SpectralModelFactory

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../../_images/SpectralModelFactory.png
class SpectralModelFactory(*args)

Base class for spectral model factory.

Parameters
mySpectralModelFactoryImplementationSpectralModelFactoryImplementation

One spectral factory algorithm.

By default, the Welch factory algorithm WelchFactory.

Notes

Let X: \Omega \times \cD \rightarrow \Rset^d be a multivariate second order stationary process, with zero mean, where \cD \in \Rset^n. We only treat here the case where the domain is of dimension 1: \cD \in \Rset (n=1).

If we note C(\vect{s}, \vect{t})=\Expect{(X_{\vect{s}}-m(\vect{s}))\Tr{(X_{\vect{t}}-m(\vect{t}))}} its covariance function, then for all (i,j), C^{stat}_{i,j} : \Rset^n \rightarrow \Rset^n is \cL^1(\Rset^n) (ie \int_{\Rset^n} |C^{stat}_{i,j}(\vect{\tau})|\di{\vect{\tau}}\, < +\infty), with C^{stat}(\vect{\tau}) = C(\vect{s}, \vect{s}+\vect{\tau}) as this quantity does not depend on \vect{s}.

The bilateral spectral density function S : \Rset^n \rightarrow \mathcal{H}^+(d) exists and is defined as the Fourier transform of the covariance function C^{stat} :

\forall \vect{f} \in \Rset^n, \,S(\vect{f}) = \int_{\Rset^n}\exp\left\{-2i\pi <\vect{f},\vect{\tau}> \right\} C^{stat}(\vect{\tau})\di{\vect{\tau}}

where \mathcal{H}^+(d) \in \mathcal{M}_d(\Cset) is the set of d-dimensional positive definite hermitian matrices.

Depending on the available data, we proceed differently :

-if the data correspond to several independent realizations of the process, the estimation is done using the empirical estimator;

  • if the data correspond to one realization of the process, we suppose the process is ergodic to split the realization into several ones.

Methods

build(*args)

Estimate the spectral model from data.

getClassName()

Accessor to the object's name.

getFFTAlgorithm()

Accessor to the FFT algorithm used for the Fourier transform.

getId()

Accessor to the object's id.

getImplementation()

Accessor to the underlying implementation.

getName()

Accessor to the object's name.

setFFTAlgorithm(fft)

Accessor to the FFT algorithm used for the Fourier transform.

setName(name)

Accessor to the object's name.
__init__(*args)
build(*args)

Estimate the spectral model from data.

Available constructors:

build(myTimeSeries)

build(myProcessSample)

Parameters
myTimeSeriesTimeSeries

The time series from which the spectral model is estimated.

myProcessSampleProcessSample

The sample of time series from which the spectral model is estimated.

Returns
mySpectralModelSpectralModel

The estimated spectral model.

getClassName()

Accessor to the object’s name.

Returns
class_namestr

The object class name (object.__class__.__name__).

getFFTAlgorithm()

Accessor to the FFT algorithm used for the Fourier transform.

Returns
fftAlgoFFT

The FFT algorithm used for the Fourier transform.

getId()

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getImplementation()

Accessor to the underlying implementation.

Returns
implImplementation

A copy of the underlying implementation object.

getName()

Accessor to the object’s name.

Returns
namestr

The name of the object.

setFFTAlgorithm(fft)

Accessor to the FFT algorithm used for the Fourier transform.

Parameters
fftAlgoFFT

The FFT algorithm used for the Fourier transform.

setName(name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.