Strong Consistency of the Contraction Mapping Method for Frequency Estimation

Abstract

Consider the super position of a sinusoid plus noise. By the application of certain parametric filter, the first-order autocorrelation becomes a contraction mapping. The sample estimator of the first-order autocorrelation is also a contraction whose fixed point converges almost surely to the cosine of the frequency to be detected. The theory is illustrated by two specific examples corresponding to two different parametric filters,