Find x(k) by using z-transform -x(k)-3x(k-1) + 2x(k − 2) = e(k), e(k)=[1, k = 0, 10, k ≥2x(-2) = x(-1)=0

Given Equation:Here, The objective is to use transform to solve the difference equation.Concept…

Answered: x(k)-3x(k-1)+2x(k-2)= e(k), e(k)= [1, k…

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x(k)-3x(k-1)+2x(k-2)= e(k), e(k)= [1, k = 0, 1 0, k ≥ 2 x(-2) = x(-1) = 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.1: Polynomial Functions Of Degree Greater Than

Problem 11E

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Question

Find x(k) by using z-transform

-
x(k)-3x(k-1) + 2x(k − 2) = e(k), e(k)=
[1, k = 0, 1
0, k ≥2
x(-2) = x(-1)=0

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Step 1: Analysis and Introduction

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Step 2: Apply Z-transform on both side of the equations and simplify.

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Step 3: Split the right side term using partial fraction

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Step 4: Apply inverse z-transform to find the value of x(k)

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Solution

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Follow-up Questions

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Follow-up Question

How should x(-2) = x(-1) = 0 be used in the question. And it contradicts the expression obtained for x(k)

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