Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

doi:10.1088/1674-1056/19/7/074205

Abstract In a preceding letter (2007 Opt. Lett. 32 554) we propose complex continuous wavelet transforms and found Laguerre—Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

Keywords: Parseval theorem complex continuous wavelet transforms entangled state representation

Received: 28 October 2009
Revised: 01 February 2010
Accepted manuscript online:

PACS:	03.65.Ud	(Entanglement and quantum nonlocality)
	42.50.Dv	(Quantum state engineering and measurements)
	42.30.Kq	(Fourier optics)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10775097), and the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ10097).

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Hu Li-Yun(胡利云) and Fan Hong-Yi(范洪义) Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation 2010 Chin. Phys. B 19 074205

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Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

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