## Program for Computing Inverse Z-Transform

**AIM:**To develop a program for Computing Inverse Z-Transform

**EQUIPMENTS:**MATLAB 7.5

**Learning Objectives:**To make the students familiar with concept of inverse Z-transform

with the use of MATLAB.

**THEORY:**

Description: In mathematics and signal processing, the Z-transform converts a discrete

time-domain signal, which is a sequence of real or complex numbers, into a complex frequency domain

representation. The Z-transform, like many other integral transforms, can be defined as

either a one-sided or two-sided transform.

The bilateral or two-sided Z-transform of a discrete-time signal x[n] is the function X(z)

defined as

In signal processing, this definition is used when the signal is causal.

Rational Z-transform to partial fraction form:

Consider the transfer function in the rational form i-e;

18z3

G(z)= ------------------------

18z3+3z2-4z-1

We can evaluate the partial fraction form of the above system using matlab command. The

partial fraction form be,

G(z)= 0.36 + __0.24__ + _0.4

-------------- ------------ ---------------

1 – 0.5z-1 1+0.33 z-1 (1+0.33 z-1)

Matlab command that converts rational z-transform in to partial fraction form is

**‘residuez’**.

If you want to see the poles and zeros in a z-plane. This function displays the poles and zeros

of discrete-time systems. Use the under given matlab command

**zplane(b,a)**

ALGORITHM:

1. Write the poles and zeros of the input sequence.

2. Returned vector R contains the residues, Column vector contains P contains the pole locations. And row vector contains the direct terms.

Input Sequence:

PROGRAM CODE:

%program to perform Inverse Z-Transform

b=[1,0.4*sqrt(2)];

a=[1,-0.8*sqrt(2),0.64];

[R,P,C]=residuez(b,a);

R

P

C

Zplane(b,a);

**Result**

## comments (0)