  We study a class of localized solutions of the wave equation, called
eigenwavelets, obtained by extending its fundamental solutions to complex
spacetime in the sense of hyperfunctions. The imaginary spacetime variables y,
which form a timelike vector, act as scale parameters generalizing the scale
variable of wavelets in one dimension. They determine the shape of the wavelets
in spacetime, making them pulsed beams that can be focused as tightly as
desired around a single ray by letting y approach the light cone. Furthermore,
the absence of any sidelobes makes them especially attractive for
communications, remote sensing and other applications using acoustic waves. (A
similar set of "electromagnetic eigenwavelets" exists for Maxwell's equations.)
I review the basic ideas in Minkowski space, then compute sources whose
realization should make it possible to radiate and absorb such wavelets. This
motivates an extension of Huygens' principle allowing equivalent sources to be
represented on shells instead of surfaces surrounding a bounded source.
