A robust orthogonal algorithm for system identification and timeseries analysis
 M. J. Korenberg
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We describe and illustrate methods for obtaining a parsimonious sinusoidal series representation or model of biological timeseries data. The methods are also used to identify nonlinear systems with unknown structure. A key aspect is a rapid search for significant terms to include in the model for the system or the timeseries. For example, the methods use fast and robust orthogonal searches for significant frequencies in the timeseries, and differ from conventional Fourier series analysis in several important respects. In particular, the frequencies in our resulting sinusoidal series need not be commensurate, nor integral multiples of the fundamental frequency corresponding to the record length. Freed of these restrictions, the methods produce a more economical sinusoidal series representation (than a Fourier series), finding the most significant frequencies first, and automatically determine model order. The methods are also capable of higher resolution than a conventional Fourier series analysis. In addition, the methods can cope with unequallyspaced or missing data, and are applicable to timeseries corrupted by noise. Fially, we compare one of our methods with a wellknown technique for resolving sinusoidal signals in noise using published data for the test timeseries.
 Billings, SA, Leontaritis, IJ (1982) Parameter estimation techniques for nonlinear systems. IFAC Symp Ident Sys Param Est 1: pp. 427432
 Box, GEP, Jenkins, GM (1976) Time series analysis: forecasting and control. HoldenDay, San Francisco
 Cooley, JW, Tukey, JW (1965) An algorithm for machine calculation of complex Fourier series. Math Comput 19: pp. 297301
 Dwight, HB (1960) Tables of integrals and other mathematical data. Macmillan, New York
 French, AS, Butz, EG (1973) Measuring the Wiener kernels of a nonlinear system using the fast Fourier transform algorithm. Int J Control 17: pp. 529539
 Haber, R, Keviczky, L (1976) Identification of nonlinear dynamic systems. IFAC Symp Ident Sys Param Est 1: pp. 79126
 Ho, T, Kwok, J, Law, J, Leung, L (1987) Nonlinear system identification. Department of Electrical Engineering, Queen's University, Kingston, Ontario, Canada
 Kay, SM, Marple, SL (1981) Spectrum analysis a modern perspective. Proc. IEEE 69: pp. 13801419
 Korenberg, MJ (1973) Identification of biological cascades of linear and static nonlinear systems. Proc Midwest Symp Circuit Theory 18.2: pp. 19
 Korenberg, MJ (1985) Orthogonal identification of nonlinear difference equation models. Proc Midwest Symp Circuit Sys 1: pp. 9095
 Korenberg, MJ (1987) Fast orthogonal identification of nonlinear difference equation and functional expansion models. Proc Midwest Symp Circuit Sys 1: pp. 270276
 Korenberg, MJ (1988) Identifying nonlinear difference equation and functional expansion representations: the fast orthogonal algorithm. Ann Biomed Eng 16: pp. 123142
 Korenberg, MJ, Bruder, SB, McIlroy, PJ (1988) Exact orthogonal kernel estimation from finite data records: extending Wiener's identification of nonlinear systems. Ann Biomed Eng 16: pp. 201214
 Korenberg, MJ, French, AS, Voo, SKL (1988) Whitenoise analysis of nonlinear behavior in an insect sensory neuron: kernel and cascade approaches. Biol Cybern 58: pp. 313320
 Lee, YW, Schetzen, M (1965) Measurement of the Wiener kernels of a nonlinear system by crosscorrelation. Int J Control 2: pp. 237254
 Marmarelis, PZ, Marmarelis, VZ (1978) Analysis of physiological systems. The white noise approach. Plenum Press, New York
 Marmarelis, PZ, Naka, KI (1972) White noise analysis of a neuron chain: an application of the Wiener theory. Science 175: pp. 12761278
 McIlroy, PJH (1986) Applications of nonlinear systems identification. Queen's University, Kingston, Ontario, Canada
 Mohanty, NC (1986) Random signals estimation and identification. Analysis and applications. Van Nostrand, New York
 Nugent, ST, Finley, JP (1983) Spectral analysis of periodic and normal breathing in infants. IEEE Trans Biomed Eng 30: pp. 672675
 Palm, G, Poggio, T (1978) Stochastic identification methods for nonlinear systems: an extension of the Wiener theory. SIAM J Appl Math 34: pp. 524534
 Rice, JR (1966) A theory of condition. SIAM J Numer Anal 3: pp. 287310
 Sterman, MB (1981) Power spectral analysis of EEG characteristics during sleep in epileptics. Epilepsia 22: pp. 95106
 Wiener, N (1958) Nonlinear problems in random theory. Wiley, New York
 Title
 A robust orthogonal algorithm for system identification and timeseries analysis
 Journal

Biological Cybernetics
Volume 60, Issue 4 , pp 267276
 Cover Date
 19890201
 DOI
 10.1007/BF00204124
 Print ISSN
 03401200
 Online ISSN
 14320770
 Publisher
 SpringerVerlag
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 Authors

 M. J. Korenberg ^{(1)}
 Author Affiliations

 1. Department of Electrical Engineering, Queen's University, K7L 3N6, Kingston, Ontario, Canada