AN ADAPTIVE ESTIMATION OF PERIODIC SIGNALS USING A FOURIER LINEAR COMBINER

Here, me present an adaptive algorithm for estimating from noisy obser vations, periodic signals of known period subject to transient disturb ances. The estimator is based on the LMS algorithm and works by tracki ng the Fourier coefficients of the data. The estimator is analyzed for convergence, noise misadjustment and lag misadjustment for signals wi th both time invariant and time variant parameters. The analysis is gr eatly facilitated by a change of variable that results in a time invar iant difference equation. At sufficiently small values of the LMS step size, the system is shown to exhibit decoupling with each Fourier com ponent converging independently and uniformly. Detection of rapid tran sients in data with low signal to noise ratio can be improved by using larger step sizes for more prominent components of the estimated sign al. An application of the Fourier estimator to estimation of brain evo ked responses is included.