On The Fourier And Wavelet Analysis Of Coronal Time Series

TL;DR

This paper critically evaluates Fourier and wavelet methods for detecting periodic signals in coronal loop data, highlighting issues with common practices and proposing improved statistical models to confirm genuine detections.

Contribution

It demonstrates that traditional detrending and noise models can lead to false positives, and offers refined analysis techniques for more reliable detection of coronal pulsations.

Findings

Detrending can produce spurious periodic detections.

Standard noise models often inadequately represent coronal data.

Refined confidence levels confirm genuine power peaks.

Abstract

Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provies a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence & Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.