zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Haar wavelet-based technique for sharp jumps classification. (English) Zbl 1046.94504
Summary: A wavelet-based technique is proposed for analysing localized significant changes in observed data in the presence of noise. The main tasks of the proposed technique are (a) denoising the observed data without removing localized significant changes, (b) classifying the detected sharp jumps (spikes), and (c) obtaining a smooth trend (deterministic function) to represent the time-series evolution. By using the Haar discrete wavelet transform, the sequence of data is transformed into a sequence of wavelet coefficients. The Haar wavelet coefficients, together with their rate of change, represent local changes and local correlation of data; therefore, their analysis gives rise to multi-dimensional thresholds and constraints which allow both the denoising and the sorting of data in a suitable space.

MSC:
94A12Signal theory (characterization, reconstruction, filtering, etc.)
65T60Wavelets (numerical methods)
42C40Wavelets and other special systems
WorldCat.org
Full Text: DOI
References:
[1] Letelier, J. C.; Weber, P. P.: Spike sorting based on discrete wavelet transform coefficients. Journal of neuroscience methods 111, 93-106 (2000)
[2] 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)
[3] Percival, D. B.; Walden, A. T.: Wavelet methods for time series analysis. (2000) · Zbl 0963.62079
[4] Rosso, O. A.; Blanco, S.; Yordanova, J.; Kolev, V.; Figliola, A.; Schiirmann, M.; Basar, E.: Wavelet entropy: A new tool for analysis of short duration brain electrical signals. Journal of neuroscience methods 105, 65-75 (2000)
[5] Daubechies, I.: Ten lectures on wavelets, CBMS-NSF regional conference series in applied mathematics. (1992)
[6] Härdle, W.; Kerkyacharian, G.; Picard, D.; Tsybakov, A.: Wavelets, approximation, and statistical applications. Lecture notes in statistics 129 (1998) · Zbl 0899.62002
[7] Berrone, S.; Emmel, L.: A realization of a wavelet Galerkin method on nontrivial domains. Math. models methods appl. Sci. 12, 1525-1554 (2002) · Zbl 1022.65127
[8] Cattani, C.: The wavelets based technique in the dispersive wave propagation. International applied mechanics 39, No. 4 (2003) · Zbl 1054.42022
[9] Cattani, C.: Reduced Haar wavelet spline analysis. Pharos 8, No. 1, 47-62 (2001) · Zbl 1019.65107
[10] Cattani, C.; Ciancio, A.: Energy wavelet analysis of time series, atti accademia peloritana dei pericolanti, classe I. Scienze fis. Mat. e nat. 80, 67-77 (2002)
[11] Cattani, C.; Ciancio, A.: Spike sorting by wavelet time decomposition. Rend. scutinario matem. Di messina, ser. II 8, 1-12 (2001)
[12] Cattani, C.: Haar wavelet spline. Journal of interdisciplinary mathematics 4, No. 1, 35-47 (2001) · Zbl 1019.65107
[13] Chui, C. K.: An introduction to wavelets. (1997) · Zbl 0925.42016
[14] Auscher, A.; Weiss, G.; Wickerhauser, M. V.: Local sine and cosine bases of coifman and Meyer and the construction of smooth wavelets. Wavelets: A tutorial in theory and applications, 237-256 (1992) · Zbl 0767.42009
[15] Coifman, R.; Meyer, Y.: Remarques sur l’analyse de Fourier a fenetre. Comptes rendus de l’académie des sciences de Paris 312, 259-261 (1991)
[16] Danilina, N. I.; Dubroskaya, N. S.; Kvasha, O. P.; Smirnov, G. L.: Computational mathematics. (1988) · Zbl 0701.65001
[17] Jansen, M.: Noise reduction by wavelet thresholding. Lecture notes in statistics 161 (2001) · Zbl 0989.94001
[18] Helbing, D.: Traffic and related self-driver many-particle systems. Rev. modern phys. 73, 1067-1141 (2001)
[19] Bellomo, N.; Delitala, M.; Coscia, V.: On the mathematical theory of vehicular traffic flow. I. fluid dynamic and kinetic modelling. Math. models methods appl. Sci. 12, 1801-1844 (2002) · Zbl 1041.76061
[20] Arlotti, L.; Bellomo, N.; De Angelis, E.: Generalized kinetic (Boltzmann) models: mathematical structures and applications. Math. models methods appl. Sci. 12, 567-591 (2002) · Zbl 1174.82325
[21] Tervo, J.; Kolmonen, P.: Inverse radiotherapy treatment planning model applying Boltzmann-transport equation. Math. models methods appl. Sci. 12, 109-141 (2002) · Zbl 1016.92017