Abstract
It is argued that there are a number of situations in life science where it is desirable to attempt a two-sided linear filter identification. A simple method is presented for the determination of a nonparametric, two-sided linear filter from system input and output data. The time-domain filter is determined from a matrix equation involving the input autocorrelation function and the two-sided cross-correlation function. The resulting filter minimises the sum of squared differences between the actual and predicted outputs.
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References
Basar, E. (1976)Biophysical and physiological systems analysis. Addison-Wesley, Massachusetts.
Bendat, J. S. andPiersol, A. G. (1971)Random data: analysis and measurement procedures, Wiley, New York.
Box, G. E. P. andJenkins, G. M. (1976)Time series analysis: forecasting and control. Revised edition Holden-Day, San Francisco.
Brigham, E. O. (1974)The fast Fourier transform. Prentice-Hall, Englewood Cliffs, N.J.
Brillinger, D. R. (1975)Time series: data analysis and theory. Holt, Rinehart & Winston, New York.
Dongarra, J. J., Moler, C. B., Bunch, J. R. andStewart, G. W. (1979)LINPACK users' quide. SIAM, Philadelphia.
Eykhoff, P. (1974)System identification: parameter and state estimation. Wiley, London.
Graupe, D. (1972)Identification of systems. Van Nostrand, New York.
Hunter, I. W. andKearney, R. E. (1982a) Dynamics of human ankle stiffness: effect of mean torque.J. Biomechanics, (in press).
Hunter, I. W. andKearney, R. E. (1982b) NEXUS: A command line decoder and task dispatcher for system and signal analysis. 15th Canadian DECUS Symposium, Toronto.
Jenkins, G. M. andWatts, D. G. (1968)Spectral analysis and its applications. Holden-Day, San Francisco.
Kearney, R. E. andHunter, I. W. (1981a) Identification of the human ankle stiffness transfer function.Soc. Neurosci. Abstr.,7, 558.
Kearney, R. E. andHunter, I. W. (1981b) APS: A package for the analysis of physiological systems. 14th Canadian DECUS Symposium, Montreal.
Kearney, R. E. andHunter, I. W. (1982) Dynamics of human ankle stiffness: variation with displacement amplitude.J. Biomechanics, (in press).
Levinson, N. (1947) The Weiner RMS (root mean square) error criterion in filter design and prediction.J. Math. Physics,25, 261–278.
Marmarelis, P. Z. andMarmarelis, V. Z. (1978)Analysis of physiological system: the white noise approach. Plenum, New York.
Marple, S. L. (1981) Efficient least squares FIR system identification.IEEE Trans.,ASSP-29, 62–73.
McFarland, D. J. (1971)Feedback mechanisms in animal behaviour, Academic Press, London.
McFarland, D. J. (1974)Motivational control systems analysis. Academic Press, London.
McRuer, D. (1980) Human dynamics in man-machine systems.Automatica,16, 237–253.
Mehra, R. K. andLainiotis, D. G. (1976)System identification: advances and case studies. Academic Press, New York.
Milhorn, H. T. (1966)The application of control theory to physiological systems. Saunders, Philadelphia.
Milsum, J. H. (1966)Biological control systems analysis. McGraw-Hill, New York.
Rabiner, L. R. andAllen, J. B. (1981) Short-time Fourier analysis techniques for FIR system identification and power spectrum estimation.IEEE Trans.,ASSP-27, 182–192.
Robinson, E. A. (1978)Multichannel time series analysis with digital computer programs. (Revised edition only. Holden-Day, San Francisco.
Schetzen, M. (1980)The Volterra and Wiener theories of nonlinear systems. Wiley, New York.
Sheridan, T. B. andFerrell, W. R. (1974)Man-machine systems: information, control, and decision models of human performance. MIT Press, Cambridge, Mass.
Toates, F. M. (1975)Control theory in biology and experimental psychology. Hutchinson, London.
Weiss, P. L., Hunter, I. W. andKearney, R. E. (1981) A combined experimental and computational method for the removal of cross talk from an electrophysiological signal.Soc. Neurosci. Abstr.,7, 685.
Zohar, S. (1967) Toeplitz matrix inversion: the algorithm of W. F. Trench.J. Ass. Comput. Mach.,16, 592–601.
Zohar, S. (1979) Fortran subroutines for the solution of Toeplitz sets of linear equations.IEEE Trans.,ASSP-27, 656–658.
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Hunter, I.W., Kearney, R.E. Two-sided linear filter identification. Med. Biol. Eng. Comput. 21, 203–209 (1983). https://doi.org/10.1007/BF02441539
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DOI: https://doi.org/10.1007/BF02441539