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Abstract

Systems and methods for the design or implementation of statistical filters for use in the spectral shaping of transmissions are disclosed. A desired power spectrum may be mapped to find pole locations that approximate the desired spectrum. These pole locations may then be mapped to the edge or inside of an equilateral polygon lying inside a unit circle, the equilateral polygon having the same number of sides as the order of the statistical filter desired and one vertex mapped to unity, to yield a set of eigenvalues. These eigenvalues may be the eigenvalues of a stochastic matrix the elements of which may be the Markov transition probabilities for use in a statistical filter designed to achieve the desired power spectrum. Use of a statistical filter employing these Markov transition values may be utilized to shape UWB or other signals to achieve the desired power spectrum.

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