Additive discrete 1D linear canonical transform
Liang Zhao, John J. Healy, Changliang Guo, John T. Sheridan · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2015
The continuous linear canonical transforms (LCT) can describe a wide variety of wave field propagations through paraxial (first order) optical systems. Digital algorithms to numerically calculate the LCT are therefore important in modelling scalar wave field propagations and are also of interest for many digital signal processing applications. The continuous LCT is additive, but discretization can remove this property. In this paper we discuss three special cases of the LCT for which constraints can be identified to ensure the DLCT is additive.