Digital computation of linear canonical transforms

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Date

2008-06-01

Author

Koc, Aykut
Ozaktas, Haldun M.
Candan, Çağatay
KUTAY, M. Alper

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We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take similar to N log N time, where N is the time-bandwidth product of the signals. The only essential deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus, the algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy.

Subject Keywords

Diffraction integrals, Fractional Fourier transform (FRT), Linear canonical transform (LCT), Time-frequency analysis, Wigner distribution

URI

https://hdl.handle.net/11511/33400

Journal

IEEE TRANSACTIONS ON SIGNAL PROCESSING

DOI

https://doi.org/10.1109/tsp.2007.912890

Collections

Department of Electrical and Electronics Engineering, Article

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Citation Formats

A. Koc, H. M. Ozaktas, Ç. Candan, and M. A. KUTAY, “Digital computation of linear canonical transforms,” IEEE TRANSACTIONS ON SIGNAL PROCESSING, pp. 2383–2394, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/33400.