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

Worked Examples

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

WORKED EXAMPLES

(1) Find the Z-transform and region of convergence of

Hence Z [u (n)] is convergent if z lies between the annulus as shown shaded in figure. Hence, ROC is 2 <z < 4.

(2) Find the Z-transform and region of convergence of

u (n) = ⁿC_k, n ≥k

This series is convergence for | 1/z | < 1 i.e., for z> 1.

Hence ROC is ❘z❘> 1.

(3) Find Z-1 {(z − 5)⁻³] when ❘z❘ > 5. Determine the region of convergence.

Solution :

The region of convergence is the exterior of the circle |z❘ = 5 i.e., with centre at origin and of radius 5.

(4) Find the Z-transform and the radius of convergence of u (n) = 2ⁿ, n < 0

Solution :

Let u (n) = 0 for n ≥ 0 we have

(5) Find the Z-transform and the radius of convergence of

Solution :

The above series is convergent for all values of z.

Hence, ROC is the entire z-plane.

Transforms And Partial Differential Equations: UNIT V: Z - Transforms And Difference Equations : Tag: : - Worked Examples

Home | Department: Mech Department | Subject: Transforms and Partial Differential Equations |

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

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

Under Subject

Transforms and Partial Differential Equations

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