Answered: Given a discrete-time linear time…

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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Question

Given a discrete-time linear time invariant system with input x[n] and output y[n] being related by y[n + 2] - 0.6y[n + 1] - 0.16y[n] = 5x[n + 2] the input x[n] = 0.4 ^ n * u[n] and the initial conditions are y[- 1] = 10, y[- 2] = 0 The zero state response is yzs [n] = [c1 (−0.2)" + c₂ (0.8)" + c3(0.4)"]u[n]. We have C₁ =, C2=, C3= ?

Expert Solution

Step 1: Summarize the details given:

Given Data:

A discrete-time linear, time-invariant system with,

Difference equation $y left square bracket n space plus space 2 right square bracket space minus space 0.6 y left square bracket n space plus space 1 right square bracket space minus space 0.16 y left square bracket n right square bracket space equals space 5 x left square bracket n space plus space 2 right square bracket$
Input $x open square brackets n close square brackets equals 0.4 to the power of n u left square bracket n right square bracket$
Zero state response $space y subscript z s end subscript left square bracket n right square bracket space equals space left square bracket c subscript 1 space left parenthesis negative 0.2 right parenthesis to the power of n plus c subscript 2 left parenthesis 0.8 right parenthesis to the power of n plus space c subscript 3 left parenthesis 0.4 right parenthesis to the power of n right square bracket u left square bracket n right square bracket$

To Find out:

The values of $open parentheses c subscript 1 comma space c subscript 1 comma space c subscript 3 close parentheses$ .

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