Determination of the analytical parametric relationship for output spectrum of Volterra systems based on its parametric characteristics

Xingjian Jing, Ziqiang Q. Lang, Stephen A. Billings

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)


The output frequency response function (OFRF) of Volterra systems can be described as a polynomial function of model parameters. However, the analytical determination of the OFRF is very computationally intensive, especially for higher order OFRF. To circumvent this problem, a numerical method can be adopted, provided that a series of simulation or experimental data for this polynomial function are given. In this study, it is theoretically shown that the analytical parametric relationship of OFRF up to any order can be determined accurately by using a simple Least Square method and every specific component of the output spectrum can also be determined explicitly, based on the OFRF's parametric characteristics. Practical techniques to obtain a unique and accurate solution for the Least Square method are discussed. This study provides a fundamental result for the determination of the analytical parametric relationship for this kind of system polynomial functions by using numerical methods.
Original languageEnglish
Pages (from-to)694-706
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Mar 2009
Externally publishedYes


  • Nonlinear systems
  • Output frequency response function
  • Parametric characteristics
  • Polynomial systems
  • Volterra systems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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