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.