Digital computation of linear canonical transforms

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


Fast Algorithms for Digital Computation of Linear Canonical Transforms
Koc, Aykut; Öktem, Sevinç Figen; Ozaktas, Haldun M.; Kutay, M. Alper (2016-01-01)
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 a...
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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: