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Chin. Phys. B, 2011, Vol. 20(12): 120305    DOI: 10.1088/1674-1056/20/12/120305
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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)
a 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
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.
Keywords:  wavelet transform      fresnel transformation      quantum state vector  
Received:  12 June 2011      Revised:  07 July 2011      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 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).

Cite this article: 

Liu Shu-Guang(刘述光), Chen Jun-Hua(陈俊华), and Fan Hong-Yi(范洪义) Wavelet transform for Fresnel-transformed mother wavelets 2011 Chin. Phys. B 20 120305

[1] Fan H Y and Hu L Y 2009 Opt. Commun. 282 3734
[2] Wigner E P 1932 Phys. Rev. 40 749
[3] Hillery M, O'Connell R F, Scully M O and Wigner E P1984 Phys. Rep. 106 121
[4] Jiang N Q 2005 Phys. Lett. A 339 255
[5] Xu Y J, Fan H Y and Liu Q Y 2010 Chin. Phys. B 19020303
[6] Fan H Y and Zaidi H R 1987 Phys. Lett. A 124 303
[7] Goodman J W 1972 Introduction to Fourier Optics (NewYork: McGraw-Hill)
[8] Zhang S N, Luo Z Y, Shen W D, Liu X and Zhang Y G2011 Acta Phys. Sin. 60 014221 (in Chinese)
[9] Ma T P, Hu L Q and Chen K Y 2010 Acta Phys. Sin. 597209 (in Chinese)
[10] Zhao W S and He Y G 2009 Acta Phys. Sin. 58 843 (inChinese)
[11] Sun H L, Jin Y H, Cui Y D and Cheng S D 2009 Chin.Phys. B 18 4760
[12] Deng Y Q,Wu Z B, Chai L,Wang C Y, Yamane K, MoritaR, Yamashita M and Zhang Z G 2005 Opt. Express 132120
[13] Ahmed F 2007 Opt. Express 15 4804
[14] Tan L Y, Ma J and Wang Q 2006 Appl. Opt. 45 3275
[15] Fu Y, Tay C J, Quan C G and Miao H 2005 Appl. Opt.44 959
[16] Daubechies I 1992 Ten Lectures on Wavelets, CBMSMSFSeries in Applied Mathematics (SIAM) (Philadelphia:Baker & Taylor Books)
[17] Pinsky M A 2002 Introduction to Fourier Analysis andWavelets (New York: Books/Cole)
[18] Fan H Y and Cheng H L 2001 Chin. Phys. Lett. 18 850
[19] Klauder J R and Skargerstam B S 1985 Coherent States(Singapore: World Scientific)
[20] Glauber R J 1963 Phys. Rev. 130 2529
[21] Hu L Y and Fan H Y 2010 Chin. Phys. B 19 074205
[22] Fan H Y and Hu L Y 2009 Chin. Phys. B 18 611
[23] Fan H Y 2003 Opt. Lett. 28 2177
[24] Zhang B, Jiang Y, Wang G, Zhang L D, Wu J H and GaoJ Y 2011 Chin. Phys. B 20 050304
[25] Terraneo M, Georgeot B and Shepelyansky D L 2005 Phys.Rev. E 71 066215
[26] Terraneo M and Shepelyansky D L 2003 Phys. Rev. Lett.90 257902
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