  We give a uniform realization of the minimal representation of a double cover
of the conformal group SO(2,n+1)_0 in the kernel of the wave operator on flat
Minkowski space as a positive energy representation H^+ for n even and odd.
Using this realization, we obtain an explicit orthonormal basis for H^+ that is
well behaved with respect to energy and angular momentum. Of special note, for
n odd, all functions in our basis are rational functions. Finally, using
Fourier analysis with respect to this basis, we prove that every classical
real-valued solution to the wave equation is the real part of a unique
continuous element in the representation H^+.
