A causal LTID system is characterized by the following difference equation: y[n] - y[n-1] + 0.16 y[n-2] = x[n] (a). Determine the system function H(z). (b). Is the system stable? Justify your answer based on H(z). (c). Plot the locations of zeroes and poles of the system on the Z plane. (d). Roughly draw the magnitude response, |H(e^iQL, of the system based upon the locations of zeros and poles of the system plotted in (c). (e). Realize the system using the DFII form. (f). Determine the impulse response h[n] for the LTID system. Also, if x[n] = (1/4)^n u[n], what is the zero-state response for the input x[n]? (g). If x[n] = cos(rın+r/3), what is the output for the input x[n]?

A causal LTID system is characterized by the following difference equation: y[n] - y[n-1] + 0.16 y[n-2] = x[n] (a). Determine the system function H(z). (b). Is the system stable? Justify your answer based on H(z). (c). Plot the locations of zeroes and poles of the system on the Z plane. (d). Roughly draw the magnitude response, |H(e^iQL, of the system based upon the locations of zeros and poles of the system plotted in (c). (e). Realize the system using the DFII form. (f). Determine the impulse response h[n] for the LTID system. Also, if x[n] = (1/4)^n u[n], what is the zero-state response for the input x[n]? (g). If x[n] = cos(rın+r/3), what is the output for the input x[n]?

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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