Impact-Site-Verification: dbe48ff9-4514-40fe-8cc0-70131430799e

## Search This Blog

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: