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

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THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION

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

  1. 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

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.

2010 MSC Number: 

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