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 $\tau$-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.