Generalized frequency estimator with rational combination of three spectrum lines

The popular Discrete Fourier Transform (DFT) is known to be a sub-optimal frequency estimation technique for a finite transform length. In order to approach the Cramer-Rao Lower Bound (CRLB), many refinement techniques have been considered, but little considering both zero padding or tapering, also known as windowing or apodisation. In this paper, a frequency estimator with closed-form combination of three DFT samples is generalized to zero padding and tapered data within the class of cosine windowing. Root Mean Squared Error (RMSE) is shown to approach the CRLB in the case of a single tone signal with additive white Gaussian noise. Compared to state-of-the-art techniques, the proposed algorithm improves the frequency RMSE up to 1 dB when using significant zero-padding lengths (K ≥ 2 N) and for small to moderate SNR, which is the most challenging case for practical radar applications.