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The identification of nonlinear biological systems: Wiener kernel approaches

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Abstract

Detection, representation, and identification of nonlinearities in biological systems are considered. We begin by briefly but critically examining a well-known test of system nonlinearity, and point out that this test cannot be used to prove that a system is linear. We then concentrate on the representation of nonlinear systems by Wiener's orthogonal functional series, discussing its advantages, limitations, and biological applications. System identification through estimating the kernels in the functional series is considered in detail. An efficient time-domain method of correcting for coloring in inputs is examined and shown to result in significantly improved kernel estimates in a biologically realistic system.

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Authors and Affiliations

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

    Michael J. Korenberg

  2. Department of Biomedical Engineering and McGill Research Centre for Intelligent Machines, McGill University and the Canadian Institute for Advanced Research, Montreal, Canada

    Ian W. Hunter

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  1. Michael J. Korenberg
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Korenberg, M.J., Hunter, I.W. The identification of nonlinear biological systems: Wiener kernel approaches. Ann Biomed Eng 18, 629–654 (1990). https://doi.org/10.1007/BF02368452

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