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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 5 — May. 1, 2013
  • pp: 987–992

Derivation and discrete implementation for analytic signal of linear canonical transform

Soo-Chang Pei and Yun-Chiu Lai  »View Author Affiliations

JOSA A, Vol. 30, Issue 5, pp. 987-992 (2013)

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Analytic signal and Hilbert transform associated with linear canonical transform (LCT) have been developed [Opt. Commun. 281, 1468 (2008)]. However, the aforementioned paper has some drawbacks; for example, this kind of analytic signal cannot preserve the positive frequency bands of the original signal under LCT operations. In this paper, these drawbacks are pointed out, and a better definition for analytic signal associated with LCT is proposed. In addition, a discrete implementation for the analytic signal associated with discrete LCT is also provided. Several numerical examples, shown with both time and Wigner time-frequency domains, are demonstrated to illustrate the efficiency and accuracy of the proposed LCT analytic signal.

© 2013 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.4790) Fourier optics and signal processing : Spectrum analysis
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: January 3, 2013
Revised Manuscript: March 16, 2013
Manuscript Accepted: March 18, 2013
Published: April 24, 2013

Soo-Chang Pei and Yun-Chiu Lai, "Derivation and discrete implementation for analytic signal of linear canonical transform," J. Opt. Soc. Am. A 30, 987-992 (2013)

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