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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" 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 c

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" 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 c

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
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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 \( y_{ZS}[n] = [c_1 (-0.2)^n + c_2 (0.8)^n + c_3 (0.4)^n u[n] \). We have \( c_1 = \underline{\hspace{1cm}} \).
Transcribed Image Text: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 \( y_{ZS}[n] = [c_1 (-0.2)^n + c_2 (0.8)^n + c_3 (0.4)^n u[n] \). We have \( c_1 = \underline{\hspace{1cm}} \).
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