udft 4.0.4

Unitary discrete Fourier Transform (and related)

UDFT: Unitary Discrete Fourier Transform (and related)

This module implements unitary discrete Fourier transform, that is orthonormal det(F) = 1 and F⁻¹ = F^*. This module existed before the introduction of the norm="ortho" keyword and is now a very (very) thin wrapper around libraries.

It is useful for convolution [1]: they respect the Perceval equality, e.g., the value of the null frequency is equal to 1/√N * ∑ₙ xₙ.

[1] B. R. Hunt "A matrix theory proof of the discrete convolution theorem", IEEE
Trans. on Audio and Electroacoustics, vol. au-19, no. 4, pp. 285-288, dec. 1971

There is also functions related to Fourier and convolution like ir2fr.

UDFT use array API standard. Thanks to this last point, any array library that follow the standard (Numpy, PyTorch, cupy, ...) can be used by udft that use their respective namespace.

If you are having issues, please let me know

francois.orieux AT universite-paris-saclay.fr

Installation and documentation

UDFT is just the file udft.py and depends on array-api-compat and numpy only and therefor is compatible with numpy, pytorch, jax, cupy...

The API is simple and opinionated for good reason. If you need more parameters or options, I simply encourage you to directly use API of your array library.

Documentation is here. I recommend using poetry or uv for installation

   poetry add udft

or

   poetry add udft[scipy]

For a quick and dirty installation, just copy the udft.py file: it is quite stable, follow the Semantic Versioning, and futur major changes are unlikely.

The code is hosted on GitHub.

License

The code is in the public domain.