Invertible time-frequency surfaces

A classical problem in time-frequency (TF) analysis is the inversion of a TF surface to recover a signal whose TF representation is that surface. A class of invertible surfaces is presented. In this class, simple processes may be used to recover the signal and "spectrum" directly from the surface. These surfaces are linear generalizations of one-dimensional linear transforms, and may be complex valued. It is shown that several of the paradoxes associated with nonlinear surfaces may be resolved in invertible surfaces.