Digital Computation of Linear Canonical Transforms

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,...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2008-06, Vol.56 (6), p.2383-2394
Main Authors: Koc, A., Ozaktas, H.M., Candan, C., Alper Kutay, M.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation algorithms
Chirp
Computation
Convolution
Diffraction integrals
Digital
Discrete Fourier transforms
Exact sciences and technology
Fast Fourier transforms
Fourier transforms
fractional Fourier transform (FRT)
Information, signal and communications theory
linear canonical transform (LCT)
Mathematical analysis
Mathematical models
Sampling methods
Signal and communications theory
Signal processing algorithms
Signal representation. Spectral analysis
Signal, noise
Telecommunications and information theory
Time frequency analysis
Transforms
Wigner distributions
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Summary: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 ~ 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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2007.912890