Mohammad Khatim Hasan

Denoising solar radiation data using Meyer wavelets

Signal processing is important in solar energy data analysis since the received solar radiation data fluctuates continuously. Some of the fluctuations can be considered as noise, and need to be filtered out before the signal will be used for other analysis. There exist various methods in order to filter the noise and one of the promising methods is wavelets transform. This paper utilized the use of wavelet transform method for solar radiation denoising. The Meyer wavelets have been utilized, instead of the usual sinusoidal or Gaussian type functions. Since Meyer wavelets are obtained directly from its Fourier transform which is in terms of sinusoidal functions, optimized Meyer wavelets may give a good indication of the solar radiation data. Results showed Heuristic Stein Unbiased Estimate of Risk (SURE) and SURE gave better denoised results as compared to Minimax and Fixed Form methods.

Denoising solar radiation data using coiflet wavelets

Signal denoising and smoothing plays an important role in processing the given signal either from experiment or data collection through observations. Data collection usually was mixed between true data and some error or noise. This noise might be coming from the apparatus to measure or collect the data or human error in handling the data. Normally before the data is use for further processing purposes, the unwanted noise need to be filtered out. One of the efficient methods that can be used to filter the data is wavelet transform. Due to the fact that the received solar radiation data fluctuates according to time, there exist few unwanted oscillation namely noise and it must be filtered out before the data is used for developing mathematical model. In order to apply denoising using wavelet transform (WT), the thresholding values need to be calculated. In this paper the new thresholding approach is proposed. The coiflet2 wavelet with variation diminishing 4 is utilized for our purpose. From numerical results it can be seen clearly that, the new thresholding approach give better results as compare with existing approach namely global thresholding value.

Data interpolation using Runge Kutta method

Runge Kutta (RK) is a famous method that can be used to solve differential equation with initial value problems (IVP). There are many variants for RK method. For instance, the most widely used are RK4 and RK5 where 4 and 5 stands for the order of the RK methods. Data interpolation are important in many engineering applications. Usually for data interpolation, the interpolant must interpolate the data set and the first derivatives. This study discusses the application of RK4 for data interpolation by interpolating the data through cubic spline interpolation i.e. RK4-CS method. Several numerical findings will be presented including comparison with some established schemes such as cubic spline. From our findings, RK4 is suitable for data interpolation with higher degree of accuracy.Runge Kutta (RK) is a famous method that can be used to solve differential equation with initial value problems (IVP). There are many variants for RK method. For instance, the most widely used are RK4 and RK5 where 4 and 5 stands for the order of the RK methods. Data interpolation are important in many engineering applications. Usually for data interpolation, the interpolant must interpolate the data set and the first derivatives. This study discusses the application of RK4 for data interpolation by interpolating the data through cubic spline interpolation i.e. RK4-CS method. Several numerical findings will be presented including comparison with some established schemes such as cubic spline. From our findings, RK4 is suitable for data interpolation with higher degree of accuracy.

Denoising using new thresholding method

This paper discusses the wavelet transform by using new technique to calculate the threshold values. This new threshold methods are used to denoised the signal obtained from Petroleum Engineering applications. From numerical results the new threshold values outperform the existing threshold methods such as global threshold, minimax and SURE methods. Some mathematical derivations to give geometrical meaning to the parameters in the description of the new threshold method is discussed in details. All numerical experiments are executed by using Mathematica and Matlab Softwares.

Electroencephalography data analysis by using discrete wavelet packet transform

Electroencephalography (EEG) is the electrical activity generated by the movement of neurons in the brain. It is categorized into delta waves, theta, alpha, beta and gamma. These waves exist in a different frequency band. This paper is a continuation of our previous research. EEG data will be decomposed using Discrete Wavelet Packet Transform (DWPT). Daubechies wavelets 10 (D10) will be used as the basic functions for research purposes. From the main results, it is clear that the DWPT able to characterize the EEG signal corresponding to each wave at a specific frequency. Furthermore, the numerical results obtained better than the results using DWT. Statistical analysis support our main findings.

Heat simulation via Scilab programming

This paper discussed the used of an open source sofware called Scilab to develop a heat simulator. In this paper, heat equation was used to simulate heat behavior in an object. The simulator was developed using finite difference method. Numerical experiment output show that Scilab can produce a good heat behavior simulation with marvellous visual output with only developing simple computer code.

Image reconstruction using singular value decomposition

The singular value decomposition (SVD) is an effective tool to reconstruct the image approximately towards the original image. This paper will introduce and explores image reconstruction by applying the SVD on gray-scale image. As quality measurements, we used Compression Ratio (CR) and Root-Mean Squared Error (RMSE). The results indicated that for certain images the value of k is smaller than for other images. The value of k is defined as the rank for the closet matrix and the constant integer k can be chosen expectantly less than diagonal matrix n, and the digital image corresponding to outer product expansion, Qk still have very close to the original image.

Complexity reduction approach for solving hyperbolic problems

Complexity reduction approach has been used to solve various science and technology problems. In this paper we will discuss the implementation of the approach to solve some hyperbolic equation such as first order hyperbolic problem and the Maxwell Equations. For solving the Maxwell equations, we implement a weighted average fourth order truncation with the complexity reduction approach. The approach shown to successfully reduce the complexity of original method. Results show to increase the speed up of its original method significantly.

Recent Development of Fast Numerical Solver for Elliptic Problem

Most elliptic solvers developed by researchers need long processing time to be solved. This is due to the complexity of the methods. The objective of this paper is to present new finite difference and finite element methods to overcome the problem. Solving scientific problems mathematically always involved partial differential equations. Two recommended common numerical methods are mesh-free solutions (Belytschko et al, 1996; Zhu 1999; Yagawa & Furukawa, 2000) and mesh-based solutions. The mesh-based solutions can be further classified as finite difference method, finite element method, boundary element method, and finite volume method. These methods have been widely used to construct approximation equations for scientific problems. The developments of numerical algorithms have been actively done by researchers. Evans and Biggins (1982) have proposed an iterative four points Explicit Group (EG) for solving elliptic problem. This method employed blocking strategy to the coefficient matrix of the linear system of equations. By implementing this strategy, four approximate equations are evaluated simultaneously. This scenario speed up the computation time of solving the problem compared to using point based algorithms. At the same time, Evans and Abdullah (1982) utilized the same concepts to solve parabolic problem. Four years later, the concept has been further extended to develop two, nine, sixteen and twenty five points EG (Yousif & Evans, 1986a). These EG schemes have been compared to one and two lines methods. As the results of comparison, the EG solve the problem efficiently compared to the lines methods. Utilizing higher order finite difference approximation, a method called Higher Order Difference Group Explicit (HODGE) was developed (Yousif & Evans, 1986b). This method have higher accuracy than the EG method. Abdullah (1991) modified the EG method by using rotated approximation scheme. The rotated scheme is actually rotate the ordinary computational molecule by 45° to the left. By rearranging the new computational molecule on the solution domain, only half of the total nodes are solved iteratively. The other half can be solved directly using the ordinary computational molecule. This method was named

An improvement in speed of FDTD processing time for free space wave propagation

In this paper, a numerical simulation by a new high speed low order FDTD (HSLO-FDTD) method will be conducted to simulate one dimensional free space wave propagation of 2.4 GHz Gaussian pulse. The efficiency of the new schemes are analyze and compared with the standard FDTD method in terms of processing time, phase velocity and global error. The amplitude in volts by both method are also displayed. Results obtained using the new schemes compare well with published results and solve the problem faster than the standard FDTD method.