Transforms And Partial Differential Equations: UNIT V: Z - Transforms And Difference Equations

Inverse Z-Transform

Methods

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Transforms And Partial Differential Equations: UNIT V: Z - Transforms And Difference Equations: Methods

INVERSE Z-TRANSFORM

Def. Inverse Z-transform

If Z[x(n)] = X(z) then Z -1[X (2)] = [x (n)]

Z-1[X (2)] can be found out by any one of the following methods.

 

(METHOD I). PARTIAL FRACTIONS METHOD

X. Problems based on Inverse Z-transform

Find the inverse Z-transform of


 

1. Find Z-1 [10z (z-1) (z-2)]


 




 






 




(Method : II). Inverse of Z-transform by Inverse integral method. (Cauchy's residue theorem)

From the relation between the Z-transform and Fourier transform of a sequence we get


i.e., x(n) Sum of the residues of X(z) 2-1 at the isolated singularities.

Note: Take the contour C such that all the poles of the function X(z) zn-1 lie within the contour.


Find the inverse Z-transform of















 


 

Transforms And Partial Differential Equations: UNIT V: Z - Transforms And Difference Equations : Tag: : Methods - Inverse Z-Transform

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Related Topics


Introduction

Problems based on Z-transform of some basic functions - Examples

Inverse Z-Transform - Methods

Convolution Theorem - Definition

Formation Of Difference Equations

Solution Of Difference Equations Using Z-transform

Exercise - Solution of difference equations using Z-transform.

Miscellaneous Problems

Convergence Of Z-Transforms

Worked Examples

Exercise - Convergence Of Z-Transforms

Questions And Answers

Related Subjects


Transforms and Partial Differential Equations

Transforms and Partial Differential Equations

MA3351 3rd semester civil, Mechanical Dept | 2021 Regulation | 3rd Semester Mechanical Dept 2021 Regulation