Frequency estimation by two- or three-point interpolated Fourier algorithms based on cosine windows

• Two iterative frequency Fourier interpolation algorithms are generalized.
• The expressions for the frequency estimators and the related variances are derived.
• Theoretical results are confirmed through computer simulations.
• Simulation results reveal the applications well suited for the proposed estimators.

This paper investigates the frequency estimation of a complex sinusoid obtained by interpolating two or three samples of the Discrete-Time Fourier Transform (DTFT) of a signal weighted by a suitable cosine window. Versions of the algorithms based on both DTFT complex values and modules are considered and the expressions for the related frequency estimators are provided. Iterative procedures are used in order to minimize the estimator variance due to additive wideband noise. Furthermore, the accuracies of the proposed estimators are verified and compared each other and with state-of-the art algorithms by means of computer simulations when applied to noisy or noisy and harmonically distorted complex sinusoids, respectively.