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 samples. This implies that a whole discrete Wigner-Ville representation can be determined 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 performance as linear receivers performing in the whole time-frequency domain. Finally, some potential implications of this property are briefly presented