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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Communicated by DAI Shi-qiang
Foundation items: the National Development Programming of Key Fundamental Researches of China (G1999022103); Planed Item for Distinguished Teacher Invested by Ministry of Education PRC
Biography: LIU Hai-feng (1971-)
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Hai-feng, L., Wei-xing, Z., Fu-chen, W. et al. The wavelet transform of periodic function and nonstationary periodic function. Appl Math Mech 23, 1062–1070 (2002). https://doi.org/10.1007/BF02437717
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DOI: https://doi.org/10.1007/BF02437717