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I am using MATLAB and trying to find ztransform of heaviside(n) which is unit step sequence

I am studying book Signals and Systems Laboratory with MATLAB Book by Alex Palamides and Anastasia Veloni

I have attached snap of book but when i try to run this code in MATLAB , i am not getting same results as book

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My MATLAB code

clc;clear;close all
syms z n
f=heaviside(n)
X=ztrans(f,z)


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1 Answer 1

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If you look up Matlab's Heaviside function, you'll see that it is not equal to the unit step sequence $u[n]$, because, unlike $u[n]$, it returns the value $1/2$ for $n=0$. Hence, it is given by

$$h[n]=u[n]-\frac12\delta[n]\tag{1}$$

and, consequently, its $\mathcal{Z}$-transform is

$$H(z)=\frac{z}{z-1}-\frac12=\frac{1}{z-1}+\frac12$$

as correctly claimed by ztrans.

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  • $\begingroup$ Can you please explain, how you wrote H(z) = z/(z-1) -1/2 = 1/(z-1)+1/2 $\endgroup$
    – DSP_CS
    Commented May 12 at 13:17
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    $\begingroup$ @DSP_CS: Have you tried to prove it yourself? Please give it a go, it's really absolutely basic. $\endgroup$
    – Matt L.
    Commented May 12 at 13:47
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    $\begingroup$ Got it. Thanks alot $\endgroup$
    – DSP_CS
    Commented May 12 at 17:43

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