Sampling of linear canonical transformed signals. (English) Zbl 1172.94344

Summary: Linear canonical transforms play an important role in many fields of optics and signal processing. Well-known transforms such as the Fourier transform, the fractional Fourier transform, and the Fresnel transform can be seen as special cases of the linear canonical transform. In this paper we develop a sampling theorem for linear canonical transformed signals. The well-known Shannon sampling theorem and previously developed sampling criteria for Fresnel and fractional Fourier transformed signals are shown to be a special cases of the theorem developed here.


94A11 Application of orthogonal and other special functions
65T60 Numerical methods for wavelets
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