Wavelet technique

Wavelet techniques (Koscielny-Bunde et al., 1998) and detrended fluctuation analysis (DFA) (Peng et al., 1994) are among the most recently used tools along these lines. Recently, much attention has been paid to DFA, because it has already proved its usefulness in a wide variety of complex systems (e.g., Stanley, 1999 Talkner and Weber, 2000 Varotsos et al., 2003a, b, 2005 Chen et al., 2005 Varotsos and Kirk-Davidoff, 2006). More information about the DFA method is given in Section 3.6.3.2. 

Fig. 12.18 Two examples (a and b) of the tubular pressure variations that one can observe in adjacent nephrons for hypertensive rats. In spite of the irregularity in the dynamics, one can see a certain degree of synchronization in the phases of the two oscillations. This synchronization is supported by formal investigations, e.g., by means of the wavelet technique.

A wavelet technique for spatial enhancement of microcalcifications in mammograms was evaluated by Kallergi et al. (1996). Digitized mammograms were... 

The impedance simulation of the dynamics was carried out with Finite Difference Method (FDM) implemented in MATLAB. Alternatively, the discretization of equations can be performed by use of Finite Element Method (FEM), wavelets techniques, etc. [15,16]. Electrodes were positioned on 2 sides of the 10 mm square tissue model, current was inserted and voltages were calculated for each case of 60 time-steps. Electric impedance maps with resolution 35 x 35 x 1 were derived from the dynamic vascular network (Figure 4). 

Nagarajaiah S, Basu B (2009) Output only identification and structural damage detection using time frequency and wavelet techniques. Earthq Eng Eng Vib 8 583-605... 

Adaptive Complex Wavelet Technique for Medical Image Denoising... 

Among these techniques, the Continuous Wavelet Transform (CWT) is particularly well suited to the eddy current signal coming from the tube control, as shown in this paper, and provides efficient detection results. 

Furthermore, one may need to employ data transformation. For example, sometimes it might be a good idea to use the logarithms of variables instead of the variables themselves. Alternatively, one may take the square roots, or, in contrast, raise variables to the nth power. However, genuine data transformation techniques involve far more sophisticated algorithms. As examples, we shall later consider Fast Fourier Transform (FFT), Wavelet Transform and Singular Value Decomposition (SVD). 

A popular technique for approximation consists of representing the data as a weighted sum of a set of basis functions. As described in Section III, A, wavelets form a convenient set of basis functions to represent signals consisting of a variety of features. A signal decomposed on an... 

In order to compress the measured data through a wavelet-based technique, it is necessary to perform a series of convolutions on the data Becau.se of the finite size of the convolution filters, the data may be decomposed only after enough data has been collected so as to allow convolution and decomposition on a wavelet basis. Therefore, point-bypoint data compression as done by the boxcar or backward slope methods is not possible using wavelets. Usually, a window of data of length 2" m e Z, is collected before decomposition and selection of the appropriate... 

Fig. 20. Performance of data compression techniques (a) orthonormal wavelet (b) backward slope (c) boxcar.

Wolkenstein M, Hutter H, Nikolov SG, Schnitz I, Grasserbauer M (1997b) Comparison of wavelet filtering with well-known techniques for EPMA image de-noising. J Trace Microprobe Techn 15 33... 

Since in many applications minor absorption changes have to be detected against strong, interfering background absorptions of the matrix, advanced chemometric data treatment, involving techniques such as wavelet analysis, principle component analysis (PCA), partial least square (PLS) methods and artificial neural networks (ANN), is a prerequisite. 

Sample Preparation Techniques in Analytical Chemistry. Edited by Somenath Mitra Analysis and Purification Methods in Combination Chemistry. Edited by Bing Yan Chemometrics From Basics to Wavelet Transform. By Foo-tim Chau, Yi-Zeng Liang, Junbin Gao, and Xue-guang Shao... 

One problem encountered in solving Eq. (11.12) is the modeling of the prior distribution P x. It is assumed that this distribution is not known in advance and must be calculated from historical data. Several methods for estimating the density function of a set of variables are presented in the literature. Among these methods are histograms, orthogonal estimators, kernel estimators, and elliptical basis function (EBF) estimators (see Silverman, 1986 Scott, 1992 Johnston and Kramer, 1994 Chen et al., 1996). A wavelet-based density estimation technique has been developed by Safavi et al. (1997) as an alternative and superior method to other common density estimation techniques. Johnston and Kramer (1998) have proposed the recursive state... 

B. A. Hess Dr. Gaspard has introduced the vibrogram as a tool to extract periodic orbits from the spectrum by means of a windowed Fourier transform. This raises the question whether other recent techniques of signal analysis like multiresolution analysis or wavelet transforms of the spectrum could be used to separate the time scales and thus to disentangle the information pertinent to the quasiclassical, semiclassical, and long-time regimes. Has this ever been tried ... 

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