Frequency estimation from phase differences

In recent publication, S. Kay (1988) described a method of estimating the frequency of a complex exponential from noisy samples of the time waveform. The method is attractive because of its computational simplicity, because it is based on phase differences (which may already be available at no cost in some systems), and because its performance attains the Cramer-Rao bound at high SNR. The authors present a novel derivation of Kay´s method, extend it to the estimation of the parameters of linear FM chirps and of multiple signals, provide an adaptive version of the algorithm, and provide an explanation for the threshold behavior of phase difference methods