周期函数和非平稳周期函数的小波变换

基金项目: 国家重点基础研究发展规划资助项目(G1999022103);高等学校骨干教师资助计划项目

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

摘要: 探讨了三角函数、周期函数以及一类非平稳周期函数小波变换的一些性质,发现周期函数的小波能谱的峰高和峰宽均正比于信号的周期.提出了一个新的只利用与信号周期有关的一个尺度小波变换系数的重构公式,它可准确地重构三角函数,对一般周期函数的重构结果优于其Fourier级数中的任何一项,对一类均值和振幅变化的非平稳周期函数的重构结果与信号非常吻合.
- 小波变换 /
- 周期函数 /
- 非平稳周期函数 /
- 傅立叶变换
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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