Recursive implementation of statistically-optimal null filters

Statistically-optimal null filters (SONFs), based on the combination of the maximum output SNR and the least-squares criteria, have been recently presented in literature. Orthogonality of the basis functions used in the series representation of the signal in question plays a key role in the implementation of such filters. In this paper, we first present the globally-optimal SONF, wherein the orthogonalization procedure is not necessary and then show how it can be implemented recursively. Simulation results are presented comparing the Gram-Schmidt (GS)-orthogonalized SONF, recursive SONF and the constrained notch filter (CNF). Ability of the SONFs to process short duration signals is emphasized.