BEYOND TIME-FREQUENCY ANALYSIS - ENERGY DENSITIES IN ONE AND MANY DIMENSIONS

Given a unitary operator A representing a physical quantity of interes t, we employ concepts from group representation theory to define two n atural signal energy densities for A. The first is invariant to A and proves useful when the effect of A is to be ignored; the second is cov ariant to A and measures the ''A'' content of signals. We also conside r joint densities for multiple operators and, in the process, provide an alternative interpretation of Cohen's general construction for join t distributions of arbitrary variables.