| THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION |
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| 作者姓名： | 刘海峰 周炜星 王辅臣 龚欣 于遵宏 |
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| 作者单位： | College of Resource and Environmental Engineering，East China University of Science and Technology，Shanghai 200237，P R China，College of Resource and Environmental Engineering，East China University of Science and Technology，Shanghai 200237，P R China，College of Resource and Environmental Engineering，East China University of Science and Technology，Shanghai 200237，P R China，College of Resource and Environmental Engineering，East China University of Science and Technology，Shanghai 200237，P R China，College of Resource and Environmental Engineering，East China University of Science and Technology，Shanghai 200237，P R China |
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| 基金项目： | Foundation items:the National Development Programming of Key Fundamental Researches of China(G1999022103)，Planed Item for Distinguished Teacher Invested by Minisny of Education PRC |
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| 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.
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| 收稿时间： | 12 May 2001 |
The wavelet transform of periodic function and nonstationary periodic function |
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| Liu Hai-feng Associate Professor, Doctor,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. |
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| Authors: | Liu Hai-feng Associate Professor Doctor Zhou Wei-xing Wang Fu-chen Gong Xin Yu Zun-hong |
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| Institution: | College of Resource and Environmental Engineering, East China University of Science and Technology, Shanghai,200237, P R China |
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| 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. |
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| Keywords: | wavelet transform periodic function nonstationary periodic function Fourier transform |
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