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IEEE Trans Biomed Eng. 1991 Sep;38(9):834-45.

Nonlinear system identification by m-pulse sequences: application to brainstem auditory evoked responses.

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Department of Electrical and Computer Engineering, University of Wisconsin, Madison 53705.


The purpose of this paper is to introduce a method for characterizing the nonlinear behavior of the auditory system. The method uses an m-pulse sequence as the stimulus and employs a general nonlinear framework for the auditory system. Like Sutter's binary m-sequence approach, the m-pulse sequence approach is computationally efficient since calculation of the first-order input-output cross-correlation function is all that is necessary for obtaining the nonlinear characteristics of the system. The nonlinear system characteristics are reflected in pulse kernels in contrast to binary kernels associated with the binary m-sequence approach. By assuming the system under study is a third-order nonlinear system, binary and pulse kernels are shown to be related to Volterra kernels. The results suggest that the m-pulse sequence can be used to study the system nonlinear effects of varying the stimulus repetition rate more effectively than conventional methods. Preliminary physiological data obtained by applying m-pulse sequences to the brainstem auditory evoked response (BAER) clearly illustrates the feasibility of obtaining replicable evoked responses using this method.

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