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 ∈ L 2 ( R d ) , the energy of a time–frequency representation contained in a measurable set M must be controlled by the standard deviations of | f | 2 and | f ˆ | 2 , and by suitable quantities measuring the size of M.