How to matlab z-transform of x(n)=((4/3)^n) u(1-n)

How to matlab z-transform of x(n)=((4/3)^n) u(1-n) by using symbolic math toolbox

[Dimitris Kalogiros]

x(n) seams to be a non-causal signal. It's values are zeros for n>1 and they are not, for n=<1...

Are sure you have formulated your question without any typo ?

[John Bravo]

yes its from here

Answer 1

[Dimitris Kalogiros]

Symbolic math toolbox, calculates only unilateral z transform. So, we have to use some properties in order to calculate what you ask. Because, you ask a bilateral z-transform

First, I will break your time-series into two parts : one for -inf<n<=0 and the other for 0<n<2.

Then, in order to calculate bilateral z-transform of the first time-series, we must use the "time reversal" property of z-transform.

You can study all these here: z transform properties

clearvars; clc; close all;

% u(t) : 0 for n<0 and 1 for n>=0
oldparam = sympref('HeavisideAtOrigin',1);

syms n z
assume(n, 'integer');

%%time series
x(n)=((4/3)^n)*heaviside(1-n);

% break into two time series
x1(n)=( (4/3)^n )* heaviside(-n)
x2(n)=( (4/3)^n )* (heaviside(n-1)-heaviside(n-2))

% plot time series
ntest=-8:1:8;

subplot(2,1,1); stem(ntest, x(ntest), 'b^');
title(texlabel(x(n))); xlabel('n'), ylabel('x(n)');

subplot(2,1,2); stem(ntest, x1(ntest), 'ro'); hold on;
subplot(2,1,2); stem(ntest, x2(ntest), 'g*','Color', [0 .5 0]); 
legend('x1', 'x2'); title('decomposition to x1(n), x2(n)');

%%z-transform of x1(n)

% create "time reversed" version
x1r(n)=subs(x1(n),n,-n);

% z-transform of x1r(n)
X1r(z)=simplifyFraction( ztrans(x1r(n),n,z) );

% z-transform of x1(n)
X1(z)=simplifyFraction( subs(X1r(z),z,z^-1) );

%%z-transform of x2(n)
X2(z)=simplifyFraction( ztrans(x2(n)) );

%%calculation of z-transform of x(n)

X(z)=X1(z)+X2(z)

And here you are, what you get, when you execute the above script:

[AlireaA Mirrabie]

Sir you're a life saver

[John D'Errico]

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