ON THE DIMENSION OF THE DISCRETE WIGNER-VILLE TRANSFORM RANGE SPACE Application to time-frequency based detectors design

The information conveyed by the discrete Wigner-Ville representations of real, complex or analytic signals is highly redundant, each time-frequency location being related to others via non-obvious relationships. In this paper, we demonstrate that there also exists a large amount of linear relationships between time-frequency sample!;. This implies that a whole discrete Wigner-Ville representation can be detennined from linear combinations of some selected time-frequency locations. A simple example illustrates this property. Next, we design a linear detector that only exploits the information provided by these locations and that yields the same performancl: as linear receivers performing in the whole time-frequency dornain. Finally, some potential implications of this property are briefly presented.