Faà Di Bruno's formula and volterra series

Daniel E. Clark, Jeremie Houssineau

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


Volterra series are used for modelling nonlinear systems with memory effects. The nth-order impulse response and the kernels in the series can be determined with Fréchet derivatives of Volterra series operators. Consequently, we can determine the kernels of composite systems by taking higher-order Fréchet derivatives of composite series. The generalisation of the higher-order chain rule, Faà di Bruno's formula for variational calculus, was recently determined and this note demonstrates how it can be used to determine kernels for composite Volterra series operators.

Original languageEnglish
Title of host publicationIEEE Workshop on Statistical Signal Processing Proceedings
Number of pages3
ISBN (Print)9781479949755
Publication statusPublished - 1 Jan 2014
Event17th IEEE Workshop on Statistical Signal Processing 2014 - Gold Coast, Australia
Duration: 29 Jun 20142 Jul 2014


Conference17th IEEE Workshop on Statistical Signal Processing 2014
Abbreviated titleSSP 2014
CityGold Coast

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications


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