Linear redundancy of information carried by the discrete Wigner distribution

The discrete Wigner distribution (WD) encodes information in a redundant fa shion since it derives N by N representations from N-sample signals. The in creased amount of data often prohibits its effective use in applications su ch as signal detection, parameter estimation, and pattern recognition. As a consequence, it is of great interest to study the redundancy of informatio n it carries. Recently, Richard and Lengelle have shown that linear relatio ns connect the time-frequency samples of the discrete WD. However, up until now, such a redundancy has still not been algebraically characterized. In this paper, the problem of the redundancy of information carried by the dis crete cross WD of complex-valued signals is addressed. We show that every d iscrete WD can be fully recovered from a small number of its samples via a linear map. The analytical expression of this linear map is derived. Specia l cases of the auto WD of complex-valued signals and real-valued signals ar e considered. The results are illustrated by means of computer simulations, and some extensions are pointed out.