Symbolic calculus on the time-frequency half-plane
Bertrand, J. ; Bertrand, P.
arXiv, 9708027 / Harvested from arXiv
Text on arXiv
The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f>0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one.
Publié le : 1997-08-24
Classification:  Mathematical Physics 
@article{9708027,
     author = {Bertrand, J. and Bertrand, P.},
     title = {Symbolic calculus on the time-frequency half-plane},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9708027}
}

Bertrand, J.; Bertrand, P. Symbolic calculus on the time-frequency half-plane. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9708027/