Bias Reduction for Direct Frequency Estimator of Complex Sinusoid

Frequency estimation of single-tone complex sinusoid is a fundamental problem in signal processing. An efficient way to estimate the frequency is to directly calculate the frequency from three discrete Fourier transform coefficients in the neighborhood of peak magnitude spectrum. Because of the approximation used in the calculation, these direct estimators exhibit non-uniform biases. In this paper, we first derive a general analytical expression for the direct estimators. Applying Taylor series to the general expression, we find two new direct estimators that can eliminate the bias up to the fourth order approximation. Experiments show that the new estimators can reduce the bias by at least five orders at large frequency offset as compared to the current best direct estimator.