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Beyond time-frequency analysis: energy densities in one and many dimensions

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1 Author(s)
Baraniuk, R.G. ; Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA

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 (see Englewood Cliffs, NJ: Prentice-Hall, 1995) general construction for joint distributions of arbitrary variables

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Signal Processing, IEEE Transactions on  (Volume:46 ,  Issue: 9 )