Search results for: perturbation method
7700 Noise Estimation for Speech Enhancement in Non-Stationary Environments-A New Method
Authors: Ch.V.Rama Rao, Gowthami., Harsha., Rajkumar., M.B.Rama Murthy, K.Srinivasa Rao, K.AnithaSheela
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This paper presents a new method for estimating the nonstationary noise power spectral density given a noisy signal. The method is based on averaging the noisy speech power spectrum using time and frequency dependent smoothing factors. These factors are adjusted based on signal-presence probability in individual frequency bins. Signal presence is determined by computing the ratio of the noisy speech power spectrum to its local minimum, which is updated continuously by averaging past values of the noisy speech power spectra with a look-ahead factor. This method adapts very quickly to highly non-stationary noise environments. The proposed method achieves significant improvements over a system that uses voice activity detector (VAD) in noise estimation.Keywords: Noise estimation, Non-stationary noise, Speechenhancement.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23477699 Price Quoting Method for Contract Manufacturer
Authors: S. Homrossukon, W. Parinyasart
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This is an applied research to propose the method for price quotation for a contract electronics manufacturer. It has had a precise price quoting method but such method could not quickly provide a result as the customer required. This reduces the ability of company to compete in this kind of business. In this case, the cause of long time quotation process was analyzed. A lot of product features have been demanded by customer. By checking routine processes, it was found that high fraction of quoting time was used for production time estimating which has effected to the manufacturing or production cost. Then the historical data of products including types, number of components, assembling method, and their assembling time were used to analyze the key components affecting to production time. The price quoting model then was proposed. The implementation of proposed model was able to remarkably reduce quoting time with an acceptable required precision.Keywords: Price quoting, Contract manufacturer, Stepwise technique, Best subset technique.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 44347698 Stabilization of Rotational Motion of Spacecrafts Using Quantized Two Torque Inputs Based on Random Dither
Authors: Yusuke Kuramitsu, Tomoaki Hashimoto, Hirokazu Tahara
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The control problem of underactuated spacecrafts has attracted a considerable amount of interest. The control method for a spacecraft equipped with less than three control torques is useful when one of the three control torques had failed. On the other hand, the quantized control of systems is one of the important research topics in recent years. The random dither quantization method that transforms a given continuous signal to a discrete signal by adding artificial random noise to the continuous signal before quantization has also attracted a considerable amount of interest. The objective of this study is to develop the control method based on random dither quantization method for stabilizing the rotational motion of a rigid spacecraft with two control inputs. In this paper, the effectiveness of random dither quantization control method for the stabilization of rotational motion of spacecrafts with two torque inputs is verified by numerical simulations.Keywords: Spacecraft control, quantized control, nonlinear control, random dither method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7127697 Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C
Authors: Minghui Wang, Luping Xu, Juntao Zhang
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Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.Keywords: Iterative method, symmetric arrowhead matrix, conjugate gradient algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14187696 Performance of the Strong Stability Method in the Univariate Classical Risk Model
Authors: Safia Hocine, Zina Benouaret, Djamil A¨ıssani
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In this paper, we study the performance of the strong stability method of the univariate classical risk model. We interest to the stability bounds established using two approaches. The first based on the strong stability method developed for a general Markov chains. The second approach based on the regenerative processes theory . By adopting an algorithmic procedure, we study the performance of the stability method in the case of exponential distribution claim amounts. After presenting numerically and graphically the stability bounds, an interpretation and comparison of the results have been done.Keywords: Markov Chain, regenerative processes, risk models, ruin probability, strong stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11477695 An Analytical Method for Solving General Riccati Equation
Authors: Y. Pala, M. O. Ertas
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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.
Keywords: Riccati Equation, ordinary differential equation, nonlinear differential equation, analytical solution, proper solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20457694 Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method
Authors: Nisha Goyal, R.K. Gupta
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This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.
Keywords: Sawada-Kotera-Kadomtsev-Petviashivili equation, Bogoyavlensky-Konoplechenko equation,
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16277693 On the Differential Geometry of the Curves in Minkowski Space-Time II
Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut
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In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated.Keywords: Frenet Apparatus, Time-like Curves, MinkowskiSpace-time.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16697692 Periodic Solutions for Some Strongly Nonlinear Oscillators by He's Energy Balance Method
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In this paper, applying He-s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy.
Keywords: He's energy balance method, periodic solution, nonlinear oscillator, discontinuous, fractional potential.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13777691 Solving 94-bit ECDLP with 70 Computers in Parallel
Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai
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Elliptic curve discrete logarithm problem(ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard’s rho method to evaluate the security of ECDLP on Barreto-Naehrig(BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.Keywords: Pollard’s rho method, BN curve, Montgomery multiplication.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18737690 Synchronization Between Two Chaotic Systems: Numerical and Circuit Simulation
Authors: J. H. Park, T. H. Lee, S. M. Lee, H. Y. Jung
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In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations for a specific chaotic system is conducted.
Keywords: Chaotic systems, synchronization, Lyapunov method, simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16907689 Element-Independent Implementation for Method of Lagrange Multipliers
Authors: Gil-Eon Jeong, Sung-Kie Youn, K. C. Park
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Treatment for the non-matching interface is an important computational issue. To handle this problem, the method of Lagrange multipliers including classical and localized versions are the most popular technique. It essentially imposes the interface compatibility conditions by introducing Lagrange multipliers. However, the numerical system becomes unstable and inefficient due to the Lagrange multipliers. The interface element-independent formulation that does not include the Lagrange multipliers can be obtained by modifying the independent variables mathematically. Through this modification, more efficient and stable system can be achieved while involving equivalent accuracy comparing with the conventional method. A numerical example is conducted to verify the validity of the presented method.Keywords: Element-independent formulation, non-matching interface, interface coupling, methods of Lagrange multipliers.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11867688 Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations
Authors: M. Zarebnia, N. Aliniya
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In this paper, a numerical solution based on sinc functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.Keywords: Calculus of variation; Sinc functions; Galerkin; Numerical method
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19677687 On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations
Authors: A. M. Sagir
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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y0, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.
Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17807686 Laplace Adomian Decomposition Method Applied to a Two-Dimensional Viscous Flow with Shrinking Sheet
Authors: M. A. Koroma, S. Widatalla, A. F. Kamara, C. Zhang
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Our aim in this piece of work is to demonstrate the power of the Laplace Adomian decomposition method (LADM) in approximating the solutions of nonlinear differential equations governing the two-dimensional viscous flow induced by a shrinking sheet.Keywords: Adomian polynomials, Laplace Adomian decomposition method, Padé Approximant, Shrinking sheet.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20347685 A Quantification Method of Attractiveness of Stations and an Estimation Method of Number of Passengers Taking into Consideration the Attractiveness of the Station
Authors: Naoya Ozaki, Takuya Watanabe, Ryosuke Matsumoto, Noriko Fukasawa
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In the metropolitan areas in Japan, in many stations, shopping areas are set up, and escalators and elevators are installed to make the stations be barrier-free. Further, many areas around the stations are being redeveloped. Railway business operators want to know how much effect these circumstances have on attractiveness of the station or number of passengers using the station. So, we performed a questionnaire survey of the station users in the metropolitan areas for finding factors to affect the attractiveness of stations. Then, based on the analysis of the survey, we developed a method to quantitatively evaluate attractiveness of the stations. We also developed an estimation method for number of passengers based on combination of attractiveness of the station quantitatively evaluated and the residential and labor population around the station. Then, we derived precise linear regression models estimating the attractiveness of the station and number of passengers of the station.Keywords: Attractiveness of the station, estimation method, number of passengers of the station, redevelopment around the station, renovation of the station.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9087684 Generalized Method for Estimating Best-Fit Vertical Alignments for Profile Data
Authors: Said M. Easa, Shinya Kikuchi
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When the profile information of an existing road is missing or not up-to-date and the parameters of the vertical alignment are needed for engineering analysis, the engineer has to recreate the geometric design features of the road alignment using collected profile data. The profile data may be collected using traditional surveying methods, global positioning systems, or digital imagery. This paper develops a method that estimates the parameters of the geometric features that best characterize the existing vertical alignments in terms of tangents and the expressions of the curve, that may be symmetrical, asymmetrical, reverse, and complex vertical curves. The method is implemented using an Excel-based optimization method that minimizes the differences between the observed profile and the profiles estimated from the equations of the vertical curve. The method uses a 'wireframe' representation of the profile that makes the proposed method applicable to all types of vertical curves. A secondary contribution of this paper is to introduce the properties of the equal-arc asymmetrical curve that has been recently developed in the highway geometric design field.Keywords: Optimization, parameters, data, reverse, spreadsheet, vertical curves
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24567683 An Improved Prediction Model of Ozone Concentration Time Series Based On Chaotic Approach
Authors: N. Z. A. Hamid, M. S. M. Noorani
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This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly Ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.
Keywords: Chaotic approach, phase space, Cao method, local linear approximation method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17887682 An Adaptive Dynamic Fracture for 3D Fatigue Crack Growth Using X-FEM
Authors: S. Lecheb, A. Nour, A. Chellil, A. Basta, D. Belmiloud, H. Kebi
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In recent years, a new numerical method has been developed, the extended finite element method (X-FEM). The objective of this work is to exploit the (X-FEM) for the treatment of the fracture mechanics problems on 3D geometries, where we showed the ability of this method to simulate the fatigue crack growth into two cases: edge and central crack. In the results we compared the six first natural frequencies of mode shapes uncracking with the cracking initiation in the structure, and showed the stress intensity factor (SIF) evolution function as crack size propagation into structure, the analytical validation of (SIF) is presented. For to evidence the aspects of this method, all result is compared between FEA and X-FEM.Keywords: 3D fatigue crack growth, FEA, natural frequencies, stress intensity factor (SIF), X-FEM.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20287681 Improvement of Ride Comfort of Turning Electric Vehicle Using Optimal Speed Control
Authors: Yingyi Zhou, Tohru Kawabe
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With the spread of EVs (electric Vehicles), the ride comfort has been gaining a lot of attention. The influence of the lateral acceleration is important for the improvement of ride comfort of EVs as well as the longitudinal acceleration, especially upon turning of the vehicle. Therefore, this paper proposes a practical optimal speed control method to greatly improve the ride comfort in the vehicle turning situation. For consturcting this method, effective criteria that can appropriately evaluate deterioration of ride comfort is derived. The method can reduce the influence of both the longitudinal and the lateral speed changes for providing a confortable ride. From several simulation results, we can see the fact that the method can prevent aggravation of the ride comfort by suppressing the influence of longitudinal speed change in the turning situation. Hence, the effectiveness of the method is recognized.Keywords: Electric vehicle, speed control, ride comfort, optimal control theory, driving support system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9237680 Embedded Singly Diagonally Implicit Runge-Kutta –Nystrom Method Order 5(4) for the Integration of Special Second Order ODEs
Authors: Fudziah Ismail
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In this paper a new embedded Singly Diagonally Implicit Runge-Kutta Nystrom fourth order in fifth order method for solving special second order initial value problems is derived. A standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first order systems and solved using the existing embedded diagonally implicit Runge-Kutta method. The results suggests the superiority of the new method.Keywords: Runge-Kutta Nystrom, Special second orderproblems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16707679 Assessment of the Energy Balance Method in the Case of Masonry Domes
Authors: M. M. Sadeghi, S. Vahdani
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Masonry dome structures had been widely used for covering large spans in the past. The seismic assessment of these historical structures is very complicated due to the nonlinear behavior of the material, their rigidness, and special stability configuration. The assessment method based on energy balance concept, as well as the standard pushover analysis, is used to evaluate the effectiveness of these methods in the case of masonry dome structures. The Soltanieh dome building is used as an example to which two methods are applied. The performance points are given from superimposing the capacity, and demand curves in Acceleration Displacement Response Spectra (ADRS) and energy coordination are compared with the nonlinear time history analysis as the exact result. The results show a good agreement between the dynamic analysis and the energy balance method, but standard pushover method does not provide an acceptable estimation.
Keywords: Energy balance method, pushover analysis, time history analysis, masonry dome.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8407678 Fuzzy Scan Method to Detect Clusters
Authors: Laureano Rodríguez, Gladys Casas, Ricardo Grau, Yailen Martínez
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The classical temporal scan statistic is often used to identify disease clusters. In recent years, this method has become as a very popular technique and its field of application has been notably increased. Many bioinformatic problems have been solved with this technique. In this paper a new scan fuzzy method is proposed. The behaviors of classic and fuzzy scan techniques are studied with simulated data. ROC curves are calculated, being demonstrated the superiority of the fuzzy scan technique.Keywords: Scan statistic, fuzzy scan, simulating study
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14037677 Approximate Confidence Interval for Effect Size Base on Bootstrap Resampling Method
Authors: S. Phanyaem
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This paper presents the confidence intervals for the effect size base on bootstrap resampling method. The meta-analytic confidence interval for effect size is proposed that are easy to compute. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence intervals with the existing confidence intervals. The best confidence interval method will have a coverage probability close to 0.95. Simulation results have shown that our proposed confidence intervals perform well in terms of coverage probability and expected length.Keywords: Effect size, confidence interval, Bootstrap Method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11507676 ISME: Integrated Style Motion Editor for 3D Humanoid Character
Authors: Ismahafezi Ismail, Mohd Shahrizal Sunar
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The motion of a realistic 3D humanoid character is very important especially for the industries developing computer animations and games. However, this type of motion is seen with a very complex dimensional data as well as body position, orientation, and joint rotation. Integrated Style Motion Editor (ISME), on the other hand, is a method used to alter the 3D humanoid motion capture data utilised in computer animation and games development. Therefore, this study was carried out with the purpose of demonstrating a method that is able to manipulate and deform different motion styles by integrating Key Pose Deformation Technique and Trajectory Control Technique. This motion editing method allows the user to generate new motions from the original motion capture data using a simple interface control. Unlike the previous method, our method produces a realistic humanoid motion style in real time.
Keywords: Computer animation, humanoid motion, motion capture, motion editing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12767675 Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions
Authors: Hailong Zhu, Zhaoxiang Li
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Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).
Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16547674 A Dictionary Learning Method Based On EMD for Audio Sparse Representation
Authors: Yueming Wang, Zenghui Zhang, Rendong Ying, Peilin Liu
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Sparse representation has long been studied and several dictionary learning methods have been proposed. The dictionary learning methods are widely used because they are adaptive. In this paper, a new dictionary learning method for audio is proposed. Signals are at first decomposed into different degrees of Intrinsic Mode Functions (IMF) using Empirical Mode Decomposition (EMD) technique. Then these IMFs form a learned dictionary. To reduce the size of the dictionary, the K-means method is applied to the dictionary to generate a K-EMD dictionary. Compared to K-SVD algorithm, the K-EMD dictionary decomposes audio signals into structured components, thus the sparsity of the representation is increased by 34.4% and the SNR of the recovered audio signals is increased by 20.9%.
Keywords: Dictionary Learning, EMD, K-means Method, Sparse Representation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26327673 Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method
Authors: Anjali Verma, Ram Jiwari, Jitender Kumar
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This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.
Keywords: Shallow water wave equation, Exact solutions, (G'/G) expansion method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18587672 Non-Polynomial Spline Method for the Solution of Problems in Calculus of Variations
Authors: M. Zarebnia, M. Hoshyar, M. Sedaghati
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In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.Keywords: Calculus of variation; Non-polynomial spline functions; Numerical method
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19937671 On Convergence Property of MINRES Method for Solving a Complex Shifted Hermitian Linear System
Authors: Guiding Gu, Guo Liu
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We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f. Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I + H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. Numerical experiments show such convergence properties.
Keywords: complex shifted linear system, Hermitian matrix, MINRES method.
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