LEGAL WIGNER SPACE FILTERING AND ITS INTERPRETATION

Filtering in Wigner space generates a time-frequency function that doe s not generally constitute a legal Wigner distribution (WD). The notio n 'legal WD' implies a time-frequency function, specified in Wigner sp ace, for which a time-domain signal exists. This illegality prevents a n exact synthesis of the corresponding time signal, and resorting to a n approximate synthesis procedure is unavoidable. Presented herein are necessary and sufficient conditions, on a filter specified in Wigner space, that guarantee the legality of the output signal. We prove that legal Wigner space filters belong either to the class of linear time- variant filters or to the class of nonlinear (quadratic) filters. Thes e two classes possess vastly different characteristics.