Tomograms and other transforms. A unified view
Mathematical Physics
2009-11-07 v1 math.MP
Abstract
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the symplectic and affine groups is treated in some detail. Special emphasis is given to the properties of the scale-time and scale-frequency tomograms. Tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector.
Cite
@article{arxiv.math-ph/0101025,
title = {Tomograms and other transforms. A unified view},
author = {M. A. Man'ko and V. I. Man'ko and R. Vilela Mendes},
journal= {arXiv preprint arXiv:math-ph/0101025},
year = {2009}
}
Comments
19 pages latex, submitted to J. Phys. A: Math and Gen