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Consider X[k] be the N-point DFT of an N-point sequence x[n]. x₁ [n] = {1, -2, 1, -3} ↑ x₂ [n] = {0, 2, -1,0,0,4} ↑ (a) Determine the linear convolution_x₁[n] * x₂ [n] (b) Determine the circular convolution x₁ [n] x₂ [n] (Please note that to perform circular convolution on two sequences with different lengths, the shorter sequence needs to be zero-padded to match the length of the longer sequence.) (c) Determine the smallest value of N so that N-point circular convolution is equal to the linear convolution.

Consider X[k] be the N-point DFT of an N-point sequence x[n]. x₁ [n] = {1, -2, 1, -3} ↑ x₂ [n] = {0, 2, -1,0,0,4} ↑ (a) Determine the linear convolution_x₁[n] * x₂ [n] (b) Determine the circular convolution x₁ [n] x₂ [n] (Please note that to perform circular convolution on two sequences with different lengths, the shorter sequence needs to be zero-padded to match the length of the longer sequence.) (c) Determine the smallest value of N so that N-point circular convolution is equal to the linear convolution.

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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Consider X[k] be the N-point DFT of an N-point sequence x[n]. x₁ [n] = {1, 2, 1, -3} ↑ x₂ [n] = {0,2,-1,0,0,4} ↑ (a) Determine the linear convolution_x₁[n] * x₂[n] (b) Determine the circular convolution x₁ [n] x₂ [n] (Please note that to perform circular convolution on two sequences with different lengths, the shorter sequence needs to be zero-padded to match the length of the longer sequence.) (c) Determine the smallest value of N so that N-point circular convolution is equal to the linear convolution.
Transcribed Image Text:Consider X[k] be the N-point DFT of an N-point sequence x[n]. x₁ [n] = {1, 2, 1, -3} ↑ x₂ [n] = {0,2,-1,0,0,4} ↑ (a) Determine the linear convolution_x₁[n] * x₂[n] (b) Determine the circular convolution x₁ [n] x₂ [n] (Please note that to perform circular convolution on two sequences with different lengths, the shorter sequence needs to be zero-padded to match the length of the longer sequence.) (c) Determine the smallest value of N so that N-point circular convolution is equal to the linear convolution.
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