[sharpneli]

Inverse fourier transform of a non transformed signal gives you basically the fourier transform with some changes (I can't remember which, were the numbers conjugates or something?). Applying it the second time gives you same result as if you'd do the forward direction transform twice.

If you apply fourier transform 4 times you get your original function back. You can think of it as 90 degree rotation. Inverse transform just rotates it in the opposite direction.

The rotation analog is not even too far fetched as fractional fourier transform allows you to do an arbitrary angle rotation.

[araes]

Having never heard of this for the Fourier Transform, needed to read.

F0: original signal

F1: frequency domain signal

F2: reverse time signal

F3: inverse fourier signal

F4: original signal

Also, has further weird applications I've never heard of with "Fractional Fourier Transforms" [1] which can apparently result in smooth smears of time -> frequency domain [2].

[1] https://en.wikipedia.org/wiki/Fractional_Fourier_transform

[2] https://en.wikipedia.org/wiki/File:FracFT_Rec_by_stevencys.j...

[laszlokorte]

See [1] for my visualization of this 4-cycle and the fractional fourier transform

[1]: https://static.laszlokorte.de/frft-cube/

[araes]

Thanks. It's neat being able to visualize them, and the 3D display's actually pretty cool looking for all the different functions.

The Fractional DFT part though, doesn't seem to do anything no matter the function chosen. Firefox 125.

Edit: Nvm, figured it out. Have to visualize from the top down to see the Fractional DFT portion. Haven't seen many visualization systems where each orientation shows a different type of data. Actually a pretty neat idea from a UI perspective.