Integral Representations of Affine Transformations in Phase Space with an211 Application to Energy Localization Problems

摘要

Applying the fractional Fourier transform and the Wigner distribution on a signal211u001ein a cascade fashion is equivalent with a rotation of the time and frequency 211u001eparameters of the Wigner distribution. This report presents a formula for all 211u001eunitary operators that are related to energy preserving transformations on the 211u001eparameters of the Wigner distribution by means of such a cascade of operators. 211u001eFurthermore, such operators are used to solve certain type of energy localization 211u001eproblems via the Weyl correspondence.