About: Volterra series

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The Volterra series is a model for non-linear behavior similar to the Taylor series. It differs from the Taylor series in its ability to capture "memory" effects. The Taylor series can be used for approximating the response of a nonlinear system to a given input if the output of this system depends strictly on the input at that particular time. In the Volterra series the output of the nonlinear system depends on the input to the system at all other times. This provides the ability to capture the "memory" effect of devices like capacitors and inductors.

Attributes	Values
rdf:type	person
rdfs:label	Serie di Volterra (it) Volterra series (en)
rdfs:comment	In matematica, lo sviluppo in serie di Volterra rappresenta un'espansione funzionale di un funzionale dinamico, non lineare e tempo-invariante, sviluppato insieme al teorema di Volterra, dal matematico Vito Volterra. Un sistema continuo tempo-invariante con ingresso ed uscita può essere espanso in serie di Volterra come: dove è chiamato kernel di Volterra di ordine n, e può essere visto come una generalizzazione della risposta impulsiva. (it) The Volterra series is a model for non-linear behavior similar to the Taylor series. It differs from the Taylor series in its ability to capture "memory" effects. The Taylor series can be used for approximating the response of a nonlinear system to a given input if the output of this system depends strictly on the input at that particular time. In the Volterra series the output of the nonlinear system depends on the input to the system at all other times. This provides the ability to capture the "memory" effect of devices like capacitors and inductors. (en)
dcterms:subject	Mathematical series Functional analysis
Wikipage page ID	5811728 (xsd:integer)
Wikipage revision ID	1108961807 (xsd:integer)
Link from a Wikipage to another Wikipage	Capacitor Neural network Non-parametric Homogeneous function Paul Lévy (mathematician) Uniformly bounded Vito Volterra Intermodulation Compact space Massachusetts Institute of Technology Mathematics Maurice René Fréchet Polynomial signal processing Operator theory Equicontinuity Functional (mathematics) Georgios B. Giannakis Empirical risk minimization Function space Time-invariant system White noise Linear regression Nonlinear Norbert Wiener Causal system Mathematical series Taylor series Arzelà–Ascoli theorem Functional analysis Biomedical engineering Dirac delta function Frequency mixer Inductor Integral kernel Brownian motion System identification Neuroscience Impulse response Computational learning theory Multilayer perceptron Wiener series dbr:Feedforward_network
Link from a Wikipage to an external page	http://alexandria.tue.nl/extra1/erap/publichtml/7704263.pdf http://rfic.eecs.berkeley.edu/~niknejad/ee242/pdf/volterra_book.pdf
sameAs	Volterra series Volterra series Volterra series Volterra series
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Short_description
has abstract	The Volterra series is a model for non-linear behavior similar to the Taylor series. It differs from the Taylor series in its ability to capture "memory" effects. The Taylor series can be used for approximating the response of a nonlinear system to a given input if the output of this system depends strictly on the input at that particular time. In the Volterra series the output of the nonlinear system depends on the input to the system at all other times. This provides the ability to capture the "memory" effect of devices like capacitors and inductors. It has been applied in the fields of medicine (biomedical engineering) and biology, especially neuroscience. It is also used in electrical engineering to model intermodulation distortion in many devices, including power amplifiers and frequency mixers. Its main advantage lies in its generality: it can represent a wide range of systems. Thus it is sometimes considered a non-parametric model. In mathematics, a Volterra series denotes a functional expansion of a dynamic, nonlinear, time-invariant functional. Volterra series are frequently used in system identification. The Volterra series, which is used to prove the Volterra theorem, is an infinite sum of multidimensional convolutional integrals. (en) In matematica, lo sviluppo in serie di Volterra rappresenta un'espansione funzionale di un funzionale dinamico, non lineare e tempo-invariante, sviluppato insieme al teorema di Volterra, dal matematico Vito Volterra. Un sistema continuo tempo-invariante con ingresso ed uscita può essere espanso in serie di Volterra come: dove è chiamato kernel di Volterra di ordine n, e può essere visto come una generalizzazione della risposta impulsiva. (it)
gold:hypernym	Model
prov:wasDerivedFrom	wikipedia-en:Volterra_series?oldid=1108961807&ns=0
page length (characters) of wiki page	22395 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Volterra_series
is Link from a Wikipage to another Wikipage of	Vito Volterra Intermodulation Chronological calculus Stephen P. Boyd Functional differential equation Adaptive filter Linear-nonlinear-Poisson cascade model Linear response function Nonlinear system identification Fiber-optic communication High-dimensional model representation Spike-triggered average Volterra (disambiguation) Volterra Semiconductor Wiener series Non-linear multi-dimensional signal processing Nonlinear system Volterra Series Volterra expansion Volterra kernel
is Wikipage redirect of	Volterra Series Volterra expansion Volterra kernel
is Wikipage disambiguates of	Volterra (disambiguation)
is foaf:primaryTopic of	wikipedia-en:Volterra_series

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