Combine User's Manual

TL;DR

Combine is a tool that enhances frequency analysis by identifying genuine signals in time series data, using heuristics to distinguish true frequencies from linear combinations, improving the reliability of spectral analysis.

Contribution

It introduces a heuristic-based method to differentiate genuine frequencies from linear combinations in spectral analysis, integrated as an add-on to existing tools.

Findings

Successfully identifies genuine frequencies in synthetic and real data.

Reduces false positives in frequency detection.

Improves spectral analysis reliability.

Abstract

{\sc Combine} is an add-on to {\sc SigSpec} and {\sc Cinderella}. A {\sc SigSpec} result file or a file generated by {\sc Cinderella} contains the significant sinusoidal signal components in a time series. In this file, {\sc Combine} checks one frequency after the other for being a linear combination of previously examined frequencies. If this attempt fails, the corresponding frequency is considered ``genuine''. Only genuine frequencies are used to form linear combinations subsequently. A purely heuristic model is employed to assign a reliability to each linear combination and to justify whether to consider a frequency genuine or a linear combination.