中国物理B ›› 2011, Vol. 20 ›› Issue (12): 120305-120305.doi: 10.1088/1674-1056/20/12/120305

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Wavelet transform for Fresnel-transformed mother wavelets

陈俊华1, 范洪义1, 刘述光2   

  1. (1)Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China; (2)School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China
  • 收稿日期:2011-06-12 修回日期:2011-07-07 出版日期:2011-12-15 发布日期:2011-12-15
  • 基金资助:
    Project supported by the Startup Research Fund for Introducing Talents of Anhui Polytechnic University (Grant No. 2009YQQ006) and the Research Foundation of the Education Department of Anhui Province of China (Grant No. KJ2011B031).

Wavelet transform for Fresnel-transformed mother wavelets

Liu Shu-Guang(刘述光)a)†, Chen Jun-Hua(陈俊华) b), and Fan Hong-Yi(范洪义)b)   

  1. a School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China; b Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2011-06-12 Revised:2011-07-07 Online:2011-12-15 Published:2011-12-15
  • Supported by:
    Project supported by the Startup Research Fund for Introducing Talents of Anhui Polytechnic University (Grant No. 2009YQQ006) and the Research Foundation of the Education Department of Anhui Province of China (Grant No. KJ2011B031).

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摘要： 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.

关键词: wavelet transform, fresnel transformation, quantum state vector

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 $|\psi\rangle$ to Fr,s+ $|\psi\rangle$ , 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.

Key words: wavelet transform, fresnel transformation, quantum state vector

中图分类号:  (Entanglement and quantum nonlocality)

  • 03.65.Ud
42.50.Dv (Quantum state engineering and measurements) 42.30.Kq (Fourier optics)