Why is the Linear Canonical Transform so little known
Why is the Linear Canonical Transform so little known
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DOI：
10.1063/1.2361224
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发表时间：
2006-10
期刊：
影响因子：
--
通讯作者：
A. Stern
中科院分区：
文献类型：
--
作者：
A. Stern
线性正则变换（LCT）是变换的参数化连续体的名称，作为特定情况，其包括工程和物理中最广泛使用的线性变换和算子，例如傅里叶变换、分数傅里叶变换（FRFT）、菲涅耳变换（FRST）、时间缩放、啁啾等。因此，LCT提供了一个统一的框架来研究光学和工程中许多实际变换和系统响应的行为。从系统工程的角度来看，LCT为设计和分析光学系统的特性提供了一个强大的工具。尽管如此，只有少数作者利用强大的和一般的LCT理论的光学系统的分析和设计。本文回顾了连续LCT的一些重要性质，并给出了关于LCT的离散化和计算的一些新结果。
The linear canonical transform (LCT), is the name of a parameterized continuum of transforms which include, as particular cases, the most widely used linear transforms and operators in engineering and physics such as the Fourier transform, fractional Fourier transform (FRFT), Fresnel transform (FRST), time scaling, chirping, and others. Therefore the LCT provides a unified framework for studying the behavior of many practical transforms and system responses in optics and engineering in general. From the system‐engineering point of view the LCT provides a powerful tool for design and analysis of the characteristics of optical systems. Despite this fact only few authors take advantage of the powerful and general LCT theory for analysis and design of optical systems. In this paper we review some important properties about the continuous LCT and we present some new results regarding the discretization and computation of the LCT.