An Accurate Method for Frequency Estimation of a Real Sinusoid

Abstract

It is well known that the positive- and negative-frequency components of a real sinusoid spectrally interact with each other; thus, introducing bias in frequency estimation based on the periodogram maximization. We propose to filter out the negative-frequency component. To that end, a coarse frequency estimation is obtained using the windowing approach, known to reduce the estimation bias, and then used to filter out the negative-frequency component via modulation and discrete Fourier transform bin excision approach. Fine estimation is performed using accurate frequency estimators, developed for complex sinusoids, on the filtered signal. The proposed method is characterized by the $ O(N\log _2N)$ complexity in terms of additions/multiplications and the $ O(N)$ complexity in terms of sine/cosine operations and comparisons. Moreover, it achieves the Cramer–Rao lower bound and is not sensitive to sinusoid frequency and initial phase, thus, outperforming the state-of-the-art methods.