Abstract: A frequency can be estimated by few Discrete Fourier Transform (DFT) coefficients, see Rife and Vincent (1970), Quinn (1994, 1997). This approach is computationally efficient. However, the statistical efficiency of the estimator depends on the location of the frequency. In this paper, we explain this approach from a point of view of an Approximate Maximum Likelihood (AML) method. Then we enhance the efficiency of this method by using more DFT coefficients. Compared to 30% and 61% efficiency in the worst cases in Quinn (1994) and Quinn (1997), respectively, we show that if 13 or 25 DFT coefficients are used, AML will achieve at least 90% or 95% efficiency for all frequency locations.
Key words and phrases: Approximate Maximum Likelihood, discrete Fourier transform, efficiency, fast algorithm, frequency estimation, semi-sufficient statistics.