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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


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