On the linear relations connecting the components of the discrete Wigner distribution in the case of real-valued signals

It was shown that information conveyed by the discrete Wigner distribution is highly redundant, linear relations connecting its time-frequency components. This means that every component of the discrete Wigner distribution can be expressed as a linear combination of the elements of a basis. This set of generators consists of particular time-frequency components of the distribution. However, up to now, this basis and the associated linear map that allows to entirely generate the representation have still not been characterized. This problem is addressed in the case of real-valued signals. Results are illustrated by means of computer simulations. Finally, some extensions are pointed out