Wavelet Theory Research Articles

ON THE BROADBAND POWER LINE COMMUNICATION SIGNALS’ DYNAMIC FEATURES

For the purpose of transmitting data in smart grids, broadband communication over power lines (PLC) is considered to be one of the feasible technologies. Due to the multi-path effect of the signal propagation in complicate electrical networks, PLC signals present some dynamic features in time and space domains. The mono-fractal and multi-fractal theories are introduced to understand such dynamic features in PLC signals. Four common methods, namely, re-scaled range analysis, variance–time plot method, periodic diagram analysis and wavelet-based method are used to study the nonlinear properties and self-similarity. Fractal analysis at different frequencies and times is also performed to verify further. The paper also tests multi-fractal properties of PLC signals by the means of multi-fractal detrended fluctuation analysis (MFDFA). The multi-fractal spectrum of power low exponents is estimated from the measured PLC signals. We also proposed a new algorithm to improve the performance of the traditional MFDFA, where wavelet theory is integrated. By simulations, the better performance of the proposed method is verified.

A New Kind of Image Edge Detection Based on The Theory of The Adaptive Lifting Wavelet and Morphology

This article describes how in traditional edge detection it is prone to defects such as fuzzy positioning, and noise influence. This article proposes a type of edge detection algorithm which combines lifting wavelet transform and adaptive mathematical morphology, which makes a lifting wavelet to analyze the wood cell image. Then, the high-frequency part is detected by using the algorithm fusing the wavelet packet and the rapid-combining multi-scale wavelet, which controls noise effectively; while for the low frequency part is detected with modified adaptive mathematical morphology, to locate the exact details. The final result will processes the edge of the image using “algebra” algorithm fusion. The example for a wood cell image which illustrates the algorithm is to detect the cell boundary relatively clearly, and effectively suppress the noise.

Elementary Theory of Wavelets and Filter Bank

Elementary Theory of Wavelets and Filter Bank

A comparative analysis of artificial neural network (ANN), wavelet neural network (WNN), and support vector machine (SVM) data-driven models to mineral potential mapping for copper mineralizations in the Shahr-e-Babak region, Kerman, Iran

The study area located in the southern section of the Central Iranian volcano–sedimentary complex contains a large number of mineral deposits and occurrences which is currently facing a shortage of resources. Consequently, prospecting potential areas in the deeper and peripheral spaces has become a high priority in this region. Different direct and indirect methods try to predict promising areas for future explorations which most of them are very time-consuming and costly. Therefore, applying an efficient method which can model the mineral potential areas correctly and decrease the uncertainty is necessary. The main objective of this study is to predict new explanatory areas associated with Cu mineralization in Shahr-e-Babak mineral region using three data-driven models, namely artificial neural network (ANN), wavelet neural network (WNN), and support vector machine (SVM). Most of the researches show that the capability (i.e., classification, pattern matching, optimization, and prediction) of an ANN is suitable for inheriting uncertainties and imperfections found in mining engineering problems considering its successful application. Despite all of the applications of ANNs in mineral potential mapping, they have limitations. In this paper, an alternative method of mineral potential mapping is presented which is based on integration between wavelet theory and ANN or WNN. The obtained results by WNN are in good agreement with the known deposits, indicating that WNN method with POLYWOG 3 transfer function have high complex ability to learn and track unknown/undefined complex systems. The efficacy of this type of network in function learning and estimation is compared with ANNs. The simulation results indicate a decrease in estimation error values that depicts its ability to enhance the function approximation capability and consequently exhibits excellent learning ability compared to the conventional neural network with sigmoid or other activation functions. Also, for better comparison, the results of neural network and wavelet neural network were evaluated using support vector machine.

Short Circuit Faults Identification and Localization in IEEE 34 Nodes Distribution Feeder Based on the Theory of Wavelets

In this paper a radial distribution feeder protection scheme against short circuit faults is introduced. It is based on utilizing the substation measured current signals in detecting faults and obtaining useful information about their types and locations. In order to facilitate important measurement signals features extraction such that better diagnosis of faults can be achieved, the discrete wavelet transform is exploited. The captured features are then utilized in detecting, identifying the faulted phases (fault type), and fault location. In case of a fault occurrence, the detection scheme will make a decision to trip out a circuit breaker residing at the feeder mains. This decision is made based on a criteria that is set to distinguish between the various system states in a reliable and accurate manner. After that, the fault type and location are predicted making use of the cascade forward neural networks learning and generalization capabilities. Useful information about the fault location can be obtained provided that the fault distance from source, as well as whether it resides on the main feeder or on one of the laterals can be predicted. By testing the functionality of the proposed scheme, it is found that the detection of faults is done fastly and reliably from the view point of power system protection relaying requirements. It also proves to overcome the complexities provided by the feeder structure to the accuracy of the identification process of fault types and locations. All the simulations and analysis are performed utilizing MATLAB R2016b version software package.

Simplified Tsunami Modeling and Waveform Reconstruction With GNSS-R Observations

This paper investigates Tsunami modeling, waveform reconstruction and parameter estimation using noisy sea surface height measurements observed by a satellite-carried global navigation satellite system (GNSS) sensor. Wavelet theory is used to mitigate the strong measurement noise. Tsunami modeling is considered and Cramer–Rao lower bound is derived for estimation of Tsunami shape parameters, wave height and wavelength. Real Tsunami data observed by altimetry satellites are used for performance evaluation and the results demonstrate the efficiency of the proposed approach.

Wavelet theory applied to the study of spectra of trans-Neptunian objects

Context. Reflection spectroscopy in the near-infrared (NIR) is used to investigate the surface composition of trans-Neptunian objects (TNOs). In general, these spectra are difficult to interpret due to the low apparent brightness of the TNOs, causing low signal-to-noise ratio even in spectra obtained with the largest telescopes available on Earth, making it necessary to use filtering techniques to analyze and interpret them. Aims. The purpose of this paper is to present a methodology to analyze the spectra of TNOs. Specifically, our aim was to filter these spectra in the best possible way: maximizing noise removal, while minimizing the loss of signal. Methods. We used wavelets to filter the spectra. Wavelets are a mathematical tool that decompose the signal into its constituent parts, allowing us to analyze the data in different areas of frequencies with the resolution of each component tied to its scale. To check the reliability of our method, we compared the filtered spectra with the spectra of water and methanol ices to identify some common structures between them. Results. Of the 50 TNOs in our sample, we identify traces of water ices and methanol in the spectra of several of them, some with previous reports, while for other objects there were no previous reports. Conclusions. We conclude that the wavelet technique is successful in filtering spectra of TNOs.

A Novel Adaptive Wavelet Thresholding with Identical Correlation Shrinkage Function for ECG Noise Removal

On the basis of wavelet theory, a novel Adaptive wavelet thresholding method (AWT) is proposed for the ECG signal enhancement. The best base wavelet for ECG signal filtering can be automatically obtained through the cross correlation coefficient and the energy to entropy ratio. The variable universal threshold (VarUniversal) is applied to different decomposition level so as to suppress diverse noise. To achieve a smooth cut-off transition, an identical correlation shrinkage function (IcoShrinkage) is also adopted in the AWT according to its correlation coefficients with the hard thresholding and the soft thresholding. The performance of AWT is compared with four threshold approaches and six shrinkage functions, respectively, on the basis of 150 practical ECG signals of 30 subjects. The filtering results reveal that the AWT can adaptively choose an optimal base wavelet for a specific ECG signal. With the VarUniversal threshold and IcoShrinkage, the AWT obtains the better filtering results than the other compared methods.

Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes II

In Ba et al. (2017), a general normal asymptotic theory for divergence measures estimators has been provided. These estimators are constructed from the wavelets empirical process and concerned the general O -divergence measures. In this paper, we first extend the aforementioned results to symmetrized forms of divergence measures. Second, the Tsallis and Renyi divergence measures as well as the Kullback-Leibler measures are investigated in details. The question of the applicability of the results, based on the boundedness assumption is also dealt, leading to future packages. Keywords: Divergence measures estimation; Asymptotic normality; Wavelet theory; wavelets empirical processes; Besov spaces AMS 2010 Mathematics Subject Classification : 62G05; 62G20; 62G07

Quantifying credit portfolio losses under multi-factor models

ABSTRACTIn this work, we investigate the challenging problem of estimating credit risk measures of portfolios with exposure concentration under the multi-factor Gaussian and multi-factor t-copula models. It is well-known that Monte Carlo (MC) methods are highly demanding from the computational point of view in the aforementioned situations. We present efficient and robust numerical techniques based on the Haar wavelets theory for recovering the cumulative distribution function of the loss variable from its characteristic function. To the best of our knowledge, this is the first time that multi-factor t-copula models are considered outside the MC framework. The analysis of the approximation error and the results obtained in the numerical experiments section show a reliable and useful machinery for credit risk capital measurement purposes in line with Pillar II of the Basel Accords.

Fractal and multi-fractal features of the broadband power line communication signals

Broadband power line communications (PLC) is considered to be one of the most promising technologies to fulfill data transmission in smart grids. To understand PLC signal characteristics and overcome the shortcomings of traditional statistical properties, the mono-fractal and multi-fractal theories are introduced to understand the self-similarity characteristics of the PLC signals. Four common methods, namely, rescaled range analysis, variance-time plot method, periodic diagram analysis and wavelet-based method are used to study the nonlinear properties. Fractal analysis at different frequencies and times are also performed to verify further. The results reveal self-similarity of the PLC signals. Besides the mono-fractal properties, the paper tests the multi-fractal properties of PLC signals by the means of multi-fractal detrended fluctuation analysis (MFDFA). We estimated the multi-fractal spectrum of power low exponents from the measured PLC signals. We also proposed a new algorithm to improve the traditional MFDFA, where wavelet theory is integrated.

Blind Maternal-Fetal ECG Separation Based on the Time-Scale Image TSI and SVD – ICA Methods

Fetal heart monitoring yields vital information about the fetus health and can support medical decision making in critical situations. A compound signal is obtained noninvasively by placing electrodes on the abdomen area of the mother which contains maternal and fetal ECG signals contaminated by various other signals from body and externally induced noises. As a result, the basic problem is to extract the fECG signal from the mixture of mECG and fECG, where the interfering mECG is a much stronger. This problem has been addressed in several works, in this paper, we propose a novel blind-source separation method to extract fetal ECG when given only a single channel recording. Our approach is based on the wavelet theory and SVD-ICA methods. It is pointed out that the presented algorithm is validated by Matlab simulation and can be implemented on real time life by using embedded system such as DSP processor.

A new method of speech transmission over space time block coded co-operative MIMO–OFDM networks using time and space diversity

Reliable and good quality of service for speech transmission over wireless network has been a major challenge for the communication engineers and researchers. In this paper a new technique of speech compression and transmission using different Daubechies wavelets in a space time block coded co-corporative MIMO–OFDM networks using time and space diversity has been proposed. The main focus has been laid on design and development of wavelet based compression of multimedia signals for cooperative MIMO–OFDM system. We tried to find out various major issues regarding the wavelet compression of a speech signal. These issues include choice of a wavelet, decomposition level and thresholding criteria suitable for speech compression and transmission in co-operative MIMO–OFDM systems. A wavelet based speech compression technique using hard and soft thresholding algorithm has been proposed. The work shows that wavelet compression with QPSK modulation is a promising compression technique in a cooperative MIMO–OFDM system which makes use of the elegant theory of wavelets. The performance has been evaluated using mean square error, peak signal to noise ratio, compression ratio, bit error rate, and retained signal energy. It has been found that the transmitted speech signal is retrieved well under noisy conditions at higher order Daubechies wavelets. From the results it is clear that proposed technique aims at a radio access technology that can provide service performance comparable to that of current fixed Line accesses. To evaluate the performance of the proposed method, various performance parameters have been compared with previously implemented techniques and it has been found that the proposed work shows better performance as compared to the already existing techniques.

Analysis of identification of digital images from a map of cosmic microwaves

This paper discusses identification of digital images from the cosmic microwave background radiation map formed according to the data of the European Space Agency “Planck” telescope by applying covariance functions and wavelet theory. The estimates of covariance functions of two digital images or single images are calculated according to the random functions formed of the digital images in the form of pixel vectors. The estimates of pixel vectors are formed on expansion of the pixel arrays of the digital images by a single vector. When the scale of a digital image is varied, the frequencies of single-pixel color waves remain constant and the procedure for calculation of covariance functions is not affected. For identification of the images, the RGB format spectrum has been applied. The impact of RGB spectrum components and the color tensor on the estimates of covariance functions was analyzed. The identity of digital images is assessed according to the changes in the values of the correlation coefficients in a certain range of values by applying the developed computer program.

Generalized exact holographic mapping with wavelets

The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N-dimensional lattice system to a N+1-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis-specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high pass wavelet filter is revealed to be proportional to the radius of the dual Anti deSitter (AdS) space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.

Nonlinear wavelet shrinkage estimator of nonparametric regularity regression function via cross-validation with simulation study

Nonparametric regression techniques provide a very effective and simple way of finding structure in data sets without the imposition of a parametric regression model. Wavelet theory has the potential to provide statisticians with powerful new techniques for nonparametric inference. In this paper, we consider the wavelet shrinkage kernel estimator of regression function with a common one-dimensional probability density function. We investigate a new nonparametric curve estimator and convergence ratio of given estimator by using cross-validation method to choice of wavelet threshold when the observations are taken on the regular grid. At the end we used simulation study to examine our proposed estimator. We survey the theoretical outcomes with numerical computation by using [Formula: see text] software to compare purpose estimator with another estimators.

Stator Faults Diagnosis and Protection in 3-Phase Induction Motor Based on Wavelet Theory

Stator Faults Diagnosis and Protection in 3-Phase Induction Motor Based on Wavelet Theory

Sampling and reconstruction of sparse signals on circulant graphs – an introduction to graph-FRI

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of Innovation (FRI) theory to the graph domain, and can be applied to arbitrary graphs via suitable approximation schemes. At its core, the introduced Graph-FRI-framework states that any K-sparse signal on the vertices of a circulant graph can be perfectly reconstructed from its dimensionality-reduced representation in the graph spectral domain, the Graph Fourier Transform (GFT), of minimum size 2K. By leveraging the recently developed theory of e-splines and e-spline wavelets on graphs, one can decompose this graph spectral transformation into the multiresolution low-pass filtering operation with a graph e-spline filter, with subsequent transformation to the spectral graph domain; this allows to infer a distinct sampling pattern, and, ultimately, the structure of an associated coarsened graph, which preserves essential properties of the original, including circularity and, where applicable, the graph generating set.

Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.

Homogeneous wavelets and framelets with the refinable structure

Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper we shall provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.