## Discrete linear canonical transforms based on dilated Hermite functions |

JOSA A, Vol. 28, Issue 8, pp. 1695-1708 (2011)

http://dx.doi.org/10.1364/JOSAA.28.001695

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### Abstract

Linear canonical transform (LCT) is very useful and powerful in signal processing and optics. In this paper, discrete LCT (DLCT) is proposed to approximate LCT by utilizing the discrete dilated Hermite functions. The Wigner distribution function is also used to investigate DLCT performances in the time–frequency domain. Compared with the existing digital computation of LCT, our proposed DLCT possess additivity and reversibility properties with no oversampling involved. In addition, the length of input/output signals will not be changed before and after the DLCT transformations, which is consistent with the time–frequency area-preserving nature of LCT; meanwhile, the proposed DLCT has very good approximation of continuous LCT.

© 2011 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

(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: April 19, 2011

Revised Manuscript: June 10, 2011

Manuscript Accepted: June 11, 2011

Published: July 27, 2011

**Citation**

Soo-Chang Pei and Yun-Chiu Lai, "Discrete linear canonical transforms based on dilated Hermite functions," J. Opt. Soc. Am. A **28**, 1695-1708 (2011)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-8-1695

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