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The wavelet transform of periodic function and nonstationary periodic function

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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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References

  1. Daubechies I. Ten lectures on wavelets[A]. In:CBMS-NSF Reg Conf Ser Appl Math[C]. Philadelphia: SIAM Press, 1992.

    Google Scholar 

  2. Farge M, Kevlahan N, Perrier V, et al. Wavelets and turbulence[J].Proc IEEE, 1996,84(4): 639–669.

    Article  Google Scholar 

  3. Jaffard S. Some mathematical results about the multifractal formalism for function[A]. In:Wavelet: Theory, Algorithms, and Applications[C]. Academic Press, 1994, 325–361.

  4. Guillemain P, Kronland-Martinet R. Characterization of acoustic signals through continuous linear time-frequency representations[J].Proc IEEE, 1996,84(4): 561–585.

    Article  Google Scholar 

  5. Holmes P, Lumley J L, Berkooz G.Turbulence, Coherent Structures, Dynamical Systems and Symmetry[M]. Cambridge: Cambridge University Press, 1996.

    Google Scholar 

  6. Baker G I, Collub J P.Chaotic Dynamics: An Introduction[M]. Cambridge: Cambridge University Press, 1996.

    Google Scholar 

  7. Perrier V. Wavelet Spectra compared to Fourier spectra[J].J Math Phys, 1995,36(3): 1506–1519.

    Article  MATH  MathSciNet  Google Scholar 

  8. CHENG Zheng-xing.Algorithm and Application of Wavelet Analysis[M]. Xi’an: Xi’an Jiaotong University Press, 1998. (in Chinese)

    Google Scholar 

  9. PAN Wen-jie.Fourier Analysis and Its Applications[M]. Beijing: Peking University Press. 2000. (in Chinese)

    Google Scholar 

  10. OUYANG Guang-zhong, YAO Yun-long.Mathematical Analysis[M]. Shanghai: Fudan University Press, 1999. (in Chinese)

    Google Scholar 

  11. Chui C K.An Introduction to Wavelets[M]. Xi’an: Xi’an Jiaotong University Press, 1995.

    Google Scholar 

  12. Forinash K, Lang W C. Frequency analysis of discrete breather modes using a continuous wavelet transform[J].Physica D, 1998,123(3): 437–447.

    Article  Google Scholar 

Download references

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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

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