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Consider two signals x₁(n) = nu(n) and x₂ (n) = cos(n)u(n). (a) Let y(n) = x₁(n) * x2 (n) be the convolution of x₁(n) and x2 (n). Use Z-transform to find y(n). Sketch the pole-zero plot of Y(Z) and its ROC. Is y(n) a bounded signal? (b) Let y₁ (n) = y(-n-2). Use time shifting and folding properties of Z-transform to sketch the pole-zero plot of Y₁(Z) and its ROC. (c) Let y2(n) = e¹y(n). Use scaling property of Z-transform to sketch the pole-zero plot of Y₂(Z) and its ROC.

Consider two signals x₁(n) = nu(n) and x₂ (n) = cos(n)u(n). (a) Let y(n) = x₁(n) * x2 (n) be the convolution of x₁(n) and x2 (n). Use Z-transform to find y(n). Sketch the pole-zero plot of Y(Z) and its ROC. Is y(n) a bounded signal? (b) Let y₁ (n) = y(-n-2). Use time shifting and folding properties of Z-transform to sketch the pole-zero plot of Y₁(Z) and its ROC. (c) Let y2(n) = e¹y(n). Use scaling property of Z-transform to sketch the pole-zero plot of Y₂(Z) and its ROC.

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 two signals x₁(n) = nu(n) and x₂ (n) = cos(πn)u(n). (a) Let y(n) = x₁(n) * x₂(n) be the convolution of x₁(n) and x2 (n). Use Z-transform to find y(n). Sketch the pole-zero plot of Y(Z) and its ROC. Is y(n) a bounded signal? (b) Let y₁(n) = y(n − 2). Use time shifting and folding properties of Z-transform to sketch the pole-zero plot of Y₁(Z) and its ROC. (c) Let y₂ (n) = ey(n). Use scaling property of Z-transform to sketch the pole-zero plot of Y₂(Z) and its ROC.
Transcribed Image Text:Consider two signals x₁(n) = nu(n) and x₂ (n) = cos(πn)u(n). (a) Let y(n) = x₁(n) * x₂(n) be the convolution of x₁(n) and x2 (n). Use Z-transform to find y(n). Sketch the pole-zero plot of Y(Z) and its ROC. Is y(n) a bounded signal? (b) Let y₁(n) = y(n − 2). Use time shifting and folding properties of Z-transform to sketch the pole-zero plot of Y₁(Z) and its ROC. (c) Let y₂ (n) = ey(n). Use scaling property of Z-transform to sketch the pole-zero plot of Y₂(Z) and its ROC.
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