Parametric spectral density functions
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
is a lattice.
is supposed to be a second order process with zero mean and
we suppose that its spectral density function
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
as a parametric model for the spectral density
The Cauchy spectral model
Its is associated to the Exponential covariance model. The Cauchy spectral model is defined by:
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).