Wavelet transform for Fresnel-transformed mother wavelets

doi:10.1088/1674-1056/20/12/120305

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 F_r,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

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