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arXiv · 0910.5354

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

Li-yun Hu·Hong-yi Fan
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Abstract

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

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Li-yun Hu, Hong-yi Fan. 2009-10-28. Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation. https://doi.org/10.1088/1674-1056%2F19%2F7%2F074205

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