A theory of adaptive filtering

This paper considers the adaptive signal extraction problem for time-discrete data when only very general a priori assumptions regarding the distributions of signal and noise are possible. Specifically, it is assumed that the noise is white, additive, and signal independent with mean zero and unknown variance and that the signal is band-limited. No stationarity assumptions are required. After a procedure is found under these conditions, the mean-square-error is derived asymptotically under narrower conditions-stationary Gaussian data with mean zero. Finally, a method of estimating the error variance from the data (without knowing the signal directly) is found.