Statistically optimal null filters for processing short record length signals

In this paper, we propose an alternate non-parametric statistically optimal method of null filtering. One of the important features of this method lies in its ability to process signals of short record lengths. The optimality criteria for maximum output SNR and the minimum mean-square error are combined to generate the new approach. The method is first designed for the coherent case (where the desired signal shape is a priori known) and later extended to include the non-coherent case based on orthogonal signal expansion. To deal with a non-orthogonal signal expansion, we propose a sliding Gram-Schmidt orthogonalization. An application to separate two closely spaced damped sinusoids is considered. Simulation results are presented comparing the proposed methods with the conventional one based on Constrained Notch Filtering