13 November 2000 Integral representations for metaplectic operators: energy localization problems
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Abstract
Applying the fractional Fourier transform (FRFT) 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. In this paper an integral representation formula is presented that yields affine transformations on the spatial and frequency parameters of the n-dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. This representation formula is used to solve certain energy localization problems in phase space.
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Patrick J. Oonincx, Hennie G. ter Morsche, "Integral representations for metaplectic operators: energy localization problems", Proc. SPIE 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X, (13 November 2000); doi: 10.1117/12.406528; https://doi.org/10.1117/12.406528
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