Some applications of wavelet transform: continuous and fractional approach
Само за регистроване кориснике
2009
Конференцијски прилог (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
Non-stationary signals are quite common in everyday life. It is well known that the conventional Fourier analysis is not capable of describing the evolution of the spectral features of a signal as this evolves in time. Since wavelets can represent signals locally in time and frequency, their application in various fields of science and engineering. Wavelets are mathematical functions generated from one basic function by the dilatation (scale parameter) (W(x) → W(2x)) and a translation (shift parameter) (W(x) → W(x+1)). Also, the mathematical idea of fractional derivatives and integrals have represented the subject of interest for various branches of science. The fractional integro-differential operators (fractional calculus) present a generalization of integration and derivation to non-integer order (fractional) operators. As it is already known the splines play a significant role on the early development of the theory of the wavelet transform. In this presentation a new wavelet transf...orm is introduced and considered. The generalization of the splines (fractional B-splines) constructions will be proposed, namely new wavelet bases with a continuous order parameter will be obtained. The main advantage of this construction is that we can build the wavelet bases parameterized by the continuously-varying regularity parameter α. Specially, in the spectral analysis, the continuous wavelet transform and fractional wavelet transform are powerful tools for the data reduction, de-noising, compressing and baseline correction of the analytical signals and resolution of multi-component overlapping signals.
Кључне речи:
wavelet transform / fractional calculusИзвор:
Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia, 2009, 64-64Издавач:
- Mathematical Society of South-Eastern Europe
- Union of Mathematicans of Macedonia
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Lazarević, Mihailo AU - Vasić, Vasilije PY - 2009 UR - https://machinery.mas.bg.ac.rs/handle/123456789/6600 AB - Non-stationary signals are quite common in everyday life. It is well known that the conventional Fourier analysis is not capable of describing the evolution of the spectral features of a signal as this evolves in time. Since wavelets can represent signals locally in time and frequency, their application in various fields of science and engineering. Wavelets are mathematical functions generated from one basic function by the dilatation (scale parameter) (W(x) → W(2x)) and a translation (shift parameter) (W(x) → W(x+1)). Also, the mathematical idea of fractional derivatives and integrals have represented the subject of interest for various branches of science. The fractional integro-differential operators (fractional calculus) present a generalization of integration and derivation to non-integer order (fractional) operators. As it is already known the splines play a significant role on the early development of the theory of the wavelet transform. In this presentation a new wavelet transform is introduced and considered. The generalization of the splines (fractional B-splines) constructions will be proposed, namely new wavelet bases with a continuous order parameter will be obtained. The main advantage of this construction is that we can build the wavelet bases parameterized by the continuously-varying regularity parameter α. Specially, in the spectral analysis, the continuous wavelet transform and fractional wavelet transform are powerful tools for the data reduction, de-noising, compressing and baseline correction of the analytical signals and resolution of multi-component overlapping signals. PB - Mathematical Society of South-Eastern Europe PB - Union of Mathematicans of Macedonia C3 - Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia T1 - Some applications of wavelet transform: continuous and fractional approach EP - 64 SP - 64 UR - https://hdl.handle.net/21.15107/rcub_machinery_6600 ER -
@conference{ author = "Lazarević, Mihailo and Vasić, Vasilije", year = "2009", abstract = "Non-stationary signals are quite common in everyday life. It is well known that the conventional Fourier analysis is not capable of describing the evolution of the spectral features of a signal as this evolves in time. Since wavelets can represent signals locally in time and frequency, their application in various fields of science and engineering. Wavelets are mathematical functions generated from one basic function by the dilatation (scale parameter) (W(x) → W(2x)) and a translation (shift parameter) (W(x) → W(x+1)). Also, the mathematical idea of fractional derivatives and integrals have represented the subject of interest for various branches of science. The fractional integro-differential operators (fractional calculus) present a generalization of integration and derivation to non-integer order (fractional) operators. As it is already known the splines play a significant role on the early development of the theory of the wavelet transform. In this presentation a new wavelet transform is introduced and considered. The generalization of the splines (fractional B-splines) constructions will be proposed, namely new wavelet bases with a continuous order parameter will be obtained. The main advantage of this construction is that we can build the wavelet bases parameterized by the continuously-varying regularity parameter α. Specially, in the spectral analysis, the continuous wavelet transform and fractional wavelet transform are powerful tools for the data reduction, de-noising, compressing and baseline correction of the analytical signals and resolution of multi-component overlapping signals.", publisher = "Mathematical Society of South-Eastern Europe, Union of Mathematicans of Macedonia", journal = "Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia", title = "Some applications of wavelet transform: continuous and fractional approach", pages = "64-64", url = "https://hdl.handle.net/21.15107/rcub_machinery_6600" }
Lazarević, M.,& Vasić, V.. (2009). Some applications of wavelet transform: continuous and fractional approach. in Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia Mathematical Society of South-Eastern Europe., 64-64. https://hdl.handle.net/21.15107/rcub_machinery_6600
Lazarević M, Vasić V. Some applications of wavelet transform: continuous and fractional approach. in Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia. 2009;:64-64. https://hdl.handle.net/21.15107/rcub_machinery_6600 .
Lazarević, Mihailo, Vasić, Vasilije, "Some applications of wavelet transform: continuous and fractional approach" in Book of abstracts MASSEE Int Congress on Mathematics MICOM2009, Sept. 16-20 2009, Ohrid, Macedonia (2009):64-64, https://hdl.handle.net/21.15107/rcub_machinery_6600 .