Time reversal and the spatio-temporal matched filter (L)

Abstract

It is known that focusing of an acoustic field by a time-reversal mirror (TRM) is equivalent to a spatio-temporal matched filter under conditions where the Green’s function of the field satisfies reciprocity and is time invariant, i.e., the Green’s function is independent of the choice of time origin. In this letter, it is shown that both reciprocity and time invariance can be replaced by a more general constraint on the Green’s function that allows a TRM to implement the spatio-temporal matched filter even when conditions are time varying.