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Shameless plug: If you are interested in Fourier Transform and signal processing you might enjoy my somewhat artistic 3D visualisation of the fourier transform

Shameless plug: If you are interested in Fourier Transform and signal processing you might enjoy my somewhat artistic 3D visualisation of the fourier transform as well as the fractional fourier transform [1] (Fractional fourier transform on the top face of the cube) And for short time fourier transform showing how a filter kernel is shiftes across the signal. [2] [1]: https://static.laszlokorte.de/frft-cube/ https://static.laszlokorte.de/frft-cube/ [2]: https://static.laszlokorte.de/time-frequency/ https://static.laszlokorte.de/time-frequency/

yshklarov 1y ago
I love the visualization! Thanks for sharing. How do you compute the fractional FT? My guess is by interpolating the DFT matrix (via matrix logarithm & exponential) -- is that right, or do you use some other method?
- laszlokorte 1y ago
  I am glad you like it! Yes the simplest way to think of it is to exponentiate the dft matrix to an exponent between 0 and 1 (1 being the classic dft). But then the runtime complexity is O(n^2) (vector multiplied with precomputed matrix) or O(n^3) opposed to the O(n log n) of fast fourier transform. There are tricks to do a fast fractional fourier transform by multiplying and convolving with a chirp signal. My implementation is in rust [1] compiled to web assembly, but it is based on the matlab of [2] who gladly answered all my mails asking many questions despite already being retired. [1]: https://github.com/laszlokorte/svelte-rust-fft/tree/master/src https://github.com/laszlokorte/svelte-rust-fft/tree/master/s... [2]: https://nalag.cs.kuleuven.be/research/software/FRFT/ https://nalag.cs.kuleuven.be/research/software/FRFT/
  - xphos 1y ago
    I made a cool rust fft tui a long time ago too https://github.com/lquinn2015/FFT-tui https://github.com/lquinn2015/FFT-tui
    - laszlokorte 1y ago
      Look great! I was already thinking about reimplementing mine as TUI
hovden 1y ago
If I might also plug ‘the Atlas of Fourier Transforms’. If your interested in understanding building intuition of symmetry and phase in fourier space, the book illustrates many structures.
- laszlokorte 1y ago
  Looks amazing! Thank you
nblgbg 1y ago
Thanks a lot for all of this ! https://tools.laszlokorte.de/ https://tools.laszlokorte.de/
- laszlokorte 1y ago
  I am glad you are enjoying it! :)
mallowdram 1y ago
Fantastic! Thanks!

yshklarov 1y ago

I love the visualization! Thanks for sharing. How do you compute the fractional FT? My guess is by interpolating the DFT matrix (via matrix logarithm & exponential) -- is that right, or do you use some other method?

laszlokorte 1y ago
I am glad you like it! Yes the simplest way to think of it is to exponentiate the dft matrix to an exponent between 0 and 1 (1 being the classic dft). But then the runtime complexity is O(n^2) (vector multiplied with precomputed matrix) or O(n^3) opposed to the O(n log n) of fast fourier transform. There are tricks to do a fast fractional fourier transform by multiplying and convolving with a chirp signal. My implementation is in rust [1] compiled to web assembly, but it is based on the matlab of [2] who gladly answered all my mails asking many questions despite already being retired. [1]: https://github.com/laszlokorte/svelte-rust-fft/tree/master/src https://github.com/laszlokorte/svelte-rust-fft/tree/master/s... [2]: https://nalag.cs.kuleuven.be/research/software/FRFT/ https://nalag.cs.kuleuven.be/research/software/FRFT/
- xphos 1y ago
  I made a cool rust fft tui a long time ago too https://github.com/lquinn2015/FFT-tui https://github.com/lquinn2015/FFT-tui
  - laszlokorte 1y ago
    Look great! I was already thinking about reimplementing mine as TUI

hovden 1y ago

If I might also plug ‘the Atlas of Fourier Transforms’. If your interested in understanding building intuition of symmetry and phase in fourier space, the book illustrates many structures.

laszlokorte 1y ago
Looks amazing! Thank you

nblgbg 1y ago

Thanks a lot for all of this ! https://tools.laszlokorte.de/ https://tools.laszlokorte.de/

laszlokorte 1y ago
I am glad you are enjoying it! :)

mallowdram 1y ago

Fantastic! Thanks!