The Estimation of Frequency

Numerical methods have been used for fitting sinusoids to data since the middle of the 18th century. Since the discovery of the Fast Fourier Transform by Cooley and Tukey in 1965, the techniques for estimating frequency have become computationally feasible. This review examines various techniques for estimating the frequency or frequencies of sinusoids in additive noise. The techniques fall into two categories - those based on Fourier, or frequency-domain methods, and those derived from a consideration of a small number of sample autocovariances. The Fourier techniques invariably have asymptotic variances of order T ^-3, where T is the sample size, and are particularly useful when T is large and the signal is noisy, whereas the other techniques are usually statistically inefficient, with asymptotic variances of order T ^-1, and are often biased, but because of their computational efficiency, can be useful when T is small and the signal is relatively noise free.