## Derivation and discrete implementation for analytic signal of linear canonical transform |

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

http://dx.doi.org/10.1364/JOSAA.30.000987

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### Abstract

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

**History**

Original Manuscript: January 3, 2013

Revised Manuscript: March 16, 2013

Manuscript Accepted: March 18, 2013

Published: April 24, 2013

**Citation**

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)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-5-987

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