Properties of Eigenfunctions of the Canonical Integral Transform
نویسنده
چکیده
The structure and the properties of the eigenfunctions of the canonical integral transform are investigated. It is shown that a signal can be decomposed into a set of the orthogonal eigenfunctions of the generalized Fresnel transform. The property that the set contains a finite number of functions is obtained. The canonical integral transform, also known as the generalized Fresnel transform (GFT) [1, 2], including as a particular case the fractional Fourier transform, is now actively used in optics, quantum theory, signal and image processing, etc. The GFT of a signal f(x) is given by FM (u) = R M [f(x)] (u) = Z 1 1 f(x)KM (x; u)dx; (1)
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