FourierTransform won't work

Questions
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1

Hi folks,

I’ve got a little problem with Mathematicas FourierTransform.
I’ve defined a rectangular function with help of the HeavisideTheta-Function.

Square[t_] := 1/2 * HeavisideTheta[(-t^2 + 1)]

When trying to FourierTransform it with

FourierTransform[Square[t], t, \[Omega]]

All I get is

FourierTransform[1/2 HeavisideTheta[1 - t^2], t, 1]

After looking through the examples I tried

FourierTransform[1, t, \[Omega]]

for testing purposes, but again all I got out was

FourierTransform[1, t, 1]

More oddly, when I emailed my two rows of code to a guy at my University,
they worked for him the way expected.

Any ideas what’s going on here?

2

Square is a built-in function. Do yourself a favour by letting start your own symbols with lower-case letters.

In[2]:= sQuare[t_] := 1/2*HeavisideTheta[(-t^2 + 1)]

In[3]:= FourierTransform[sQuare[t], t, \[Omega]]
Out[3]= Sin[\[Omega]]/(Sqrt[2 \[Pi]] \[Omega])

In[4]:= FourierTransform[1, t, \[Omega]]
Out[4]= Sqrt[2 \[Pi]] DiracDelta[\[Omega]]
3

Thanks for your answer and thanks for your hint with upper cases.
Sadly, it still won’t work. I copied your corrected functions into a new notebook, but still won’t get a proper result.

6508Mathematica.png
6508Mathematica.png1366×768 33 KB

4

Unbelievable! Then you should to research whether FourierTransform is a command available in the \mathit{Mathematica} \mathit{Student} \mathit{Edition}. If something tends to absurdity, it might have a legal reason.

5

Luckily, somebody else came with a solution which actually works.

Clear @"Global`*"
Square[t_] := 1/2*HeavisideTheta[(-t^2 + 1)]
FourierTransform[Square[t], t, \[Omega]]

So seems like something messed mathematica up which needed correction.

6

Hi Sebastian,

the problem seems to be that your new variable had a value, i.e. you obviously executed before

\[omega]=1

Starting a new notebook does not change that. Clearing all variables - as you did in your solution - does make the difference!
Therefore it is a good idea (and often seen) to start every “new” notebook with the command

ClearAll["Global`*"]

Henrik