Fourier Transformation of periodic functions

Questions
1

Hi,
I was wondering whether there is a reason why Mathematica can not perform the Fourier Transformation of a square wave signal outlined as follows:

  FourierTransform[SquareWave[t], t, \[Omega]]

Thanks in advance

2

Perhaps you want FourierSeries instead of FourierTransform?

FourierSeries[SquareWave[t], t, 5]
3

This is definitely a good question! This calculation is so easy that it can be done in ones head: A SquareWave can basically be written as a convolution of DiracComb and HeavisidePi; so the answer is a produce of DiracComb and Sinc. Obviously Mathematica does not know the convolution theorem. Similar strange effects have been reported, e.g. here .

4

Thanks for responding. Actually, I was examining the ability of Mathematica to perform Fourier Transform on periodic functions.

5

The wave function, on which I wanted to apply Fourier Transform, was a bit more complex. But then I realized that Mathematica can’t perform Fourier Transform, in general, on periodic signals such as SquareWave, TriangleWave and SawtoothWave. Knowing that, Fourier Transform of periodic functions is fundamental in Signal Processing, I hope the abilities of FourierTransform function will be improved in future Mathematica releases. Thanks for your response anyways.