中国物理B ›› 2008, Vol. 17 ›› Issue (1): 170-179.doi: 10.1088/1674-1056/17/1/030

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇    下一篇

Wavelet--fractional Fourier transforms

袁琳   

  1. College of Mathematics Physics and Information, Zhejiang Normal University, Jinhua 321004, China
  • 出版日期:2008-01-20 发布日期:2008-01-20
  • 基金资助:
    Project supported by the Young People Foundation of Zhejiang Normal University, China (Grant No KYJ06Y07150).

Wavelet--fractional Fourier transforms

Yuan Lin(袁琳)†   

  1. College of Mathematics Physics and Information, Zhejiang Normal University, Jinhua 321004, China
  • Online:2008-01-20 Published:2008-01-20
  • Supported by:
    Project supported by the Young People Foundation of Zhejiang Normal University, China (Grant No KYJ06Y07150).

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摘要： This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for $L^{2}\left( R \right)$ instead of Hermite--Gaussian functions. The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.

Abstract: This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for $L^{2}\left( R \right)$ instead of Hermite--Gaussian functions. The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.

Key words: multiresolution analysis, fractional Fourier transform, wavelets-fractional Fourier transform

中图分类号:  (Fourier optics)

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