Fitting FFT-derived Spectra: Theory, Tool, and Application to Solar Radio Spike Decomposition

TL;DR

This paper develops a statistical theory and software tool for accurately fitting FFT-derived spectra, accounting for fluctuations, and demonstrates its application to solar radio spike data from a significant event.

Contribution

It introduces a novel theory for statistical fluctuations in FFT spectra and provides an automated fitting tool for large spectral datasets.

Findings

Improved spectral fitting accuracy by accounting for statistical fluctuations.

Successful application to real solar radio spike data from 2006.

Enhanced understanding of spectral features in solar radio observations.

Abstract

Spectra derived from fast Fourier transform (FFT) analysis of time-domain data intrinsically contain statistical fluctuations whose distribution depends on the number of accumulated spectra contributing to a measurement. The tail of this distribution, which is essential for separation of the true signal from the statistical fluctuations, deviates noticeably from the normal distribution for a finite number of the accumulations. In this paper we develop a theory to properly account for the statistical fluctuations when fitting a model to a given accumulated spectrum. The method is implemented in software for the purpose of automatically fitting a large body of such FFT-derived spectra. We apply this tool to analyze a portion of a dense cluster of spikes recorded by our FST instrument during a record-breaking event that occurred on 06 Dec 2006. The outcome of this analysis is briefly discussed.