Linear filtering

Abstract

A simple linear smoothing operator of general order <italic>p</italic> is constructed for discretized functions. It is particularly suited for problems in numerical integration where it is necessary or desirable to suppress two-grid-interval waves. The operator is ideal in the sense that for the class of damping operators of order <italic>p</italic>, which remove two-grid-interval waves without changing the phase of any wave component, this operator produces the least damping of the amplitudes of all other waves.