Beyond Time Frequency Analysis: Energy Densities in One and Many Dimensions
Baraniuk, Richard G.
group representation theory; signal energy densities
Given a unitary operator <i>A</i> representing a physical quantity of interest, we employ concepts from group representation theory to define two natural signal energy densities for <i>A</i>. The first is invariant to <i>A</i> and proves useful when the effect of <i>A</i> is to be ignored; the second is covariant to <i>A</i> and measures the "<i>A</i>" content of signals. The construction is quite general and is also easily extended to the multi-operator case, which generalizes previously derived joint densities such as the time-frequency and time-scale distributions.