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In the context of quantum mechanics the classical wavelet transform of a function f with the mother wavelet can be recast into a matrix element of the squeezing-displacing operator U(,s) as 〈|U(,s) |f〉. The technique of integral within an ordered product of operators is used to support this theory. Based on this, wavelet transforms are done for even- and odd-binomial states, and the corresponding numerical calculation leads to the spectrum of wavelet transform, which is helpful for recognizing the difference between even- and odd-states.
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Keywords:
- wavelet transform /
- odd- and even-binomial states /
- integration within an ordered product of operators
[1] Daubechies I 1992 Ten Lectures on Wavelet (Philadelphia: SIAM)
[2] [3] Jaffard S, Meyer Y, Ryan R D 2001 Wavelet, Tools for Science and Technology (Philadelphia: SIAM)
[4] Chui C K 1992 An Introduction to Wavelets (New York: Academic)
[5] [6] [7] Burrus C S, Gopinath R A, Guo H T 1998 Introduction to Wavelet and Wavelet Transformation (A Primer) (New Jersey: Prentice Hall)
[8] Pinsky M A 2002 Introduction to Fourier Analysis and Wavelets (Pacific Grove: Brooks/Cole)
[9] [10] [11] Fan H Y, Lu H L 2006 Opt. Lett. 31 407
[12] Song J, Fan H Y 2010 Chin. Phys. Lett. 27 024210
[13] [14] Fan H Y, Lu H L 2007 Opt. Lett. 32 554
[15] [16] [17] Fan H Y, Liu S G 2007 Opt. Lett. 32 1507
[18] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[19] [20] Fan H Y, Zaidi H R 1988 Phys. Rev. A 37 2985
[21] [22] Fan H Y 2003 J. Opt. B 5 R147
[23] [24] [25] Stoler D, Saleh B E A, Teich M C 1985 Opt. Acta 32 345
[26] Fan H Y, Jing S C 2001 Mod. Phys. Lett. B 23 1047
[27] [28] Dattoli G, Galarde J, Torre A 1987 J. Opt. Soc. Am. B 2 185
[29] [30] Agarwal G S 1992 Phys. Rev. A 45 1787
[31] [32] Fan H Y, Jing S C 1994 Phys. Rev. A 50 1909
[33] [34] Barranco A V, Roversi J 1994 Phys. Rev. A 50 5233
[35] [36] [37] Wang X G, Yu R J, Li W 1998 Acta Phys. Sin. 47 1798 (in Chinese) [王晓光、于荣金、李 文 1998 47 1798]
[38] [39] Song J, Cao Z L 2005 Acta Phys. Sin. 54 696 (in Chinese) [宋 军、曹卓良 2005 54 696]
[40] Hu Y H, Fang M F, Liao X P, Zheng X J 2006 Acta Phys. Sin. 55 4631 (in Chinese) [胡要花、方卯发、廖湘萍、郑小娟 2006 55 4631]
[41] [42] Zhang X Y, Wang J S, Meng X G, Su J 2009 Chin. Phys. B 18 604
[43] [44] Jiang N Q, Zheng Y Z 2006 Phys. Rev. A 74 012306
[45] [46] [47] Jiang N Q, Jin B Q, Zhang Y, Cai G C 2008 Eur. Phys. Lett. 84 14002
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[1] Daubechies I 1992 Ten Lectures on Wavelet (Philadelphia: SIAM)
[2] [3] Jaffard S, Meyer Y, Ryan R D 2001 Wavelet, Tools for Science and Technology (Philadelphia: SIAM)
[4] Chui C K 1992 An Introduction to Wavelets (New York: Academic)
[5] [6] [7] Burrus C S, Gopinath R A, Guo H T 1998 Introduction to Wavelet and Wavelet Transformation (A Primer) (New Jersey: Prentice Hall)
[8] Pinsky M A 2002 Introduction to Fourier Analysis and Wavelets (Pacific Grove: Brooks/Cole)
[9] [10] [11] Fan H Y, Lu H L 2006 Opt. Lett. 31 407
[12] Song J, Fan H Y 2010 Chin. Phys. Lett. 27 024210
[13] [14] Fan H Y, Lu H L 2007 Opt. Lett. 32 554
[15] [16] [17] Fan H Y, Liu S G 2007 Opt. Lett. 32 1507
[18] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[19] [20] Fan H Y, Zaidi H R 1988 Phys. Rev. A 37 2985
[21] [22] Fan H Y 2003 J. Opt. B 5 R147
[23] [24] [25] Stoler D, Saleh B E A, Teich M C 1985 Opt. Acta 32 345
[26] Fan H Y, Jing S C 2001 Mod. Phys. Lett. B 23 1047
[27] [28] Dattoli G, Galarde J, Torre A 1987 J. Opt. Soc. Am. B 2 185
[29] [30] Agarwal G S 1992 Phys. Rev. A 45 1787
[31] [32] Fan H Y, Jing S C 1994 Phys. Rev. A 50 1909
[33] [34] Barranco A V, Roversi J 1994 Phys. Rev. A 50 5233
[35] [36] [37] Wang X G, Yu R J, Li W 1998 Acta Phys. Sin. 47 1798 (in Chinese) [王晓光、于荣金、李 文 1998 47 1798]
[38] [39] Song J, Cao Z L 2005 Acta Phys. Sin. 54 696 (in Chinese) [宋 军、曹卓良 2005 54 696]
[40] Hu Y H, Fang M F, Liao X P, Zheng X J 2006 Acta Phys. Sin. 55 4631 (in Chinese) [胡要花、方卯发、廖湘萍、郑小娟 2006 55 4631]
[41] [42] Zhang X Y, Wang J S, Meng X G, Su J 2009 Chin. Phys. B 18 604
[43] [44] Jiang N Q, Zheng Y Z 2006 Phys. Rev. A 74 012306
[45] [46] [47] Jiang N Q, Jin B Q, Zhang Y, Cai G C 2008 Eur. Phys. Lett. 84 14002
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