Accurate frequency estimation through iterative parabolic interpolations

Extracting the frequency from a complex signal is a common task in many applications, and multiple methods exist for accurate frequency estimation under different noise conditions. Iterative algorithms based on the interpolation of the discrete Fourier transform (DFT) are known to achieve high accuracy, and methods that employ auxiliary coefficients around the peak of the DFT are recurrent in the literature. This paper presents a novel iterative algorithm for frequency estimation based on successive parabolic interpolations of three DFT coefficients. Unlike other similar methods, which typically require auxiliary fine estimators for bias reduction, the proposed method refines the frequency estimate by progressively decreasing the offset of the DFT coefficients employed at each iteration. This approach eliminates the need for external correction steps and enhances estimation accuracy as the interpolation narrows around the true frequency. The algorithm achieves performance very close to the Cramér-Rao lower bound while maintaining computational efficiency, and the fine estimation step implemented can be flexibly applied to signals with or without zero-padding, making its use suitable for a wide range of signal processing applications. Simulations confirm the high accuracy and robustness to noise of the proposed estimator, showing comparable or better performance than existing iterative techniques.