How to matlab ztransform with time shift?

How to code z-transform with time shift. For example F(n) = (1/3)^n u(n-2) using symbolic math toolbox and other ways

[Star Strider]

What Toolbox are you using for this?

[John Bravo]

Symbolic math toolbox. Are there other ways?

[Star Strider]

Signal Processing Toolbox, Control system Toolbox, System Identification Toolbox, perhaps others.

Try this:

syms n z 
f(n) = (1/3)^n;                             % Discrete Domain
s(n) = heaviside(n-2);                      % Discrete Domain
F(z) = ztrans(f, n, z);                     % Z Domain
S = ztrans(s, n, z);                        % Z Domain
FS(z) = F * S;                              % Convolve To Get Shifted Function

Answer 1

[Dimitris Kalogiros]

If you like to use symbolic math toolbox :

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');
assumeAlso(n>=0);

%time series
x(n)=( (1/3)^n )* heaviside(n-2)

% plot time series
fplot(x(n), '-b','LineWidth',3);
title(texlabel(x(n))); xlabel('n'), ylabel('x(n)')

% z-transform
X(z)=simplifyFraction( ztrans(x(n-2),n,z) )

If you execute this script: