Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation |
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| Authors: | Hu Li-Yun and Fan Hong-Yi |
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| Institution: | College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China; Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China |
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| 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. |
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| Keywords: | Parseval theorem complex continuous wavelet transforms entangled state representation |
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