Simple and Accurate Bias and Variance Expressions of Some Instantaneous Frequency Estimators including the DESAs

Instantaneous estimation of the frequency of a real sinusoid in noise from a small number of data samples is an important problem in the signal processing area. Several frequency estimators are proposed for this problem in the literature. In this paper, some of the popular ones including the discrete energy separation algorithms (DESAs) are considered. Using a Taylor series expansion technique, very simple and yet accurate closed form expressions for the bias and the variance of the estimators are derived. Computer simulations are included to validate the theoretical results.