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Unexpected Fourier transform (including time shifting property) result in Mathematica/WolframAlpha?

Posted 5 months ago

This is what Mathematica produces for the Fourier transform of Sin[w0 t]: enter image description here

Ignoring the Sqrt(Pi/2) factor, the Fourier transform of Sin[w0 t] is: enter image description here

(source: https://www.tutorialspoint.com/fourier-transform-of-the-sine-and-cosine-functions & many others). Notice the sign difference of the i (or j, in the engineering world) in the above expressions. Also, quite disturbingly, the time shifting property of the Fourier transform appears to be wrong in WolframAlpha, but nevertheless consistent with the Mathematica behavior reported above: enter image description here

compare with: enter image description here

What am I doing wrong? I sure hope this is not a bug.

POSTED BY: Alex C
2 Replies

Check the documentation for the FourierParameters option defaults and alternative settings.

POSTED BY: Daniel Lichtblau
Posted 5 months ago

Thank you - I can breathe easier now, although I'm still a little shaken, was not aware of the FourierParameters option and different definitions: enter image description here

Much appreciated, we can close this.

POSTED BY: Alex C
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