Title :
Beyond time-frequency analysis: energy densities in one and many dimensions
Author :
Baraniuk, Richard G.
Author_Institution :
Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA
fDate :
9/1/1998 12:00:00 AM
Abstract :
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
Keywords :
group theory; mathematical operators; signal representation; statistical analysis; time-frequency analysis; Cohen´s method; Hermitian operators; arbitrary variables; energy content; group representation theory; joint densities; joint distributions; multiple operators; natural signal energy densities; signal processing; signal representation; time-frequency analysis; unitary operator; Geophysical measurements; Radar applications; Radar signal processing; Signal analysis; Signal processing; Signal representations; Speech analysis; Speech processing; Time frequency analysis; Transient analysis;
Journal_Title :
Signal Processing, IEEE Transactions on
