The Wavelet Transform of Periodic Function and Nonstationary Periodic Function

LIU Hai-feng; ZHOU Wei-xing; WANG Fu-chen; GONG Xin; YU Zun-hong

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(9): 943-950

LIU Hai-feng, ZHOU Wei-xing, WANG Fu-chen, GONG Xin, YU Zun-hong. The Wavelet Transform of Periodic Function and Nonstationary Periodic Function[J]. Applied Mathematics and Mechanics, 2002, 23(9): 943-950.

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The Wavelet Transform of Periodic Function and Nonstationary Periodic Function

College of Resource and Environmental Engineering, East China University of Science and Technology, Shanghai 200237, P. R. China

Received Date: 2000-10-16
Rev Recd Date: 2002-03-28
Publish Date: 2002-09-15

Abstract

Abstract

Some properties of the wavelet transform of trigonometric function, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with the equation agress well with the function.
- wavelet transform,
- periodic function,
- nonstationary periodic function,
- Fourier transform

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References(12)

References

[1]	Daubechies I.Ten lectures on wavelets[A].In:CBMS-NSF Reg Conf Ser Appl Math.Philadelphia:SIAM Press,1992.
[2]	Farge M,Kevlahan N,Perrier V,et al.Wavelets and turbulence[J].Proc IEEE,1996,84(4):639-669.
[3]	Jaffard S.Some mathematical results about the multifractal formalism for function[A].In:Wavelet.Theory,Algorithms,and Applications[C].Academic Press,1994,325-361.
[4]	Guillemain P,Kronland-Martinet R.Characterization of acoustic signals through continuous linear time-frequency representations[J].Proc IEEE,1996,84(4):561-585.
[5]	Holmes P,Lumley J L,Berkooz G.Turbulence,Coherent Structures,Dynamical Systems and Symmetry[M].Cambridge:Cambridge University Press,1996.
[6]	Baker G I,Collub J P.Chaotic Dynamics:An Introduction[M].Cambrdge:Cambridge University Press,1996.
[7]	Perrier V.Wavelet Spectra compared to Fourier spectra[J].J Math Phys,1995,36(3):1506-1519.
[8]	程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,1998.
[9]	潘文杰.傅立叶分析及其应用[M].北京:北京大学出版社,2000.
[10]	欧阳光中,姚允龙.数学分析[M].上海:复旦大学出版社,1999.
[11]	Chui C K.An Introduction to Wavelets[M].Xi'an:Xi'an Jiaotong University Press,1995.
[12]	Forinash K,Lang W C.Frequency analysis of discrete breather modes using a continuous wavelet transform[J].Physica D,1998,123(3):437-447.