A Fast Chi-squared Technique For Period Search of Irregularly Sampled Data

TL;DR

The paper introduces the Fast χ² algorithm, an efficient method for detecting periodic signals with harmonics in irregularly-sampled data, leveraging FFTs for high performance.

Contribution

It presents a novel, computationally-efficient algorithm that improves period search in irregularly-sampled data with non-uniform errors.

Findings

Achieves O(N log N) performance using FFTs.

Effectively detects harmonic signals in irregular data.

Provides reference implementation code.

Abstract

A new, computationally- and statistically-efficient algorithm, the Fast $\chi^2$ algorithm, can find a periodic signal with harmonic content in irregularly-sampled data with non-uniform errors. The algorithm calculates the minimized $\chi^2$ as a function of frequency at the desired number of harmonics, using Fast Fourier Transforms to provide $O (N \log N)$ performance. The code for a reference implementation is provided.