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Is there a simple algorithm for computing the fractional discrete fourier transform analog to the FFT algorithm or even naive DFT matrix multiplication?

I am kind of new into signal processing. For my own understanding I built this tool in order to grasp an intuitive understanding for the relation between time and frequency domain. I was intrigued by the 4-cyclic behavior of the FT operation. I stumbled upon the idea of fractional fourier transform and would love to include it in my tool to play around with.

But I only found very few papers about fractional fourier transforms mostly focusing on the math side of things and ignoring an algorithmic implementation.

This paper discusses various possible implementations but relies heavly on CAS like matlab to do the heavy lifting like determining eigen values.

So my question is if there are any straight forward self contained implementations for fractional discrete fourier transform.

Update I accomplished to use the matlab code provided here as reference. The Python implementation from Ashs answer is also based on this matlab code.

Translating the matlab implementation into Rust and compiling to WASM allowed me to build this interactive visualization (video demonstration)

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    $\begingroup$ Thanks for the update! I've shared the visualization with some interested students. $\endgroup$
    – Peter K.
    Jan 28 at 20:16

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That's a really cool visualization, well done! Here is a Python implementation of the Fast FrFT, with a link in the code to the MATLAB version as well:

https://github.com/nanaln/python_frft/blob/master/frft/frft.py

Some implementations I have tested have bugs in them, but this one seems to work well.

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