Abstract
White-noise analysis and related methods of nonlinear systems identification describe a physical system’s response to its input in terms of “kernels” of progressively higher orders. A popular analytic scheme in the laboratory uses a class of pseudorandom binary sequences, m-sequences, as a test signal. The m-sequence method has several advantages for investigating linear and nonlinear systems: ease of implementation, rapid calculation of system kernels, and a solid theoretical framework. One difficulty with this method for nonlinear analysis comes from the algebraic structure of m-sequences: linear and nonlinear terms can be confounded, especially in the analysis of systems with many inputs. We have developed a modification of the m-sequence method which allows control of these anomalies. This method is based on input signals consisting of a superposition of m-sequences whose lengths are relatively prime. The fast computational methods which facilitate kernel calculation for a single m-sequence input are readily extended to this new setting. We describe the theoretical foundation of this method and present an application to the study of ganglion cells of the macaque retina.
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References
Barker, H.A., and Pradisthayon, T. (1970) High-order autocorrelation functions of pseudoramdom signals based on M-sequences. Proc. IEE, 177:1857–1863.
Benardete, E.A., Victor, J.D. and Kaplan, E. (1992) Temporal properties of primate P retinal ganglion cells investigated with a new discrete multi-level stimulus. Invest. Opthalmol. & Visual Sci., 33, abstr. #3591.
Derrington, A.M., Krauskopf, J. and Lennie, P. (1984) Chromatic mechanisms in lateral geniculate nucleus of macaque. J. Physiol. (London), 357:241–265.
Feller, W. (1968) An Introduction to Probability Theory and Statistics, 3rd ed., John Wiley & Sons, New York, New York.
Golomb, S.W. (1968) Shift Register Sequences, Holden-Day, San Francisco, California.
Gyftopoulos, E.P., and Hooper, R.J. (1964) Signals for transfer function measurement in nonlinear systems. Noise Analysis in Nuclear Systems, USAEC Symposium series 4, TID-7679.
Ingling, C.R. and Martinez-Uriegas, E. (1983) The relationship between spectral sensitivity and spatial sensitivity in the primate r-g X-channel. Vision Res., 23:1495–1500.
Kaplan, E. and Shapley, R.M. (1986) The primate retina contains two types of ganglion cells with high and low contrast sensitivity. PNAS USA, 83:2755–2757.
Kaplan, E., Lee, B.B. and Shapley, R.M. (1990) New views of primate retinal function, In: Progress in Retinal Research, Vol. 9, N.N. Osborne & J.G. Chader, eds., Pergamon Press, New York, New York.
Klein, S. (1987) Relationships between kernels measured with different stimuli, In: Advanced Methods of Physiological Systems Modeling, Volume I, V.Z. Marmarelis, (Ed.), Biomedical Simulations Resource, University of Southern California, Los Angeles, California.
Klein, S.A. (1992) Optimizing the estimation of nonlinear kernels, In: Nonlinear Vision: Determination of Neural Receptive Fields, Function, and Networks, R.B. Pinter & B. Nabet, Eds., CRC Press, Boca Raton, Horida.
Lee, Y.N. and Schetzen, M. (1965) Measurement of the kernels of a nonlinear system by cross-correlation. Int. J. Control, 2:237–254.
Marmarelis, P.Z. and Naka, K.-I. (1972) White-noise analysis of a neuron chain: An application of the Wiener theory. Science, 175:1276–1278.
Marmarelis, R.Z. and Marmarelis, V.Z. (1978) Analysis of Physiological Systems: The White-Noise Approach, Plenum Press, New York, New York.
Pinter, C.C. (1990) A Book of Abstract Algebra, , McGraw-HillNew York, New York.
Ream, N. (1970) Nonlinear identification using inverse-repeat m-sequences. Proc. IEE, 117: 213–218.
Schetzen, M. (1980) The Volterra and Wiener Theories of Nonlinear Systems, John Wiley & Sons, New York, New York.
Sutter, E.E. (1987) A practical nonstochastic approach to nonlinear time-domain analysis, In: Advanced Methods of Physiological Systems Modeling, Vol. I, V.Z. Marmarelis, ed., Biomedical Simulations Resource, University of Southern California, Los Angeles, California.
Sutter, E.E. (1991) The fast m-transform: a fast computation of cross-correlation with binary m-sequences. SIAM J. Comput., 20(4):686–694.
Sutter, E.E. (1992) A deterministic approach to nonlinear systems analysis, In: Nonlinear Vision: Determination of Neural Receptive Fields, Function, and Networks, R.B. Pinter & B. Nabet, Eds., CRC Press, Boca Raton, Horida.
Victor, J.D. and Knight, B.W. (1979) Nonlinear analysis with an arbitrary stimulus ensemble. Q. Appl. Math., 37:113–136.
Victor, J.D. and Shapley, R.M. (1979) The nonlinear pathway of Y ganglion cells in the cat retina. J. Gen. Physiol., 74:671–689.
Victor, J.D. and Shapley, R.M. (1980) A method of nonlinear analysis in the frequency domain. Biophys.J., 29:459–484.
Victor, J.D. (1991) Asymptotic approach of generalized functional expansions to Wiener kernels. Ann. Biomed. Eng., 19:383–399.
Victor, J.D. (1992) Nonlinear systems analysis in vision: Overview of kernel methods, In: Nonlinear Vision: Determination of Neural Receptive Fields, Function, and Networks, R.B. Pinter & B. Nabet, Eds., CRC Press, Boca Raton, Florida.
Volterra, V. (1932) The Theory of Functionals and of Integral and Integro-Differential Equations, Blackie London, England
Wiener, N. (1958) Nonlinear Problems in Random Theory, John Wiley & Sons, New York, New York.
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Benardete, E.A., Victor, J.D. (1994). An Extension of the M-Sequence Technique for the Analysis of Multi-Input Nonlinear Systems. In: Marmarelis, V.Z. (eds) Advanced Methods of Physiological System Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9024-5_4
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DOI: https://doi.org/10.1007/978-1-4757-9024-5_4
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