Abstract
The theory of detecting ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges. To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal’s instantaneous amplitude and period.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Carmona R, Hwang W L, Torresani B.Practical Time-frequency Analysis: Gaber and Wavelet Transforms with an Implementation S. San Diego: Academic Press, 1998.
Cohen I.Time-frequency Analysis: Theory and Application. New York: Prentice Hall, 1995.
Hess-Niselsen N, Wickerhause M V. Wavelets and Time-frequency Analysis.Proceedings of the IEEE, 1996,84(4): 523–540.
Grossmann A, Morlet J. Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shap.SIAM J Math, 1984,15:723–736.
Mallat S, Hwang W L. Singularity Detection and Processing with Wavelets.IEEE Transaction on Information Theory, 1992,38(2):617–643.
Mallat S. A Theory for Multiresolution Signal Decomposition: the Wavelet Representation.IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989,11(7): 674–693.
Mallat S.A Wavelet Tour of Signal Processing. Second Edition. San Diego: Academic Press, 1999.
Meyer Y.Wavelets: Algorithms and Applications. Philadelphia: SIAM, 1993.
Bachman G, Narici L, Beckenstein E.Fourier and Wavelet Analysis. New York: Springer Verlag, 2000.
Fan Qi-bin. An Overview on Wavelet Software Packages.Wuhan University Journal of Natural Sciences, 2001,6(1–2): 593–600.
Carmona R, Hwang W L, Torresani B. Characterization of Signals by the Ridges of their wavelet transforms.IEEE Trans on Signal Processing, 1997,45(10):2586–2590.
Carmona R, Hwang W L, Torresani B.Practical Time-Frequenly Analysis. San Diego: Academic Press, 1998.
Carmona R, Hwang W L, Torresani B. Multiridge Detection and Time-Frequenly Relonstruction.IEEE Trans on Signal Processing, 1999,47(2):480–492.
Yao Duan-zheng, Liang Jia-bao.Methods of Mathematical Physics. Wuhan: Wuhan University Press, 2001 (Ch).
Kosaku Yosida.Functional Analysis. New York: Springer-Verlag, 1999.
Author information
Authors and Affiliations
Additional information
Foundation item: Supported by the National Natural Science Foundation of China (49771060)
Biography: Fan Qi-bin (1956-), male, Professor, research direction: the theory and application of wavelet analysis, image compression and signal processing.
Rights and permissions
About this article
Cite this article
Qi-bin, F., Xiao-yan, S. Local extrema of periodic function’s wavelet transform. Wuhan Univ. J. Nat. Sci. 10, 949–952 (2005). https://doi.org/10.1007/BF02832445
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02832445