Accurate single-tone frequency estimation from DFT coefficients using time-window´s frequency spectrum

Frequency estimation algorithms are utilized to find target doppler frequency accurately in radars using DFT/FFT doppler filter-banks and target range in FMCW radars. Although there are many different single-tone frequency estimation methods published in the literature, the algorithms that combine few of the DFT/FFT coefficients around the target frequency with simple arithmetic operations are of interest because of their low computational-complexity. Although these techniques are reasonably accurate, almost all of them assume no window is applied before DFT/FFT operation. However, in reality, a tapered window is often used to minimize the frequency spread from the sidelobes of time-window´s frequency spectrum. When such windows are used, either those algorithms do not work at all or the estimate is multiplied by some heuristic numbers to improve the results. In this work, we propose a method that can be used by any window applied prior to DFT/FFT operation. We use time-window´s frequency spectrum sampled at a fractional resolution of DFT/FFT order as a template to accurately find the frequency of the tone. Experiments shows that frequency estimation error variance approaches the Cramer-Rao bound for all time-windows. Therefore, this algorithm not only allows the use of any time-window before FFT/DFT operation, but also provides excellent performance with low computational-complexity.