Frequency Estimation in Interpolated Discrete Fourier Transform With Generalized Maximum Sidelobe Decay Windows for the Control of Power
Józef Borkowski, Janusz Mroczka, Adam Matusiak, Dariusz Kania
Abstract
The study presented in this article demonstrates that the sin <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> time window family is an extension of class I Rife-Vincent windows to a more general class, i.e., generalized maximum sidelobe decay (GMSD) windows. The presented frequency characteristics and other useful formulas derived for GMSD windows allow the derivation of a method to estimate the frequency of a sinusoidal component of a multifrequency signal based on the interpolated discrete Fourier transform. The presented estimation method is a significant generalization of methods already known. The method uses GMSD windows and takes into account the conjugate component in the spectrum. The method can be widely used, and, in particular, it allows for fast and accurate estimation of the frequency for a short data record (even below 1-2 signal periods). One of the many possible applications is frequency estimation in a power control system, which was studied in the accuracy analysis.