Spectral Derivatives
Signal Processing
2025-12-08 v4 History and Overview
Abstract
One of the happiest accidents in all math is the ease of transforming a function to and taking derivatives in the Fourier frequency domain. But in order to exploit this extraordinary fact without serious artefacting, and in order to be able to use a computer, we need quite a bit of extra knowledge and care. This document sets out the math behind the spectral-derivatives Python package. I touch on fundamental signal processing and calculus concepts as necessary and build upwards.
Cite
@article{arxiv.2506.06210,
title = {Spectral Derivatives},
author = {Pavel Komarov},
journal= {arXiv preprint arXiv:2506.06210},
year = {2025}
}
Comments
Package at https://pypi.org/project/spectral-derivatives/