# Parametric spectral density functions¶

Let be a multivariate stationary normal process of dimension . We only treat here the case where the domain is of dimension 1: ().
If the process is continuous, then . In the discrete case, is a lattice.
is supposed to be a second order process with zero mean and we suppose that its spectral density function defined in (8) exists. is the set of -dimensional positive definite hermitian matrices.
This use case illustrates how the User can create a density spectral function from parametric models. The library proposes the Cauchy spectral model as a parametric model for the spectral density function .

The Cauchy spectral model

Its is associated to the Exponential covariance model. The Cauchy spectral model is defined by:

(1)

where , and are the parameters of the Exponential covariance model defined in section [ParamStationaryCovarianceFunction]. The relation (1) can be explained with the spatial covariance function defined in (6).

API:

Examples: