Abstract
Wavelets give significant information on the evolution of a time series. In particular, due to their localization properties the significant local changes in observed data (both in time and in frequency) can be easily detected by a limited set of their corresponding wavelet coefficients. Some examples will be given, in the following, showing the effectiveness of this method.
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References
Auscher, A., Weiss, G., Wickerhauser, M.V.: Local sine and cosine bases of Coifman and Meyer and the construction of smooth wavelets. In: Chui, C.K. (ed.) Wavelets: A tutorial in Theory and Applications, pp. 237–256. Academic Press, San Diego (1992)
Cattani, C.: Haar Wavelet based Technique for Sharp Jumps Classification, vol. 39, pp. 255–279 (2004)
Cattani, C.: Wavelet Analysis of Nonlinear Dynamical Systems. Bulletin of Academy of Sciences of Moldova, Mathematics (Buletinul Academiei de Stiinte a Republicii Moldova, Matematica) 1(41), 58–69 (2003)
Cattani, C.: Wavelet Analysis of Dynamical Systems. Electronics and Communications 17, 115–124 (2002)
Cattani, C.: Reduced Haar Wavelet Spline Analysis. Pharos 8(1), 47–62 (2001)
Cattani, C.: Haar Wavelet Spline. Journal of Interdisciplinary Mathematics 4(1), 35–47 (2001)
Cattani, C., Ciancio, A.: Wavelet estimate of time series. Atti Accademia dei Pericolanti, Classe I, Scienze Fis. Mat. e Nat. LXXIX, 105–116 (2001)
Cattani, C., Ciancio, A.: Spike Sorting by Wavelet Time Decomposition. Rend. Seminario Matem. di Messina, Ser.II 8, 1–12 (2001)
Cattani, C., Ciancio, A.: Energy wavelet analysis of time series. Atti Accademia Peloritana dei Pericolanti, Classe I, Scienze Fis.Mat. e Nat. LXXX, 67–77 (2002)
Cattani, C., Ciancio, A.: Jumps Detection by Adapted Haar Wavelet Time Decomposition. U.P.B. Scientific Bulletin of Politechnic University of Bucharest, Series A: Applied Mathematics and Physics 66(1-4), 13–22 (2004)
Coifman, R., Meyer, Y.: Remarques sur l’analyse de Fourier á fenetre. Comptes Rendus de l’Académie des Sciences de Paris 312, 259–261 (1991)
Daubechies, I.: Ten lectures on wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia (1992)
Hulata, E., Segev, R., Ben-Jacob, E.: A method for spike sorting and detection based on wavelet packets and Shannon’s mutual information. Journal of Neuroscience Methods 117, 1–12 (2002)
Percival, D.B., Walden, A.T.: Wavelet Methods for Time Series Analysis. Cambridge University Press, Cambridge (2000)
Rosso, O.A., Blanco, S., Yordanova, J., Kolev, V., Figliola, A., Schürmann, M., Basar, E.: Wavelet entropy: a new tool for analysis of short duration brain electrical signals. Journal of Neuroscience Methods 105, 65–75 (2000)
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Ciancio, A., Cattani, C. (2006). Analysis of Singularities by Short Haar Wavelet Transform. In: Gavrilova, M., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751540_90
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DOI: https://doi.org/10.1007/11751540_90
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