Wavelet transform for Fresnel-transformed mother wavelets |
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Authors: | Liu Shu-Guang Chen Jun-Hua and Fan Hong-Yi |
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Institution: | School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China;Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China;. |
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Abstract: | In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from |ψ> to Fr,s+ |ψ> , except for variation within the family of dilations and translations. The Parseval's equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented. |
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Keywords: | wavelet transform fresnel transformation quantum state vector |
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