Asymptotic approach of generalized orthogonal functional expansions to Wiener kernels

Jonathan D. Victor

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Wiener-like orthogonal functional expansions may be constructed with respect to test ensembles that are non-Gaussian, nonwhite, or both. Although the original Wiener expansion has particularly advantageous analytical properties, orthogonal expansions constructed with respect to other ensembles have practical advantages for laboratory implementation. We show how functional expansions based on two classes of input ensembles - white but non-Gaussian discrete noises and the sum of sinusoids-converge to the standard Wiener kernels. For discrete noises, the disparity between the standard and nonstandard kernels of a linear-static nonlinear transducer is proportional to the kurtosis of the input signal and inversely proportional to the ratio of the integration time of the linear filter to the time discretization. For the sum of sinusoids, the disparity is inversely proportional to the effective number of sinusoids passed by the initial linear stage.

Original languageEnglish
Pages (from-to)383-399
Number of pages17
JournalAnnals of Biomedical Engineering
Issue number4
StatePublished - Jul 1991
Externally publishedYes


  • Central limit theorem
  • M-sequence
  • Nonlinear systems analysis
  • Orthogonal functional
  • Sum of sinusoids
  • Wiener kernel


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