# SpectralModel¶

class SpectralModel(*args)

Spectral density model.

Notes

We consider a multivariate stochastic process of dimension , where is an event, is a domain of , is a multivariate index and .

We note the random variable at index defined by and a realization of the process , for a given defined by .

If the process is a second order process, zero-mean and weakly stationary, we define its bilateral spectral density function with:

• is the set of d-dimensional positive hermitian matrices

Using the stationary covariance function with and the Fourier transform, the spectral density writes:

A SpectralModel object can be created only through its derived classes: CauchyModel

Methods

 __call__(frequency) Evaluate the spectral density function for a specific frequency. computeStandardRepresentative(frequency) Compute the standard representant of the spectral density function. draw(*args) Draw a specific component of the spectral density function. getAmplitude() Get the amplitude parameter of the spectral density function. getClassName() Accessor to the object’s name. getDimension() Get the dimension of the SpectralModel. getId() Accessor to the object’s id. getImplementation(*args) Accessor to the underlying implementation. getName() Accessor to the object’s name. getScale() Get the scale parameter of the spectral density function. getSpatialCorrelation() Get the spatial correlation matrix of the spectral density function. getSpatialDimension() Get the spatial dimension of the spectral density function. setAmplitude(amplitude) Set the amplitude parameter of the spectral density function. setName(name) Accessor to the object’s name. setScale(scale) Set the scale parameter of the spectral density function.
__init__(*args)
computeStandardRepresentative(frequency)

Compute the standard representant of the spectral density function.

Parameters: tau : float Frequency value. rho : Complex Standard representant factor of the spectral density function.

Notes

According to definitions in CovarianceModel, as the spectral density function is the Fourier transform of the stationary covariance function and using the expression of the last one, the spectral density function writes as a matrix-complex product where the matrix is the constant spatial covariance structure and the complex represents the standard representative:

Thus,

where is a covariance matrix that explains the covariance structure and

draw(*args)

Draw a specific component of the spectral density function.

Parameters: rowIndex : int, The row index of the component to draw. Default value is 0. columnIndex: int, :math:0 leq columnIndex < dimension The column index of the component to draw. Default value is 0. minimumFrequency : float The lower bound of the frequency range over which the model is plotted. Default value is SpectralModel-DefaultMinimumFrequency in ResourceMap. maximumFrequency : float The upper bound of the frequency range over which the model is plotted. Default value is SpectralModel-DefaultMaximumFrequency in ResourceMap. frequencyNumber : int, The discretization of the frequency range over which the model is plotted. Default value is SpectralModel-DefaultFrequencyNumber in class:~openturns.ResourceMap. module : bool Flag to tell if module has to be drawn (True) or if it is the argument to be drawn (False). Default value is True. graph : Graph Graphic of the specified component
getAmplitude()

Get the amplitude parameter of the spectral density function.

Returns: amplitude : Point The used amplitude parameter.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getDimension()

Get the dimension of the SpectralModel.

Returns: dimension : int Dimension of the SpectralModel.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getImplementation(*args)

Accessor to the underlying implementation.

Returns: impl : Implementation The implementation class.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getScale()

Get the scale parameter of the spectral density function.

Returns: scale : Point The used scale parameter.
getSpatialCorrelation()

Get the spatial correlation matrix of the spectral density function.

Returns: spatialCorrelation : CorrelationMatrix Correlation matrix .
getSpatialDimension()

Get the spatial dimension of the spectral density function.

Returns: spatialDimension : int SpatialDimension of the SpectralModel.
setAmplitude(amplitude)

Set the amplitude parameter of the spectral density function.

Parameters: amplitude : Point The amplitude parameter to be used in the spectral density function.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setScale(scale)

Set the scale parameter of the spectral density function.

Parameters: scale : Point The scale parameter to be used in the spectral density function. It should be of size dimension.