Parametric characteristic analysis for generalized frequency response functions of nonlinear systems

Xingjian Jing, Zi Qiang Lang, Stephen A. Billings

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)


In order to explicitly reveal the relationship between system frequency response functions and model parameters which define system nonlinearities, and consequently unveil a direct connection from model parameters to system frequency response characteristics, a parametric characteristic analysis approach is proposed for Volterra systems described by a nonlinear differential equation (NDE). The parametric characteristics of the generalized frequency response functions (GFRFs) for the NDE model are established, and some important properties are discussed, which can explicitly reveal what model parameters contribute and how these parameters affect the GFRFs. Based on the parametric characteristic analysis, it is demonstrated how the system frequency domain characteristics are related to the system time domain model parameters and how the output frequency response function can now be determined explicitly with a detailed polynomial structure. These new results provide a significant and novel insight into the analysis and design of nonlinear systems in the frequency domain. Several examples are included to illustrate the results.
Original languageEnglish
Pages (from-to)699-733
Number of pages35
JournalCircuits, Systems, and Signal Processing
Issue number5
Publication statusPublished - 23 Apr 2009
Externally publishedYes


  • Generalized frequency response functions (GFRFs)
  • Nonlinear differential equations (NDEs)
  • Nonlinear systems
  • Parametric characteristics
  • Volterra series

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics


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