Detecting non-sinusoidal periodicities in observational data using multi-harmonic periodograms

TL;DR

This paper develops and validates analytic methods to assess the statistical significance of non-sinusoidal periodic signals detected using multi-harmonic periodograms, enhancing detection reliability in observational data.

Contribution

It extends previous work on Lomb-Scargle periodograms to multi-harmonic periodograms, providing efficient analytic false alarm probability approximations for non-sinusoidal signal detection.

Findings

Analytic approximations are accurate and robust across various conditions.

Monte Carlo simulations confirm the effectiveness of the proposed methods.

The methods improve the reliability of detecting non-sinusoidal periodicities.

Abstract

We address the problem of assessing the statistical significance of candidate periodicities found using the so-called `multi-harmonic' periodogram, which is being used for detection of non-sinusoidal signals, and is based on the least-squares fitting of truncated Fourier series. The recent investigation (Baluev 2008) made for the Lomb-Scargle periodogram is extended to the more general multi-harmonic periodogram. As a result, closed and efficient analytic approximations to the false alarm probability, associated with multi-harmonic periodogram peaks, are obtained. The resulting analytic approximations are tested under various conditions using Monte Carlo simulations. The simulations showed a suitable precision and robustness of these approximations.