On the Contraction Mapping Method for Frequency Detection

Abstract

The contraction mapping method for frequency estimation in the presence of noise, identifies the cosine of the frequency to be detected as a fixed point of a certain correlation mapping. At its hear, the method provides a plan for automatic self tuning of parametric filters. A variant of the method, called the HK algorithm, produces recursive zero-crossing rates (normalized HOC sequences) that converge to the frequency of interest. A statistical explanation for the contraction mapping method as epitomized by the HK algorithm is provided when the HOC sequences are produced by bandpass filters. The outright consistency of the zero-crossing rate is not required. Examples show that the method performs quite remarkably.