TIME-FREQUENCY PROJECTION FILTERS AND TIME-FREQUENCY SIGNAL EXPANSIONS

We consider the problems of designing a linear, time-varying filter wi th a specified ''time-frequency (TF) pass region'' and of constructing an orthonormal basis for the parsimonious expansion of signals locate d in a given TF support region. These problems of TF filtering and TF signal expansion are reduced to the problem of designing a ''TF subspa ce,'' i.e., a linear signal space comprising all signals located in a given TF region. Specifically, the TF filter is taken to be the orthog onal projection operator on the TF subspace. We present an optimum des ign of TF subspaces that is based on the Wigner distribution of a line ar signal space that was recently introduced and is an extension of th e well-known signal synthesis problem. The optimum TF subspace is show n to be an ''eigenspace'' of the TF region, and some properties of eig enspaces are discussed. The performance of TF projection filters and T F signal expansions is studied both analytically and via computer simu lation.