  Fourier methods well known in signal processing are applied to
three-dimensional wave propagation problems. The Fourier transform of the Green
function, when written explicitly in terms of a real-valued spatial frequency,
consists of homogeneous and inhomogeneous components. Both parts are necessary
to result in a pure out-going wave that satisfies causality. The homogeneous
component consists only of propagating waves, but the inhomogeneous component
contains both evanescent and propagating terms. Thus we make a distinction
between inhomogenous waves and evanescent waves. The evanescent component is
completely contained in the region of the inhomogeneous component outside the
k-space sphere. Further, propagating waves in the Weyl expansion contain both
homogeneous and inhomogeneous components. The connection between the Whittaker
and Weyl expansions is discussed. A list of relevant spherically symmetric
Fourier transforms is given.
