Tomograms, Wavelets, and Quasidistributions in the Geometric Picture

M. R. Bazrafkan, E. Nahvifard

Margarita A. Man’ko

Vladimir I. Man’ko, Giuseppe Marmo, Alberto Simoni +2 more

Margarita A. Man’ko

Integral transforms of analytic signal and quantum-system states like wavelets, tomograms, Ville-Wigner and other quasidistributions are constructed for systems with several degrees of freedom. Mutual relations of the integral transforms are presented. Quantum propagator is interpreted as the kernel of the integral transform. An example of the integral transforms with generic Gaussian kernels is studied. The fractional Fourier transform is discussed.

Y. S. Kim

M A Man'ko, V I Man'ko, R. Vilela Mendes

A general framework is presented which unifies the treatment of wavelet-like, quasidistribution and tomographic transforms. Explicit formulae relating the three types of transforms are obtained. The case of transforms associated with 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.