scholarly journals A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Nagma Irfan ◽  
A. H. Siddiqi
Keyword(s):  
Wavelet Decomposition ◽  
Numerical Evaluation ◽  
Input Function ◽  
Wavelet Method ◽  
Stable Algorithm ◽  
Bessel Transform ◽  
Cas Wavelets ◽  
Wavelet Algorithm

The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order ν,  ν>-1, using wavelets. The philosophy behind the proposed algorithm is to replace the part tf(t) of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing Fν(p) as a Fourier-Bessel series with coefficients depending strongly on the input function tf(t). The wavelet method indicates that the approach is easy to implement and thus computationally very attractive.

scholarly journals Stable Numerical Evaluation of Finite Hankel Transforms and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Manoj P. Tripathi ◽  
B. P. Singh ◽  
Om P. Singh
Keyword(s):  
Stability Analysis ◽  
Heat Equation ◽  
Numerical Experiments ◽  
Numerical Evaluation ◽  
Radiation Condition ◽  
Hankel Transform ◽  
Basis Functions ◽  
Infinite Cylinder ◽  
Stable Algorithm ◽  
Hankel Transforms

A new stable algorithm, based on hat functions for numerical evaluation of Hankel transform of order ν>-1, is proposed in this paper. The hat basis functions are used as a basis to expand a part of the integrand, rf(r), appearing in the Hankel transform integral. This leads to a very simple, efficient, and stable algorithm for the numerical evaluation of Hankel transform. The novelty of our paper is that we give error and stability analysis of the algorithm and corroborate our theoretical findings by various numerical experiments. Finally, an application of the proposed algorithm is given for solving the heat equation in an infinite cylinder with a radiation condition.

Application of a new hybrid method for solving singular fractional Lane–Emden-type equations in astrophysics

2019 ◽  
Vol 34 (03) ◽  
pp. 2050049 ◽  
Author(s):  
Wen-Xiu Ma ◽  
Mohamed M. Mousa ◽  
Mohamed R. Ali
Keyword(s):  
Numerical Method ◽  
Nonlinear Equations ◽  
Hybrid Method ◽  
Computational Efficiency ◽  
Iterative Scheme ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Hybrid Numerical Method ◽  
Novel Method ◽  
Cas Wavelets

In this research, a hybrid numerical method combining cosine and sine (CAS) wavelets and Green’s function approach is created to acquire the arrangements of fractional Lane–Emden Problem. The suggested methodology for detecting the solution of nonlinear equations dependent on variations of germinal algorithms is applied on nonlinear fractional Lane–Emden Problem under some smooth conditions and results in an iterative scheme of nonlinear equations Because of its efficiency, this technique is applied on a large variety of equations from the boundary value problems to the optimization. This paper is extending the suggested methodology technique for fractional Lane–Emden Problem. Moreover, the feature of the present novel method is utilized to convert the problem under observance into a system of algebraic equations that can be illuminated by suitable algorithms. A rapprochement of results has likewise been obtained using the present strategy and those reported using other techniques seem to indicate the precision and computational efficiency to establish the suitability of the Green-CAS wavelet method.

Characterization of Cavitation Eroded Surfaces at Different Temperatures Using Wavelet Method

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
A. Abouel-Kasem ◽  
B. Saleh ◽  
K. M. Emara ◽  
S. M. Ahmed
Keyword(s):  
Wavelet Decomposition ◽  
Cavitation Erosion ◽  
Average Particle Size ◽  
Image Features ◽  
Average Particle ◽  
Wavelet Method ◽  
Wavelet Energy ◽  
Cavitation Intensity ◽  
Different Temperatures

In the present work, the image features of cavitation erosion surfaces at different temperatures are extracted using wavelet decomposition transform. The results obtained indicate that the extract parameters, wavelet energy, and entropy can characterize the cavitation intensity in a similar manner to that of the mass loss and average particle size at different temperatures. Based on the analysis of the eroded surface and particle morphologies for different temperatures, it was found that the predominant failure mode was fatigue.

Wavelet method of edge detection in images with high-noise level

2020 ◽  
Vol 2 (3) ◽  
pp. 119-130
Author(s):  
Tadeusz Niedziela
Keyword(s):  
Mathematical Model ◽  
Integral Transform ◽  
Wavelet Method ◽  
High Noise ◽  
Matching Algorithm ◽  
Frequency Domains ◽  
Sharp Edges ◽  
Exploration Tool ◽  
High Level ◽  
Wavelet Algorithm

In the paper a mathematical model addressed to non-sharp edges in the images is proposed. This model is based on and integral transform with Haar-Gauss wavelet and matching algorithm of bandwidth, such model is used to detection of the edges in images with high-level noises, both in the x plane and the frequency domains. There is shown that applying the integral Haar-Gaussian transformation the detection of single and double edges is possible. Demonstrated in the paper results confirm that wavelet transform supported by the matching wavelet algorithm of wavelength bandwidth make an important exploration tool of the images with the edges possessing a large depth of sharpness.

scholarly journals Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1164 ◽  
Author(s):  
Muhammad Ismail ◽  
Umer Saeed ◽  
Jehad Alzabut ◽  
Mujeeb ur Rehman
Keyword(s):  
Differential Equations ◽  
Boundary Value ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Operational Matrices ◽  
Wavelet Method ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Cas Wavelets

In this study, we present a novel numerical scheme for the approximate solutions of linear as well as non-linear ordinary differential equations of fractional order with boundary conditions. This method combines Cosine and Sine (CAS) wavelets together with Green function, called Green-CAS method. The method simplifies the existing CAS wavelet method and does not require conventional operational matrices of integration for certain cases. Quasilinearization technique is used to transform non-linear fractional differential equations to linear equations and then Green-CAS method is applied. Furthermore, the proposed method has also been analyzed for convergence, particularly in the context of error analysis. Sufficient conditions for the existence of unique solutions are established for the boundary value problem under consideration. Moreover, to elaborate the effectiveness and accuracy of the proposed method, results of essential numerical applications have also been documented in graphical as well as tabular form.

scholarly journals The Study of Large-Scale Fading Using a Wavelet Transform Method

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Guizhen Lu ◽  
Zhi Cao ◽  
Xingning Jia ◽  
Jingjing Liang
Keyword(s):  
Wavelet Decomposition ◽  
Large Scale ◽  
Path Loss ◽  
Propagation Loss ◽  
Transform Method ◽  
Wavelet Method ◽  
Second Order Statistics ◽  
Slow Fading ◽  
Different Levels ◽  
Selection Of

A wavelet method is proposed to evaluate the modeling of the first- and second-order statistics of large-scale fading from the signal strength measurement. The selection of wavelet is very important in using a wavelet method, and the steps of the wavelet method are given for the study of wave propagation loss. The path loss of measurement is analysed with different levels of wavelet decomposition and compared with an optimized Hata model. The correlation of slow fading on different scales shows that the correlation distance is related to the spatial scale.

Study on Traffic Prediction Algorithm Based on Multi-Scale Bi-Orthogonal Wavelet

2013 ◽  
Vol 340 ◽  
pp. 722-726
Author(s):  
Yan Li ◽  
Yao Chen
Keyword(s):  
Wavelet Decomposition ◽  
Prediction Method ◽  
Prediction Algorithm ◽  
Traffic Prediction ◽  
Actual Situation ◽  
Prediction Problem ◽  
Network Configuration ◽  
Orthogonal Wavelet ◽  
Multi Scale ◽  
Wavelet Algorithm

The traffic prediction carried out in the communication enterprises is of great significance for the optimization of the network configuration and the improvement of the communication quality. To solve the inaccurate prediction problem under the actual situation, a traffic prediction method based on the bi-orthogonal multi-scale wavelet algorithm is developed. The process of the wavelet decomposition and reconstruction are studied, and the reconstruction results for the different scales wavelet are obtained. Take a set of the special actual samples as the object, the traffic prediction for the future dates is completed, and compared with the actual results. The results show that the relative error between the proposed traffic prediction model and the actual results is less than 10%. The bi-orthogonal multi-scale wavelet algorithm has some advantages as compared with other similar ones, which will provide the important technology means for the traffic prediction forecasting and assessing in the various types of communication enterprises.

scholarly journals About calculation of the Hankel transform using preliminary wavelet transform

2003 ◽  
Vol 2003 (6) ◽  
pp. 319-325 ◽  
Author(s):  
E. B. Postnikov
Keyword(s):  
Wavelet Transform ◽  
Numerical Evaluation ◽  
Hankel Transform ◽  
Input Function ◽  
Analytical Representation ◽  
Wavelet Coefficients ◽  
Test Function ◽  
Struve Functions

The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied by the wavelet coefficients of the input function. Numerical evaluation of the test function with known analytical Hankel transform illustrates the proposed algorithm.

scholarly journals Isolation of a periodic component by singular wavelet decomposition

2020 ◽  
pp. 4-8
Author(s):  
V. M. Romanchak ◽  
M. A. Hundzina
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Wavelet Decomposition ◽  
Periodic Component ◽  
Discrete Wavelet ◽  
Real Problem ◽  
Wavelet Method ◽  
Parametric Regression ◽  
Validity Condition ◽  
Wavelet Transformations

In this paper, we propose to use a discrete wavelet transform with a singular wavelet to isolate the periodic component from the signal. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet is zero). For singular wavelets, the validity condition is not met. As a singular wavelet, you can use the Delta-shaped functions, which are involved in the estimates of Parzen-Rosenblatt, Nadaraya-Watson. Using singular value of a wavelet is determined by the discrete wavelet transform. This transformation was studied earlier for the continuous case. Theoretical estimates of the convergence rate of the sum of wavelet transformations were obtained; various variants were proposed and a theoretical justification was given for the use of the singular wavelet method; sufficient conditions for uniform convergence of the sum of wavelet transformations were formulated. It is shown that the wavelet transform can be used to solve the problem of nonparametric approximation of the function. Singular wavelet decomposition is a new method and there are currently no examples of its application to solving applied problems. This paper analyzes the possibilities of the singular wavelet method. It is assumed that in some cases a slow and fast component can be distinguished from the signal, and this hypothesis is confirmed by the numerical solution of the real problem. A similar analysis is performed using a parametric regression equation, which allows you to select the periodic component of the signal. Comparison of the calculation results confirms that nonparametric approximation based on singular wavelets and the application of parametric regression can lead to similar results.

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