xp[n]. Notation difference: in Lecture 16, ro[n] represents one period, and x[n] repre- sents the periodic signal. In Lecture 17 and this problem, x[n] represents one period, and xp[n] represents the periodic signal. (b) Let W = e. Find W" for n = 0,1,...,9 and plot them on the complex plane. (c) Use the DTFT formula for periodic sequences, find X(N) = DTFT[x[n]] and Xp() = DTFT[xp[n]]. (d) Use the DFT formula or the matrix representation to find X[k] = DTF[x[n]], k = 0, 1,2,3. (e) How do you compare X(2), X(N), X[k]?
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