Synthesis of legal Wigner filter

A novel approach is proposed where time-varying filtering is carried out by an approximate filter belonging to the class of legal Wigner space filters. A legal Wigner filter is one that guarantees legality of the time-frequency output signal, for an arbitrary input signal, i.e. the time-frequency output is a distribution corresponding to a unique desired time signal. Two classes are identified: (1) the class of linear time-varying filters, and (2) a class of nonlinear (bilinear) filters. Imposition of the least-squared error criterion leads in either case to eigenvalue problems coupled with a renormalization of the eigenvectors