Consider two signals \( x_1(n) = \frac{1}{2} n u(n) \) and \( x_2(n) = \cos(\pi n) u(n) \).(a) Let \( y(n) = x_1(n) * x_2(n) \) be the convolution of \( x_1(n) \) and \( x_2(n) \). 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 \( y_1(n) = y(-n-2) \). Use time shifting and folding properties of Z-transform to sketch the pole-zero plot of \( Y_1(Z) \) and its ROC.(c) Let \( y_2(n) = e^{j \frac{\pi n}{3}} y(n) \). Use scaling property of Z-transform to sketch the pole-zero plot of \( Y_2(Z) \) and its ROC.

Given: x1(n)=12nu(n)x2(n)=cos(πn) u(n) To find: a) y(n)=x1(n)*x2(n) using Z-transform. Sketch pole…

I 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) = ey(n). Use scaling property of Z-transform to sketch the pole-zero plot of Y₂(Z) and its ROC.

I 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) = ey(n). Use scaling property of Z-transform to sketch the pole-zero plot of Y₂(Z) and its ROC.

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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