Volterra series
E645177
The Volterra series is a mathematical framework that generalizes the Taylor series to model nonlinear and time-varying systems, widely used in physics, engineering, and signal processing.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
functional series
ⓘ
integral series ⓘ mathematical expansion ⓘ nonlinear system representation ⓘ |
| appliedTo |
RF power amplifier modeling
ⓘ
biological system modeling ⓘ loudspeaker modeling ⓘ optical communication systems ⓘ |
| assumes |
causality in many applications
ⓘ
fading memory in many applications ⓘ |
| basedOn | multidimensional convolution integrals ⓘ |
| challenge |
computational complexity grows rapidly with order
ⓘ
kernel estimation complexity ⓘ |
| domain |
continuous-time systems
ⓘ
discrete-time systems ⓘ |
| field |
functional analysis
ⓘ
nonlinear dynamics ⓘ systems theory ⓘ |
| firstOrderTermEquivalentTo | linear convolution ⓘ |
| generalizes | Taylor series NERFINISHED ⓘ |
| hasComponent |
Volterra kernels
NERFINISHED
ⓘ
first-order Volterra kernel ⓘ higher-order Volterra kernels ⓘ second-order Volterra kernel ⓘ |
| hasRepresentation |
discrete Volterra series
ⓘ
frequency-domain Volterra series ⓘ time-domain Volterra series ⓘ |
| higherOrderTermsCapture | nonlinear interactions ⓘ |
| introducedBy | Vito Volterra NERFINISHED ⓘ |
| models |
fading-memory systems
ⓘ
nonlinear input-output relationships ⓘ time-varying systems ⓘ weakly nonlinear systems ⓘ |
| namedAfter | Vito Volterra NERFINISHED ⓘ |
| property |
can approximate any fading-memory nonlinear system under suitable conditions
ⓘ
nonparametric representation ⓘ |
| relatedTo |
Hammerstein model
NERFINISHED
ⓘ
Wiener model NERFINISHED ⓘ Wiener series NERFINISHED ⓘ polynomial nonlinear models ⓘ |
| requires | identification of Volterra kernels ⓘ |
| usedIn |
biomedical engineering
ⓘ
communications engineering ⓘ control theory ⓘ nonlinear system analysis ⓘ physics ⓘ signal processing ⓘ time-varying system analysis ⓘ |
Referenced by (1)
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