Class-dependent, discrete time-frequency distributions via operator theory

We propose a property for kernel design which results in distributions for each of two classes of signals which maximally separates their energies in the time-frequency plane. Such maximally separated distributions may result in improved classification because the signal representation is optimized to accentuate the differences in signal classes. This is not the case with other time-frequency kernels which are optimized based upon some criteria unrelated to the classification task. Using our operator theory formulation for time-frequency representations, our "maximal separation" criteria takes on a very easily solved form. Analysis of the solution in both the time-frequency and ambiguity planes is given along with an example on discrete signals.