Frequency estimation of sinusoids from nonuniform samples

Abstract

Sinusoid signals with multiple frequencies appear in various systems and their frequencies may carry some important features. Frequency estimation from their discrete samples is one of the fundamental problems and many frequency estimators have been proposed for uniform sampling setting. In this paper, frequency estimators based on adaptive notch filtering are proposed for nonuniform sampling setting. We observe that some dynamic systems associated with adaptive notch filters can be solved in nonuniformly sampled time steps with high accuracy. This leads us to propose a digital adaptive notch filtering method to estimate frequency of a sinusoidal signal with single frequency from its nonuniform samples. The proposed method exhibits convergent and robust frequency estimation in the presence of random sampling noises, and its variance is comparable to the Cramer–Rao lower bound in the presence of additive white noise. The above method designed for single frequency estimation could track abrupt single frequency change of an input signal, but it is not applicable directly for multiple frequency estimation. Our simulations show that the proposed estimators have robust performance for sinusoidal signals with multiple distinct frequencies, and they can be used to separate two very close frequencies of an input signal in a highly noisy sampling environment.