An Intrinsic Metric for Power Spectral Density Functions

An Intrinsic Metric for Parts

Spectral global intrinsic symmetry invariant functions

We introduce spectral Global Intrinsic Symmetry Invariant Functions (GISIFs), a class of GISIFs obtained via eigendecomposition of the Laplace-Beltrami operator on compact Riemannian manifolds, and provide associated theoretical analysis. We also discretize the spectral GISIFs for 2D manifolds approximated either by triangle meshes or point clouds. In contrast to GISIFs obtained from geodesic d...

Estimating Spectral Density Functions Robustly

• We consider in the following the problem of robust spectral density estimation. Unfortunately, conventional spectral density estimators are not robust in the presence of additive outliers (cf. [18]). In order to get a robust estimate of the spectral density function, it turned out that cleaning the time series in a robust way first and calculating the spectral density function afterwards lead...

Kullback-Leibler approximation of spectral density functions

We introduce a Kullback-Leibler type distance between spectral density functions of stationary stochastic processes and solve the problem of optimal approximation of a given spectral density Ψ by one that is consistent with prescribed second-order statistics. In general, such statistics are expressed as the state covariance of a linear filter driven by a stochastic process whose spectral densit...

Generating data with prescribed power spectral density

Data generation is straightforward if the parameters of a time series model define the prescribed spectral density or covariance function. Otherwise, a time series model has to be determined. An arbitrary prescribed spectral density will be approximated by a finite number of equidistant samples in the frequency domain. This approximation becomes accurate by taking more and more samples. Those s...