Wigner Representations Associated with Linear Transformations of the Time-Frequency Plane

In this paper we define a variation of the Wigner form depending on a linear transformation of the time-frequency plane and study the corresponding properties. This construction yields a natural geometric interpretation of the so-called "ghost frequencies" showed, among others, by the Wigner quadratic representation. In particular we prove that the representations in this new class which satisfy the support properties are just the so-called r-Wigner forms. On the other hand for these new forms an "essential" re-adjustement of the supports is showed to be possible, whereas their features of moving almost arbitrarily the ghost frequencies is used to define representations with no interferences at all for a certain class of signals.