9:59 AM Program for Computing Inverse ZTransform  
AIM: To develop a program for Computing Inverse ZTransform
EQUIPMENTS: MATLAB 7.5
Learning Objectives: To make the students familiar with concept of inverse Ztransform
with the use of MATLAB.
THEORY:
Description: In mathematics and signal processing, the Ztransform converts a discrete
timedomain signal, which is a sequence of real or complex numbers, into a complex frequency domain
representation. The Ztransform, like many other integral transforms, can be defined as
either a onesided or twosided transform.
The bilateral or twosided Ztransform of a discretetime signal x[n] is the function X(z)
defined as
In signal processing, this definition is used when the signal is causal.
Rational Ztransform to partial fraction form:
Consider the transfer function in the rational form ie;
18z3
G(z)= 
18z3+3z24z1
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 – 0.5z1 1+0.33 z1 (1+0.33 z1)
Matlab command that converts rational ztransform in to partial fraction form is
‘residuez’.
If you want to see the poles and zeros in a zplane. This function displays the poles and zeros
of discretetime 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 ZTransform
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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