On filtering short-duration sinusoids, periodic signals and damped sinusoids

Adaptive filtering of damped sinusoids is considered in this paper. Damped sinusoids include sinusoids as a special case. The recently proposed instantaneous matched filter (IMF) approach, its limitation, and a remedy, are discussed. Its recursive implementation that circumvents the limitation is shown to consist of the same equations as those of recursive least squares (RLS) adaptive linear combiner. A procedure that does not require a knowledge of the frequencies and damping factors, is discussed. Its modified version leads to the idea of using projection matrix for orthogonalization, and to the interpretation that an autoregressive RLS scheme is an adaptive null-filter to the class of sinusoidal signals.