Using the fast orthogonal search with first term reselection to find subharmonic terms in spectral analysis

Area of Science:

• Signal Processing
• Time Series Analysis
• Computational Mathematics

Background:

• The fast orthogonal search (FOS) algorithm accurately models time series using specialized orthogonal basis sets.
• FOS offers superior frequency resolution compared to the discrete Fourier transform (DFT) for periodic components, including subharmonic frequencies.
• Existing FOS methods have limitations in determining model complexity and accurately resolving subharmonic frequencies.

Purpose of the Study:

• To investigate and enhance the resolution of subharmonic frequencies using the FOS algorithm.
• To introduce a novel criterion for identifying non-noise terms in time series models.
• To develop an iterative FOS algorithm for improved sinusoidal modeling and frequency selection.

Main Methods:

• Application of the fast orthogonal search (FOS) algorithm to time series data.
• Introduction of a new criterion for selecting the number of model terms, independent of a DC component.
• Development and implementation of an iterative FOS algorithm named FOS first-term reselection (FOS-FTR).

Main Results:

• The proposed new criterion effectively determines the number of non-noise terms without assuming a DC component.
• The FOS-FTR algorithm demonstrates reduced mean-square error in sinusoidal modeling.
• FOS-FTR achieves more accurate selection of subharmonic frequencies compared to the standard FOS algorithm.

Conclusions:

• The enhanced FOS-FTR algorithm provides a more accurate and robust method for time series frequency analysis, particularly for subharmonic components.
• The novel stopping criterion improves model term selection in FOS.
• This research advances the capabilities of FOS for detailed analysis of time series with periodic and subharmonic frequencies.