Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

Title: Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms
Authors: Hennelly, Bryan M.
Sheridan, John T.
Permanent link: http://hdl.handle.net/10197/3384
Date: 1-May-2005
Abstract: By use of matrix-based techniques it is shown how the space–bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadraticphase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.
Funding Details: Science Foundation Ireland
Irish Research Council for Science, Engineering and Technology
Type of material: Journal Article
Publisher: Optical Society of America
Copyright (published version): 2005 Optical Society of America
Subject LCSH: Algorithms
Transformations (Mathematics)
Optical data processing
Image processing--Digital techniques
DOI: 10.1364/JOSAA.22.000917
Language: en
Status of Item: Not peer reviewed
Appears in Collections:Electrical and Electronic Engineering Research Collection

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