# 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:

See

`CauchyModel`

Examples: