Faà Di Bruno's formula and volterra series

Daniel E. Clark; Jeremie Houssineau

doi:10.1109/SSP.2014.6884614

Faà Di Bruno's formula and volterra series

Daniel E. Clark, Jeremie Houssineau

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

Volterra series are used for modelling nonlinear systems with memory effects. The n^th-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 language	English
Title of host publication	IEEE Workshop on Statistical Signal Processing Proceedings
Publisher	IEEE
Pages	217-219
Number of pages	3
ISBN (Print)	9781479949755
DOIs	https://doi.org/10.1109/SSP.2014.6884614
Publication status	Published - 1 Jan 2014
Event	17th IEEE Workshop on Statistical Signal Processing 2014 - Gold Coast, Australia Duration: 29 Jun 2014 → 2 Jul 2014

Conference

Conference	17th IEEE Workshop on Statistical Signal Processing 2014
Abbreviated title	SSP 2014
Country/Territory	Australia
City	Gold Coast
Period	29/06/14 → 2/07/14

ASJC Scopus subject areas

Electrical and Electronic Engineering
Applied Mathematics
Signal Processing
Computer Science Applications

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10.1109/SSP.2014.6884614

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title = "Fa{\`a} Di Bruno's formula and volterra series",

abstract = "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 Fr{\'e}chet derivatives of Volterra series operators. Consequently, we can determine the kernels of composite systems by taking higher-order Fr{\'e}chet derivatives of composite series. The generalisation of the higher-order chain rule, Fa{\`a} 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.",

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AU - Houssineau, Jeremie

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N2 - 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.

AB - 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.

U2 - 10.1109/SSP.2014.6884614

DO - 10.1109/SSP.2014.6884614

M3 - Conference contribution

AN - SCOPUS:84907399727

SN - 9781479949755

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EP - 219

BT - IEEE Workshop on Statistical Signal Processing Proceedings

PB - IEEE

T2 - 17th IEEE Workshop on Statistical Signal Processing 2014

Y2 - 29 June 2014 through 2 July 2014

ER -

Faà Di Bruno's formula and volterra series

Abstract

Conference

ASJC Scopus subject areas

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