of linear canonical transformations. In this approach, the electric charge, weak hypercharge and weak isospin of the particles are expressed as linear combinations of some operators defined from the generators of the Clifford algebra associated with the spin representation of linear canonical transformations. See also Segal–Shale–Weil distribution, a metaplectic group of operators related to the chirplet transform Other time–frequency transforms: Fractional Fourier transform Continuous Fourier transform Chirplet transform Applications: Focus recovery based on the linear canonical transform Ray transfer matrix analysis Notes References J.J. Healy, M.A. Kutay, H.M. Ozaktas and J.T. Sheridan, "Linear Canonical Transforms: Theory and Applications", Springer, New York 2016. J.J. Ding, "Time–frequency analysis and wavelet transform course note", the Department of Electrical Engineering, National Taiwan University (NTU), Taipei, Taiwan, 2007. K.B. Wolf, "Integral Transforms in Science and Engineering", Ch. 9&10, New York, Plenum Press, 1979. S.A. Collins, "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Amer. 60, 1168–1177 (1970). M. Moshinsky and C. Quesne, "Linear canonical transformations and their unitary representations," J. Math. Phys. 12, 8, 1772–1783, (1971). B.M. Hennelly and J.T. Sheridan, "Fast Numerical Algorithm for the Linear Canonical Transform", J. Opt. Soc. Am. A 22, 5, 928–937 (2005). H.M. Ozaktas, A. Koç, I. Sari, and M.A. Kutay, "Efficient computation of quadratic-phase integrals in optics", Opt. Let. 31, 35–37, (2006). Bing-Zhao Li, Ran Tao, Yue Wang, "New sampling formulae related to the linear canonical transform", Signal Processing '87', 983–990, (2007). A. Koç, H.M. Ozaktas, C. Candan, and M.A. Kutay, "Digital computation of linear canonical transforms", IEEE Trans. Signal Process., vol. 56, no. 6, 2383–2394, (2008). Ran Tao, Bing-Zhao Li, Yue Wang, "On sampling of bandlimited signals associated with the linear canonical transform", IEEE Transactions on Signal Processing, vol. 56, no. 11, 5454–5464, (2008). D. Stoler, "Operator methods in Physical Optics", 26th Annual Technical Symposium. International Society for Optics and Photonics, 1982. Tian-Zhou Xu, Bing-Zhao Li, " Linear Canonical Transform and Its Applications ", Beijing, Science Press, 2013. Raoelina Andriambololona, R. T. Ranaivoson, H.D.E Randriamisy, R. Hanitriarivo, "Dispersion Operators Algebra and Linear Canonical Transformations",Int. J. Theor. Phys., 56, 4, 1258–1273, (2017) R.T. Ranaivoson et al, "Linear Canonical Transformations in Relativistic Quantum Physics", Phys. Scr. 96, 065204, (2021). Tatiana Alieva., Martin J. Bastiaans. (2016) The Linear Canonical Transformations: Definition and Properties. In: Healy J., Alper Kutay M., Ozaktas H., Sheridan J. (eds) Linear Canonical Transforms. Springer Series in Optical Sciences, vol 198. Springer, New