Linear redundancy of information carried by the discrete Wigner distribution

The discrete Wigner distribution (WD) encodes information in a redundant fashion since it derives by representations from -sample signals. The increased amount of data often prohibits its effective use in applications such as signal detection, parameter estimation, and pattern recognition. As a consequence, it is of great interest to study the redundancy of information it carries. Recently, Richard and Lengellé have shown that linear relations 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 discrete cross WD of complex-valued signals is addressed. We show that every discrete 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. Special cases of the auto WD of complex-valued signals and realvalued signals are considered. The results are illustrated by means of computer simulations, and some extensions are pointed out.