title: Using the fast orthogonal search with first term reselection to find subharmonic terms in spectral analysis.
abstract: The fast orthogonal search (FOS) algorithm has been shown to accurately model various types of time series by implicitly creating a specialized orthogonal basis set to fit the desired time series. When the data contain periodic components, FOS can find frequencies with a resolution greater than the discrete Fourier transform (DFT) algorithm. Frequencies with less than one period in the record length, called subharmonic frequencies, and frequencies between the bins of a DFT, can be resolved. This paper considers the resolution of subharmonic frequencies using the FOS algorithm. A new criterion for determining the number of non-noise terms in the model is introduced. This new criterion does not assume the first model term fitted is a dc component as did the previous stopping criterion. An iterative FOS algorithm called FOS first-term reselection (FOS-FTR), is introduced. FOS-FTR reduces the mean-square error of the sinusoidal model and selects the subharmonic frequencies more accurately than does the unmodified FOS algorithm.
authors.affiliation: Royal Military College of Canada, Box 17000, Station Forces, Kingston, Ontario, Canada. mcgaughey-d@rmc.ca
authors.forename: Donald R
authors.initials: DR
authors.lastname: McGaughey
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Korenberg
authors.forename: Kathryn M
authors.initials: KM
authors.lastname: Adeney
authors.forename: Susan D
authors.initials: SD
authors.lastname: Collins
authors.forename: G J M
authors.initials: GJ
authors.lastname: Aitken
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D005583:Fourier Analysis; D008954:Models, Biological; D009038:Motion; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013057:Spectrum Analysis / Q000379:methods; D013269:Stochastic Processes