Method and system for statistical filters and design of statistical filters

A statistical filter, comprising:

• a set of transition probabilities, the set of transition probabilities determined by:
• mapping a power spectrum to find pole locations that approximate the power spectrum;
• determining a set of eigenvalues, wherein determining the set of eigenvalues comprises mapping the pole locations to the edges of, or inside of, a polygon laying inside a unit circle, the polygon having the same number of sides as an order of the statistical filter and a vertex mapped to unity;
• obtaining a stochastic matrix from the set of eigenvalues, wherein the stochastic matrix comprises the set of transition probabilities;
• and
• storing the set of transition probabilities.

A statistical filter for implementing a band stop filter for use with a UWB signal, comprising:

• a set of transition probabilities, the set of transition probabilities determined by:
• mapping a power spectrum to find pole locations that approximate the power spectrum, wherein the power spectrum has substantially reduced power between around 3.5 GHz and around 4.2 GHz.;
• determining a set of eigenvalues, wherein determining the set of eigenvalues comprises mapping the pole locations to the edges of, or inside of, a polygon laying inside a unit circle, the polygon having the same number of sides as an order of the statistical filter and a vertex mapped to unity;
• obtaining a circulant matrix from the set of eigenvalues, wherein the circulant matrix comprises the set of transition probabilities;
• and
• storing the set of transition probabilities.

A method for implementing a statistical filter, comprising:

• mapping a power spectrum to find pole locations that approximate the power spectrum;
• determining a set of eigenvalues, wherein determining the set of eigenvalues comprises mapping the pole locations to the edges of, or inside of, a polygon laying inside a unit circle, the polygon having the same number of sides as an order of the statistical filter and a vertex mapped to unity;
• obtaining a stochastic matrix from the set of eigenvalues, wherein the stochastic matrix comprises a set of values;
• utilizing the set of values of the stochastic matrix as transition probabilities for the statistical filter;
• and
• filtering a signal using the statistical filter.