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.

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Accurate sinusoidal series models of biological time-series data may be obtained using a modeling algorithm known as fast orthogonal search (FOS). FOS does not require equally spaced data, and can resolve sinusoidal frequencies much more closely spaced than can a discrete Fourier transform. FOS has been less successful at obtaining accurate exponential series models. We here consider a modification of FOS in which iteration of the original procedure is used to further reduce the mean-squared error (m.s.e.) between model and data, approaching a minimum in the m.s.e. Iteration of the FOS procedure greatly improves the accuracy of estimated exponential series models. The application of iterative FOS (IFOS) to exponential and sinusoidal series models is described. Finally, the use of FOS and IFOS procedures for finding a single model from the results of multiple experiments is described.

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