Iterative sine-wave frequency estimation by generalized Fourier interpolation algorithms

In this paper two iterative interpolation algorithms proposed in the scientific literature for estimating the frequency of complex-valued sine-waves are generalized to a generic Maximum Sidelobe Decay (MSD) window in order to achieve highly accurate estimates even when real-valued pure or harmonically distorted sine-waves are analyzed. The analytical expressions for the frequency estimations formulas are derived. Moreover the accuracy achieved when pure, noisy, and noisy and harmonically distorted sine-waves are analyzed is compared with those provided by the classical Interpolated Discrete Fourier Transform (IpDFT) and three-point IpDFT algorithms through computer simulations. The performed comparison allows us to determine in which situations the proposed algorithms can be advantageously used.