Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms
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|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
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|DOI:||10.1364/JOSAA.22.000917||Language:||en||Status of Item:||Not peer reviewed|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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