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

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John Bravo
John Bravo 2018-9-21
评论： John D'Errico 2022-11-12
How to matlab z-transform of x(n)=((4/3)^n) u(1-n) by using symbolic math toolbox
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Dimitris Kalogiros
Dimitris Kalogiros 2018-9-21
x(n) seams to be a non-causal signal. It's values are zeros for n>1 and they are not, for n=<1...
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回答（1 个）

Dimitris Kalogiros
Dimitris Kalogiros 2018-9-21
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:
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John D'Errico
John D'Errico 2022-11-12
No. You are not a life saver, but someone who is teaching a student that Answers is here as a service to do their homeowrk, when no effort was shown or made. Please do not answer obvious homework assignments for Students. That hurts the student, because now this student will vome to believe they can continue posting their homework assignments on Answers. It hurts Answers, because now other students will think they too have the right to get their assignments done for them on Answers.

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