Beyond time-frequency analysis: energy densities in one and many dimensions
نویسنده
چکیده
Given a unitary operator A representing a physical quantity of interest, we employ concepts from group representation theory to define two natural 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 covariant to A and measures the “A” content of signals. We also consider joint densities for multiple operators and, in the process, provide an alternative interpretation of Cohen’s general construction for joint distributions of arbitrary variables.
منابع مشابه
BEYOND TIME - FREQUENCY ANALYSIS : ENERGY DENSITIES IN ONE AND MANY DIMENSIONSRichard
Given a unitary operator A representing a physical quantity of interest, we employ concepts from group representation theory to deene two natural signal energy densities for A. The rst is invariant to A and proves useful when the eeect of A is to be ignored; the second is covariant to A and measures the \A" content of signals. The construction is quite general and is also easily extended to the...
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