Sequential frequency estimation and detection using the discrete Fourier transform

This paper addresses the problem of obtaining a coherent gain in signal-to-noise ratio by recursively processing blocks of Fourier transform data for detecting the presence of a sinusoidal signal in noise and estimating its frequency. The method described here consists of recursively estimating the change of phase angle of the signal component as successive DFT coefficients are processed and using this estimate to rotate the successive complex coefficients so that the signal components tend to have the same phase, i.e., are aligned. The approach is based upon maximum-likelihood estimation theory. Two different algorithms are presented here for estimating this rate of change of phase: a) an extended Kalman filtering algorithm using the complex DFT coefficients, and b) a linear Kalman filtering algorithm using the phase angle of the DFT coefficients. These algorithms require a fixed memory for their implementation, independent of the number of transforms processed. Computer simulation results are presented to assess the performance of the algorithms.