THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (9): 1062-1070.

THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION

刘海峰, 周炜星, 王辅臣, 龚欣, 于遵宏

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

收稿日期:2001-05-12 修回日期:2002-03-28 出版日期:2002-09-18 发布日期:2002-09-18
通讯作者: DAI Shi-qiang
基金资助:
Foundation items:the National Development Programming of Key Fundamental Researches of China(G1999022103);Planed Item for Distinguished Teacher Invested by Minisny of Education PRC

THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION

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

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

Received:2001-05-12 Revised:2002-03-28 Online:2002-09-18 Published:2002-09-18
Supported by:
Foundation items:the National Development Programming of Key Fundamental Researches of China(G1999022103);Planed Item for Distinguished Teacher Invested by Minisny of Education PRC

摘要/Abstract

摘要： 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 this equation agrees well with the function.

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 this equation agrees well with the function.

中图分类号:

O174

刘海峰;周炜星;王辅臣;龚欣;于遵宏. THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(9): 1062-1070.

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 (English Edition), 2002, 23(9): 1062-1070.

THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION

THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION

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