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 Numpy, pyFFTW, and Scipy (maybe others in the future), mainly done for my personal usage. There is also functions related to Fourier and convolution like ir2fr.

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

If you are having issues, please let me know

francois.orieux AT l2s.centralesupelec.fr

Installation and documentation

UDFT is just the file udft.py and depends on numpy and Python 3.7+ only. Optional dependency are pyFFTW and scipy. Documentation is here. I recommend using poetry for installation

   poetry add udft

or

   poetry add udft[fftw]

to install pyFFTW, or pip

   pip install udft

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

The code is hosted on GitHub.

License

The code is in the public domain.