An Extension of the M-Sequence Technique for the Analysis of Multi-Input Nonlinear Systems

  • Ethan A. Benardete
  • Jonathan D. Victor

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.

Keywords

Kernel Estimate Volterra Series Volterra Kernel Order Kernel Functional Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Ethan A. Benardete
    • 1
    • 2
  • Jonathan D. Victor
    • 1
    • 2
  1. 1.Laboratory of BiophysicsThe Rockefeller UniversityUSA
  2. 2.Department of Neurology and NeuroscienceCornell University Medical CollegeUSA

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