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Singularity and Similarity Detection from Signals Using Wavelet Transform
[article]
2021
arXiv
pre-print
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The wavelet transform and related techniques are used to analyze singular and fractal signals. ...
The wavelet auto-covariance is applied to estimate the self-similarity exponent for statistical self-affine signals. ...
ACKNOWLEDGMENT The authors gratefully acknowledge that this work was supported by EPSRC (UK). ...
arXiv:2110.15825v1
fatcat:5u6gyvi3jveszjqhuzwachk4ue
A comparison of different analytical techniques for identifying structures in turbulence
1994
Applied Scientific Research : an international journal on the applications of fluid dynamics
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New methods for investigating complex (self-similar) structures based on fractal and wavelet analyses are presented. ...
Methods of distinguishing between locally (accumulating) and globally (fractal) selfsimilar structures are suggested. ...
Acknowledgement N K R K and J C V have been supported by British Gas during this work. ...
doi:10.1007/bf00849109
fatcat:cobeawt3s5fmbpr6aqg327i7fa
A comparison of different analytical techniques for identifying structures in turbulence
[chapter]
1993
Fluid Mechanichs and its Application
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New methods for investigating complex (self-similar) structures based on fractal and wavelet analyses are presented. ...
Methods of distinguishing between locally (accumulating) and globally (fractal) selfsimilar structures are suggested. ...
Acknowledgement N K R K and J C V have been supported by British Gas during this work. ...
doi:10.1007/978-94-011-2098-2_27
fatcat:rqq2oal5bfg4rk4yhmrmawxfye
The solar activity by wavelet-based multifractal analysis
2016
NRIAG Journal of Astronomy and Geophysics
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The influence of the solar activity on the total ozone was shown by the wavelet coherence, phase and the similarity of the change of fractality. ...
These findings will contribute to the research of the relationship between the solar activity and climate. ...
We used the Daubechies wavelet as the analyzing wavelet because it is widely used in solving a broad range of problems, e.g., self-similarity properties of a signal or fractal problems and signal discontinuities ...
doi:10.1016/j.nrjag.2016.10.003
fatcat:azxwdsk7u5gnhopbj5erzoin34
Analysis of the geomagnetic activity of the Dst index and self-affine fractals using wavelet transforms
2004
Nonlinear Processes in Geophysics
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The geomagnetic activity of the D st index is analyzed using wavelet transforms and it is shown that the D st index possesses properties associated with self-affine fractals. ...
One of the advantages of wavelet analysis is that many inherent problems encountered in Fourier transform methods, such as windowing and detrending, are not necessary. ...
Sailhac and one anonymous reviewer for their constructive and helpful comments to improve the manuscripts. Edited by: J. Büchner Reviewed by: K. Sauer and another referee ...
doi:10.5194/npg-11-303-2004
fatcat:vd2dkiar7rfirjesae2g4e3pc4
Gait Recognition Using Fractal Scale and Wavelet Moments
2006
18th International Conference on Pattern Recognition (ICPR'06)
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Fractal scale based on wavelet analysis represents the self-similarity of signals, and improves the flexibility of wavelet moments. ...
Optimal wavelets based on generalized multi-resolution analysis are used to improve the recognition rate. Descriptors of fractal scale are translation, scale and rotation invariant. ...
Fractal scale (FS) is an efficient method for onedimensional signal classification and recognition, and can describe the self-similarity of signals. ...
doi:10.1109/icpr.2006.594
dblp:conf/icpr/ZhaoCLP06
fatcat:xqwahommhffyzlqyn7keb2vpna
Relationship between the Northern Hemisphere Sea Ice Area and Global Temperature by Multifractal Analysis
2020
Journal of Applied Mathematics and Physics
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The relationship between the solar activity: solar flux, sunspot number (SSN), and ultraviolet B (UV-B), and NH sea ice area was assessed based on changes in fractality. ...
We identified the existing relations among the NH sea ice area, global temperature, and PDO based on changes in fractality and wavelet coherence. ...
For the examination, we used the Daubechies wavelet, which is widely used in solving a broad range of problems, e.g., self-similarity properties of a signal and signal discontinuities. ...
doi:10.4236/jamp.2020.85069
fatcat:d7j6wmfs3nggngdt3vqipu5bau
A class of multiresolution stochastic models generating self-affine images
1999
IEEE Transactions on Signal Processing
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The accuracy of this assumption is evaluated by a comparison between the statistics of natural images and those of a multiresolution stochastic model designed to generate images exhibiting affine self-similarity ...
Fractal image compression is based on the rather poorly motivated assumption that "natural" images exhibit significant affine self-similarity. ...
ACKNOWLEDGEMENT The authors wish to thank G. Cox and the anonymous reviewers for valuable comments on the manuscript. ...
doi:10.1109/78.765153
fatcat:ncvovfzjajeyxbv4fbbnpx3wli
Solar Influences on the North Atlantic Oscillation by Wavelet-Based Multifractal Analysis
2018
Journal of Geoscience and Environment Protection
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The strong interactions were inferred from the similarity of fractality changes and the wavelet coherence. ...
The purpose of this research is to investigate the relationship between the solar activity, total ozone, and the North Atlantic Oscillation (NAO) from a viewpoint of multi-fractality. ...
We used the Daubechies wavelet as the analyzing wavelet because it is widely used in solving a broad range of problems, e.g., self-similarity properties of a signal or fractal problems and signal discontinuities ...
doi:10.4236/gep.2018.68010
fatcat:mnsjh6f2nbhfvnxh244u5l3ur4
Relationship between the Atmospheric CO2 and Climate Indices by Wavelet-Based Multifractal Analysis
2019
Journal of Geoscience and Environment Protection
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The changes of CO 2 and ENSO were closely related and the influence of the CO 2 on the ENSO was strong from the change in fractality and wavelet coherence. ...
To study the relation between the atmospheric CO 2 concentration and the climate indices, we investigated the change of fractal behavior of the CO 2 , the carbon isotope ratio (δ 13 C) of atmospheric CO ...
For the examination, we used the Daubechies wavelet, which is widely used in solving a broad range of problems, e.g., self-similarity properties of a signal and signal discontinuities. ...
doi:10.4236/gep.2019.71004
fatcat:mudy2a62mjdn3gemdlfs5pz7cu
Multifractal aspects of software development
2011
Proceeding of the 33rd international conference on Software engineering - ICSE '11
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This analysis can be used when a signal exhibits multiscale self-similarity, as in the case of complex data drawn from power-law distributions. ...
Specifically we utilize multifractal analysis to demonstrate that software development is multifractal, that is the signal is a fractal composed of multiple fractal dimensions along a range of Hurst exponents ...
Self-similarity and Fractal Behaviour Multi-scale self-similarity is the similarity of a signal to itself at multiple scales. ...
doi:10.1145/1985793.1985962
dblp:conf/icse/HindleGH11
fatcat:uymw4wo44bcw7lkottu7xgtdqi
Multirate diversity strategy of fractal modulation
2011
Chinese Physics B
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As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. ...
Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total ...
On the other hand, under the actual circumstances, the relationship between the signals and the fractal noises has increasingly become an important issue, therefore, the theoretical analysis of whether ...
doi:10.1088/1674-1056/20/4/040509
fatcat:v3blm3gijjanpfb64sji47v4au
Stiffness Indices and Fractal Dimension relationship in Arterial Pressure and Diameter Time Series in-Vitro
2011
Journal of Physics, Conference Series
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The aim of this study consisted on arterial pressure and diameter signals processing, by means of nonlinear techniques based on fractal geometry. ...
Fractal geometry can be mentioned as one of those techniques. ...
Self-similarity in arterial pressure and diameter time series Self-similarity presence in arterial pressure and diameter signals was verified by the application of the wavelet transform (WT) [9] . ...
doi:10.1088/1742-6596/332/1/012024
fatcat:opyjqvudf5esjjnf3e2433fe3i
Review of Methods for Texture Analysis of Myocardium From Echocardiographic Images: A Means of Tissue Characterization
2003
Echocardiography
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This review discusses the definition of texture and identifies its utility in echocardiography for characterization of tissue. ...
Several methodologies, particularly the wavelet method of texture quantification, seem to be promising. Image texture analysis appears to be a fertile area for research in echocardiography. ...
Geometrical self-similarity means that an object is self-similar exactly at differing resolutions. Fractal biologic objects, however, have statistical self-similarity. ...
doi:10.1111/j.0742-2822.2003.01126.x
pmid:14641378
fatcat:r7fotajrqjfc7l6egfaqvsjfnu
Image denoising using fractal- and wavelet-based methods
2004
Wavelet Applications in Industrial Processing
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Within this multiple representation we do a fractal coding which tries to approximate a noise free image. The inverse wavelet transform of the fractal collage leads to the denoised image. ...
Using a non-subsampled overcomplete wavelet transform we present the image as a collection of translation invariant copies in different frequency subbands. ...
Denoising results are significantly improved compared to a subsampled wavelet decomposition. For some images the denoising results are comparable to other state of the art wavelet denoisers. ...
doi:10.1117/12.516206
fatcat:ydbsbjgdojd5ve62vsfcfhkcey
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