# 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**

It is associated to the Kronecker covariance model built upon an exponential covariance model (AbsoluteExponential). The Cauchy spectral model is defined by:

(1)¶

where is the covariance matrix of the Kronecker covariance model and is the vector of scale parameters of the AbsoluteExponential covariance model.