Please note that the content of this book primarily consists of
articles available from Wikipedia or other free sources online. In
Hamiltonian mechanics, the linear canonical transformation is a
family of integral transforms that generalizes many classical
transforms. It has 4 parameters and 1 constraint, so it is a
3-dimensional family, and can be visualized as the action of the
special linear group SL2 on the time-frequency plane. The LCT
generalizes the Fourier, fractional Fourier, Laplace,
Gauss-Weierstrass, Bargmann and the Fresnel transforms as
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