Let x[n] = e³, for n = 0,1,...,5 and x[n] = 0 otherwise. (a) Find the length N of the signal x[n]. (b) Using the DFT formula, find the DFT X[k], k = 0,1,..., N-1. Hint: use the important geometric sum from Lecture 17. (c) From X[k] in Part (b), find x[n] using the inverse DFT formula.
Let x[n] = e³, for n = 0,1,...,5 and x[n] = 0 otherwise. (a) Find the length N of the signal x[n]. (b) Using the DFT formula, find the DFT X[k], k = 0,1,..., N-1. Hint: use the important geometric sum from Lecture 17. (c) From X[k] in Part (b), find x[n] using the inverse DFT formula.
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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![Let x[n] = e³, for n = 0,1,...,5 and x[n] = 0 otherwise.
(a) Find the length N of the signal x[n].
(b) Using the DFT formula, find the DFT X[k], k = 0,1,..., N-1. Hint: use the
important geometric sum from Lecture 17.
(c) From X[k] in Part (b), find x[n] using the inverse DFT formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e474a39-969f-407e-9a2c-2532ad775665%2F7bea3af6-2a4c-480d-bd17-7ef5894225f8%2Fyi9uwpi_processed.png&w=3840&q=75)
Transcribed Image Text:Let x[n] = e³, for n = 0,1,...,5 and x[n] = 0 otherwise.
(a) Find the length N of the signal x[n].
(b) Using the DFT formula, find the DFT X[k], k = 0,1,..., N-1. Hint: use the
important geometric sum from Lecture 17.
(c) From X[k] in Part (b), find x[n] using the inverse DFT formula.
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