Integral representations of affine transformations in phase space with an application to energy localization problems
Applying the fractional Fourier transform and the Wigner distribution on a signal in a cascade fashion is equivalent with a rotation of the time and frequency parameters of the Wigner distribution. This report presents a formula for all unitary operators that are related to energy preserving transformations on the parameters of the Wigner distribution by means of such a cascade of operators. Furthermore, such operators are used to solve certain type of energy localization problems via the Weyl correspondence.
|Applications of group representations to physics (msc 20C35), Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (msc 33D45), Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (msc 42A38), Representations of groups, semigroups, etc. (msc 43A65), Signal theory (characterization, reconstruction, filtering, etc.) (msc 94A12)|
|CWI. Probability, Networks and Algorithms [PNA]|
ter Morsche, H.G, & Oonincx, P.J. (1999). Integral representations of affine transformations in phase space with an application to energy localization problems. CWI. Probability, Networks and Algorithms [PNA]. CWI.