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
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. 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
Keywords :
group theory; signal representation; statistical analysis; time-frequency analysis; covariant signal energy densities; group representation theory; invariant signal energy densities; joint densities; time-frequency analysis; time-frequency distributions; time-scale distributions; unitary operator; Density measurement; Eigenvalues and eigenfunctions; Energy measurement; Radar applications; Radar signal processing; Signal analysis; Signal processing; Speech analysis; Speech processing; Time frequency analysis;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1994. ICASSP-94., 1994 IEEE International Conference on
Conference_Location :
Adelaide, SA
Print_ISBN :
0-7803-1775-0
DOI :
10.1109/ICASSP.1994.390016
