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 a projection matrix for orthogonalization, and to the interpretation that an autoregressive RLS scheme is an adaptive null-filter to the class of sinusoidal signals.