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In Hamiltonian mechanics, the linear canonical transformation (LCT) 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(R) on the time–frequency plane (domain). The LCT generalizes the Fourier, fractional Fourier, Laplace, Gauss–Weierstrass, Bargmann and the Fresnel transforms as particular cases. The name "linear canonical transformation" is from canonical transformation, a map that preserves the symplectic structure, as SL2(R) can also be interpreted as the symplectic group Sp2, and thus LCTs are the linear maps of the time–frequency domain which preserve the symplectic form. ==Definition== The LCT can be represented in several ways; most easily,〔de Bruijn, N. G. (1973). "A theory of generalized functions, with applications to Wigner distribution and Weyl correspondence", ''Nieuw Arch. Wiskd.'', III. Ser., 21 205-280.〕 it can be parameterized by a 2×2 matrix with determinant 1, i.e., an element of the special linear group SL2(R). Then for any such matrix with ''ad'' − ''bc'' = 1, the corresponding integral transform from a function to is defined as : \cdot e^ u^} \int_^\infty e^ ut}e^ t^2} x(t) \; dt \, , || when ''b'' ≠ 0, |- | 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Linear canonical transformation」の詳細全文を読む スポンサード リンク
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