Fast Algorithms for Digital Computation of Linear Canonical Transforms

Date

2016-01-01

Author

Koc, Aykut
Öktem, Sevinç Figen
Ozaktas, Haldun M.
Kutay, M. Alper

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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 logN/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.

Subject Keywords

Fractional-fourier-transform, Wigner distribution function, Gyrator transform, Fresnel transform, Series expansion, Finite systems, Wave-functions, Implementation, Representation, Signal

URI

https://hdl.handle.net/11511/46855

Collections

Department of Electrical and Electronics Engineering, Article