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.

Estimates of closely spaced signals using adaptive FOS

“…Introduction: Fast orthogonal search (FOS) is a modelling technique that has been shown to be able to accurately estimate the frequency and magnitude of closely spaced signals with up to ten times the fast Fourier transform (FFT) resolution [1][2][3]. These results were found using a set of candidate functions with closely spaced frequencies and fitting the candidate functions one frequency at a time in order of significance.…”

Fast orthogonal search (FOS) versus fast Fourier transform (FFT) as spectral model estimations techniques applied for structural health monitoring (SHM)

“…The fast orthogonal search (FOS) algorithm (Korenberg 1989;Korenberg and Paarmann 1989;Ali 2003;McGaughey et al 2003;Chon 2001) is a general purpose modeling technique which can be applied to spectral estimation and time-frequency analysis. The algorithm uses an arbitrary set of non-orthogonal candidate functions p m (n) and finds a functional expansion of an input y(n) in order to minimize the mean squared error (MSE) between the input and the functional expansion.…”

“…By fitting a sine and cosine pair at each candidate frequency, the magnitude and phase at the candidate frequency can be determined (Ali 2003;McGaughey et al 2003). There are two significant differences between FOS and conventional Fourier Transform techniques (i.e.…”

“…As FOS is generally known to be a data dependent algorithm (Korenberg 1989;Korenberg and Paarmann 1989;Ali 2003;McGaughey et al 2003;Chon 2001); the accuracy of the model produced by FOS depends on the data record being modelled, the candidate functions used to compute correlations, and the stopping conditions (thresholds) in the algorithm.…”

Interpreting Microarray Data and Related Applications Using Nonlinear System Identification

“…However, the latter method has computational complexity and storage requirement dependent upon the square of the number of candidate terms that are searched, while in FOS the dependence is reduced to a linear relationship. In addition FOS and/or iterative forms [44 -47] of FOS have been used for high-resolution spectral analysis [42,45,47,48], direction finding [44,45], constructing generalized single-layer networks [46], and design of two-dimensional filters [49], among many applications. Wu et al [50] have compared FOS with canonical variate analysis for biological applications.…”