MATLAB Program for Z-transform and Inverse Z-transform (m file)

In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation.

MATLAB Program: 

clc ;

close all;

syms n;

a=2;

x=a^n;

X=ztrans(x); %finding z transform

disp('z tranform of a^n a>1');

disp(X);

syms n;

a=0.5;

x=a^n;

X1=ztrans(x);

disp('z tranform of a^n 0<a<1');

disp(X1);

syms n;

a=2;

x=1+n;

X2=ztrans(x);

disp('z tranform of 1+n');

disp(X2);

A=iztrans(X);

disp('inverse z tranform of a^n a>1');

disp(A);

B=iztrans(X1);

disp('inverse z tranform of a^n 0<a<1');

disp(B);

C=iztrans(X2);

disp('inverse z tranform of 1+n');

disp(C);

subplot(1,3,1);

zplane([1 0],[1 -2]);

subplot(1,3,2);

zplane([1 0],[1 -1/2]);

subplot(1,3,3);

zplane([1  0 0],[1 -2 1]);

OUTPUT:

z tranform of a^n 0<a<1
z/(z - 1/2)

z tranform of 1+n
z/(z - 1) + z/(z - 1)^2

inverse z tranform of a^n a>1
2^n

inverse z tranform of a^n 0<a<1
(1/2)^n

inverse z tranform of 1+n
n + 1

Figure: