Classification of the linear canonical transformation and its associated real symplectic matrix

M.J. Bastiaans, T. Alieva

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)

Abstract

Based on the eigenvalues of the real symplectic ABCD-matrix that characterizes the linear canonical integral transformation, a classification of this transformation and the associated ABCD-system is proposed and some nuclei (i.e. elementary members) in each class are described. In the one-dimensional case, possible optical nuclei are the magnifier, the lens, and the fractional Fourier transformer; in the two-dimensional case, we have - in addition to the obvious concatenations of one-dimensional nuclei - the four combinations of a magnifier or a lens with a rotator or a shearing operator, where the rotator and the shearer are obviously inherently two-dimensional. Any ABCD-system belongs to one of the classes described in this paper and is similar (in the sense of similarity of the respective symplectic matrices) to the corresponding nucleus.
Original languageEnglish
Title of host publicationProc. ISSPA 2007, International Symposium on Signal Processing and its Applications, Sharjah, United Arab Emirates
Place of PublicationPiscataway, New Jersey, USA
PublisherInstitute of Electrical and Electronics Engineers
Pages1238.1-1238.4
ISBN (Print)978-1-424-40778-1
DOIs
Publication statusPublished - 2007
Eventconference; ISSPA 2007, Sharjah, United Arab Emirates; 2007-02-12; 2007-02-15 -
Duration: 12 Feb 200715 Feb 2007

Conference

Conferenceconference; ISSPA 2007, Sharjah, United Arab Emirates; 2007-02-12; 2007-02-15
Period12/02/0715/02/07
OtherISSPA 2007, Sharjah, United Arab Emirates

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    Bastiaans, M. J., & Alieva, T. (2007). Classification of the linear canonical transformation and its associated real symplectic matrix. In Proc. ISSPA 2007, International Symposium on Signal Processing and its Applications, Sharjah, United Arab Emirates (pp. 1238.1-1238.4). Piscataway, New Jersey, USA: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISSPA.2007.4555352