Complex-Valued Noisy Sinewaves Frequency Estimator Based on DTFT Linearization and Interpolation

Abstract

This paper proposes an Interpolated Discrete-Time Fourier Transform (LIpDTFT) estimator for complex-valued noisy sinewave frequency based on the Linearization of the DTFT module behavior around the spectrum peak. It belongs to a class of LIpDTFT estimators that compensate the poor Discrete Fourier Transform (DFT) frequency resolution by interpolating two DTFT samples located very close to an initial frequency estimate. As compared with other DTFT-based frequency estimators recently proposed in the literature, the proposed LIpDTFT estimator ensures a smaller interpolation error and a lower processing effort. Moreover, if the rectangular window is adopted, it almost attains the unbiased Cramér-Rao Lower Bound (CRLB) even if a very small number of samples is analyzed. The accuracies ensured in different operating conditions by the proposed frequency estimator and other state-of-the-art DTFT-based algorithms are compared to each other through computer simulations.