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Fast Algorithms for Digital Computation of Linear Canonical Transforms

  • Chapter
Linear Canonical Transforms

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 198))

Abstract

Fast and accurate algorithms for digital computation of linear canonical transforms (LCTs) are discussed. Direct numerical integration takes O(N 2) time, where N is the number of samples. Designing fast and accurate algorithms that take \(O(N\log N)\) time is of importance for practical utilization of LCTs. There are several approaches to designing fast algorithms. One approach is to decompose an arbitrary LCT into blocks, all of which have fast implementations, thus obtaining an overall fast algorithm. Another approach is to define a discrete LCT (DLCT), based on which a fast LCT (FLCT) is derived to efficiently compute LCTs. This strategy is similar to that employed for the Fourier transform, where one defines the discrete Fourier transform (DFT), which is then computed with the fast Fourier transform (FFT). A third, hybrid approach involves a DLCT but employs a decomposition-based method to compute it. Algorithms for two-dimensional and complex parametered LCTs are also discussed.

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Acknowledgement

H.M. Ozaktas acknowledges partial support of the Turkish Academy of Sciences.

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Authors and Affiliations

  1. Intelligent Data Analytics Research Program Department, ASELSAN Research Center, ASELSAN Inc., Ankara, Turkey

    Aykut Koç

  2. Department of Electrical and Electronics Engineering, Middle East Technical University, 06800, Çankaya, Ankara, Turkey

    Figen S. Oktem

  3. Department of Electrical Engineering, Bilkent University, 06800, Bilkent, Ankara, Turkey

    Haldun M. Ozaktas

  4. The Scientific and Technological Research Council of Turkey, 06100, Kavaklıdere, Ankara, Turkey

    M. Alper Kutay

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  1. Aykut Koç
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  2. Figen S. Oktem
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  3. Haldun M. Ozaktas
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  4. M. Alper Kutay
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Correspondence to Aykut Koç .

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Editors and Affiliations

  1. School of Electrical and Electronic Engineering, University College Dublin, Dublin, Ireland

    John J. Healy

  2. The Scientific and Technological Research Council of Turkey, Ankara, Ankara, Turkey

    M. Alper Kutay

  3. Department of Electrical Engineering, Bilkent University, Ankara, Ankara, Turkey

    Haldun M. Ozaktas

  4. School of Electrical and Electronic Engineering, University College Dublin, Dublin, Dublin, Ireland

    John T. Sheridan

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Koç, A., Oktem, F.S., Ozaktas, H.M., Kutay, M.A. (2016). Fast Algorithms for Digital Computation of Linear Canonical Transforms. In: Healy, J., Alper Kutay, M., Ozaktas, H., Sheridan, J. (eds) Linear Canonical Transforms. Springer Series in Optical Sciences, vol 198. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3028-9_10

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