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.

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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.