Some uncertainty principles for time-frequency transforms of the Cohen class

The question of how the time-frequency-concentration of transforms of the Cohen class is affected by fundamental properties is addressed. The investigated transform properties are the marginal property, the property of energy conservation, and Moyal's relation. We show that each of these transform properties imply restrictions on the time-frequency concentration of the Cohen class and is thus related to an uncertainty principle. Different notions of time-frequency concentration, adapted to the property under consideration, are applied.