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I am trying to learn about Laplace transform and especially about ROC and i found out on this weblink.

I have also attached a snapshot of this link and highlighted where it is being said that although the signals are differing, their Laplace Transforms are identical

My MATLAB code

clc
clear
close all
syms s t a
x1=exp(-a*t)*heaviside(t)
x2=-exp(-a*t).*heaviside(-t)
X1=laplace(x1,s)
X2=laplace(x2,s)

When i run above script i get X2=0, but as per above mentioned web link , i should have got $1/(s+a)$

Why i am getting different values of X1 and X2?

enter image description here

I have also attached snapshot of above weblink

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1 Answer 1

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The Matlab implementation of the Laplace transform computes the uni-lateral (one-sided) Laplace transform:

Screenshot of Laplace page on Mathworks website

Since $x_2(t)$ is zero for $t\gt0$, the result of the uni-lateral Laplace transform must be zero.

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