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Discrete frequency estimation using parametric filtering and the contraction mapping method

Recently several authors have investigated the use of parametric families of linear filters for discrete frequency estimation. The proposed methods are similar in that they use iterative filtering procedures for estimating the frequencies of underlying periodic components embedded in noise. In this paper we combine parametric filtering with a contraction mapping principle to recursively estimate the frequencies of discrete spectral components. By incorporating the contraction mapping idea with parametric filtering a fundamental property is determined which when satisfied, guarantees the convergence of the iterative procedure. Several examples are provided which illustrate the method.