Applications of fast orthogonal search: Time-series analysis and resolution of signals in noise

Abstract

In this paper a technique is examined for obtaining accurate and parsimonious sinusoidal series representations of biological time-series data, and for resolving sinusoidal signals in noise. The technique operates via a fast orthogonal search method discussed in the paper, and achieves economy of representation by finding the most significant sinusoidal frequencies first, in a least squares fit sense. Another reason for the parsimony in representation is that the identified sinusoidal series model is not restricted to frequencies which are commensurate or integral multiples of the fundamental frequency corresponding to the record length. Biological applications relate to spectral analysis of noisy time-series data such as EEG, ECG, EMG, EOG, and to speech analysis. Simulations are provided to demonstrate precise detection of component frequencies and weights in short data records, coping with missing or unequally spaced data, and recovery of signals heavily contaminated with noise. The technique is also shown to be capable of higher frequency resolution than is achievable by conventional Fourier series analysis.

Interpreting Microarray Data and Related Applications Using Nonlinear System Identification

“…As noted above, the latter is a general-purpose method of searching through a candidate set of basis functions to build a concise model of a system, where computation time scales linearly with number of candidate functions. Introduced in 1987 [41], FOS has been applied in system identification [42,73], in time-series analysis [42,74], and within an iterative version, to build generalized single-layer ANNs, where it determined model size as well as its significant terms [46]. Applications of FOS have included Raman spectral estimation [75] and detection of abnormalities in prosthetic heart valves [76].…”

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.…”

“…There are two significant differences between FOS and conventional Fourier Transform techniques (i.e. Discrete Fourier Transform (DFT) or FFT) (Korenberg and Paarmann 1989;Chon 2001): (1) FOS yields a parsimonious sinusoidal series representation by selecting the most significant sinusoidal components first; and (2) the frequencies of the sinusoids selected need not be commensurate nor integral multiples of the fundamental frequency corresponding to the record length (Korenberg 1989). This translates to better frequency resolution in the spectral model.…”

“…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.…”

Multimilling-Insert Wear Assessment Using Non-Linear Virtual Sensor, Time-Frequency Distribution and Neural Networks

“…Such a model could contain, as many as 69 linear terms and 2346 non-linear terms. An orthogonal method [35,36] was employed to identify the signi"cant terms and their appropriate coe$cients. The algorithm resulted in a model consisting of 50 terms and an example of its output is given in Fig.…”