Time-frequency signal synthesis with time-frequency extrapolation and don't-care regions

The application of Wigner distribution (WD)-based signal synthesis to signal separation problems is often adversely affected by WD interference terms. We present a modified signal synthesis method where the use of a masked WD allows the definition of don’t-care regions. In the don’t-care regions, detrimental interference terms (whose timefrequency location is assumed to be known) are ignored. The synthesis result is calculated using a modified version of the quasi power algorithm previously proposed for smoothed WD’s. The new synthesis method is shown to possess a desirable time-frequency extrapolation capability as well as a potential tendency to produce spurious signal components in the don’t-care regions. The occurrence of spurious signal components can be avoided by the inclusion of an “energy penalty.” I. SIGNAL SYNTHESIS USING MASKED WIGNER DISTRIBUTIONS The discrete-time Wigner distribution’ (WD) [ 11, [2] I V ~ ( n , B ) = 2 c,. ( n , m )