Complete signal processing bases and the Jacobi group

The continuous windowed Fourier and wavelet transforms are created from the actions of the Heisenberg and affine groups, respectively. Both wavelet and windowed Fourier bases are known to be complete; that is, the only signal which is orthogonal to every element of each basis is the zero signal. The Jacobi group is a group which contains both the Heisenberg and affine groups, and it can also be used to produce bases for signal processing. This paper investigates completeness for bases of one and two real variables which are produced by the Jacobi group.