Fast and accurate algorithms for quadratic phase integrals in optics and signal processing

Aykut Koç; Haldun M. Ozaktas; Lambertus Hesselink

doi:10.1117/12.884676

19 May 2011 Fast and accurate algorithms for quadratic phase integrals in optics and signal processing

Aykut Koç; Haldun M. Ozaktas; Lambertus Hesselink

Author Affiliations +

Proceedings Volume 8043, Three-Dimensional Imaging, Visualization, and Display 2011; 804304 (2011) https://doi.org/10.1117/12.884676
Event: SPIE Defense, Security, and Sensing, 2011, Orlando, Florida, United States

Abstract

The class of two-dimensional non-separable linear canonical transforms is the most general family of linear canonical transforms, which are important in both signal/image processing and optics. Application areas include noise filtering, image encryption, design and analysis of ABCD systems, etc. To facilitate these applications, one need to obtain a digital computation method and a fast algorithm to calculate the input-output relationships of these transforms. We derive an algorithm of NlogN time, N being the space-bandwidth product. The algorithm controls the space-bandwidth products, to achieve information theoretically sufficient, but not redundant, sampling required for the reconstruction of the underlying continuous functions.

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Aykut Koç, Haldun M. Ozaktas, Lambertus Hesselink, "Fast and accurate algorithms for quadratic phase integrals in optics and signal processing", Proc. SPIE 8043, Three-Dimensional Imaging, Visualization, and Display 2011, 804304 (19 May 2011); doi: 10.1117/12.884676; https://doi.org/10.1117/12.884676

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