Local uncertainty principles for the Cohen class

In this paper we analyze time-frequency representations in the Cohen class, i.e., quadratic forms expressed as a convolution between the classical Wigner transform and a kernel, with respect to uncertainty principles of local type. More precisely the results we obtain concerning the energy distribution of these representations show that a "too large" amount of energy cannot be concentrated in a "too small" set of the time-frequency plane. In particular, for a signal $f\in L^2(\Rd)$, the energy of a time-frequency representation contained in a measurable set $M$ must be controlled by the standard deviations of $\vert f\vert^2$ and $\vert \hat{f}\vert^2$, and by suitable quantities measuring the size of $M$.