A Midpoint-Search Frequency Estimator Based on the Discrete Fourier Transform (MS-DFT)

This paper proposes a frequency-estimation method based on an iterative midpoint search applied to the discrete Fourier transform (MS-DFT). The method is designed to reduce the sensitivity of classical interpolation-based estimators to fractional-bin offsets and noise variations. The proposed approach exploits the unimodal structure of the spectral magnitude and performs iterative interval contraction using midpoint evaluation and magnitude ordering. This mechanism enables consistent estimation behavior across different spectral alignments without relying on interpolation formulas. Extensive simulations show that the method achieves a nearly constant ratio between the root mean square error (RMSE) and the Cramér–Rao lower bound (CRLB) over a wide range of signal-to-noise ratios (−7.5 dB to 65 dB). This behavior indicates stable relative efficiency with respect to the theoretical limit, rather than optimization at isolated operating points. In addition, the method reaches near-optimal accuracy within a small number of iterations (typically 8–9), resulting in low and predictable computational complexity. These properties make the MS-DFT estimator suitable for real-time and resource-constrained applications such as embedded sensing and biosignal processing.