Search results for: Time Spectral Method

Authors: Mohamad Reza. Mohaghegh, Majid. Malek Jafarian

Abstract:

This research proposes an algorithm for the simulation of time-periodic unsteady problems via the solution unsteady Euler and Navier-Stokes equations. This algorithm which is called Time Spectral method uses a Fourier representation in time and hence solve for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. It has shown tremendous potential for reducing the computational cost compared to conventional time-accurate methods, by enforcing periodicity and using Fourier representation in time, leading to spectral accuracy. The accuracy and efficiency of this technique is verified by Euler and Navier-Stokes calculations for pitching airfoils. Because of flow turbulence nature, Baldwin-Lomax turbulence model has been used at viscous flow analysis. The results presented by the Time Spectral method are compared with experimental data. It has shown tremendous potential for reducing the computational cost compared to the conventional time-accurate methods, by enforcing periodicity and using Fourier representation in time, leading to spectral accuracy, because results verify the small number of time intervals per pitching cycle required to capture the flow physics.

Keywords: Time Spectral Method, Time-periodic unsteadyflow, Discrete Fourier transform, Pitching airfoil, Turbulence flow

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Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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Authors: C. Ganesh Babu, P. T. Vanathi

Abstract:

In this paper we present an enhanced noise reduction method for robust speech recognition using Adaptive Gain Equalizer with Non linear Spectral Subtraction. In Adaptive Gain Equalizer method (AGE), the input signal is divided into a number of subbands that are individually weighed in time domain, in accordance to the short time Signal-to-Noise Ratio (SNR) in each subband estimation at every time instant. Instead of focusing on suppression the noise on speech enhancement is focused. When analysis was done under various noise conditions for speech recognition, it was found that Adaptive Gain Equalizer method algorithm has an obvious failing point for a SNR of -5 dB, with inadequate levels of noise suppression for SNR less than this point. This work proposes the implementation of AGE when coupled with Non linear Spectral Subtraction (AGE-NSS) for robust speech recognition. The experimental result shows that out AGE-NSS performs the AGE when SNR drops below -5db level.

Keywords: Adaptive Gain Equalizer, Non Linear Spectral Subtraction, Speech Enhancement, and Speech Recognition.

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Authors: Zhenyu Zhao, Lei You

Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: Kui Du

Abstract:

Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions.

Keywords: Spectral norm, Numerical radius, Spectral radius, Ratios

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Authors: Liping Li, Changchun Liu, Ke Li, Chengyu Liu

Abstract:

Non-stationary trend in R-R interval series is considered as a main factor that could highly influence the evaluation of spectral analysis. It is suggested to remove trends in order to obtain reliable results. In this study, three detrending methods, the smoothness prior approach, the wavelet and the empirical mode decomposition, were compared on artificial R-R interval series with four types of simulated trends. The Lomb-Scargle periodogram was used for spectral analysis of R-R interval series. Results indicated that the wavelet method showed a better overall performance than the other two methods, and more time-saving, too. Therefore it was selected for spectral analysis of real R-R interval series of thirty-seven healthy subjects. Significant decreases (19.94±5.87% in the low frequency band and 18.97±5.78% in the ratio (p<0.001)) were found. Thus the wavelet method is recommended as an optimal choice for use.

Keywords: empirical mode decomposition, heart rate variability, signal detrending, smoothness priors, wavelet

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Authors: Anirut Luadsong, Nitima Aschariyaphotha

Abstract:

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating convection term are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting upwind schemes for avoiding stability problems and prove that it is consistent to the upwind scheme with same accuracy. The splitting upwind schemes was adopted to split the wave spectral action balance equation into four onedimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-processor computer.

Keywords: upwind scheme, parallel algorithm, spectral action balance equation, splitting method.

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Authors: R. Sabre, W. Horrigue, J. C. Simon

Abstract:

This paper is interested in two difficulties encountered in practice when observing a continuous time process. The first is that we cannot observe a process over a time interval; we only take discrete observations. The second is the process frequently observed with a constant additive error. It is important to give an estimator of the spectral density of such a process taking into account the additive observation error and the choice of the discrete observation times. In this work, we propose an estimator based on the spectral smoothing of the periodogram by the polynomial Jackson kernel reducing the additive error. In order to solve the aliasing phenomenon, this estimator is constructed from observations taken at well-chosen times so as to reduce the estimator to the field where the spectral density is not zero. We show that the proposed estimator is asymptotically unbiased and consistent. Thus we obtain an estimate solving the two difficulties concerning the choice of the instants of observations of a continuous time process and the observations affected by a constant error.

Keywords: Spectral density, stable processes, aliasing, periodogram.

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Authors: Khalid M. Aamir, Mohammad A. Maud

Abstract:

Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transform algorithm. The main difference in this algorithm and STFT is that the sliding window (SW) and window for spectral estimation (WSA) are separately defined. WSA is updated and its PSD is computed only when change in statistics is detected in the SW. The computational complexity of the proposed algorithm is found to be lesser than that for standard STFT technique.

Keywords: Power Spectral Density (PSD), quasi-stationarytime series, short time Fourier Transform, Sliding window DFT.

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Authors: R. Sabre

Abstract:

This work focuses on the symmetric alpha stable process with continuous time frequently used in modeling the signal with indefinitely growing variance, often observed with an unknown additive error. The objective of this paper is to estimate this error from discrete observations of the signal. For that, we propose a method based on the smoothing of the observations via Jackson polynomial kernel and taking into account the width of the interval where the spectral density is non-zero. This technique allows avoiding the “Aliasing phenomenon” encountered when the estimation is made from the discrete observations of a process with continuous time. We have studied the convergence rate of the estimator and have shown that the convergence rate improves in the case where the spectral density is zero at the origin. Thus, we set up an estimator of the additive error that can be subtracted for approaching the original signal without error.

Keywords: Spectral density, stable processes, aliasing, p-adic.

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Authors: R. B. Ogunrinde, C. C. Jibunoh

Abstract:

In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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Authors: Martin De Biasio, Raimund Leitner, Franz G. Wuertz, Sergey Verzakov, Pierre J. Elbischger

Abstract:

Breast carcinoma is the most common form of cancer in women. Multicolour fluorescent in-situ hybridisation (m-FISH) is a common method for staging breast carcinoma. The interpretation of m-FISH images is complicated due to two effects: (i) Spectral overlap in the emission spectra of fluorochrome marked DNA probes and (ii) tissue autofluorescence. In this paper hyper-spectral images of m-FISH samples are used and spectral unmixing is applied to produce false colour images with higher contrast and better information content than standard RGB images. The spectral unmixing is realised by combinations of: Orthogonal Projection Analysis (OPA), Alterating Least Squares (ALS), Simple-to-use Interactive Self-Modeling Mixture Analysis (SIMPLISMA) and VARIMAX. These are applied on the data to reduce tissue autofluorescence and resolve the spectral overlap in the emission spectra. The results show that spectral unmixing methods reduce the intensity caused by tissue autofluorescence by up to 78% and enhance image contrast by algorithmically reducing the overlap of the emission spectra.

Keywords: breast carcinoma, hyperspectral imaging, m-FISH, spectral unmixing

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Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou

Abstract:

In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.

Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.

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Authors: Tanapat Brikshavana, Anirut Luadsong

Abstract:

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating propagation velocity terms are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting modified donorcell scheme for avoiding stability problems and prove that it is consistent to the modified donor-cell scheme with same accuracy. The splitting modified donor-cell scheme was adopted to split the wave spectral action balance equation into four one-dimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-cores computer.

Keywords: donor-cell scheme, parallel algorithm, spectral action balance equation, splitting method.

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Authors: Ashutosh Kumar Singh, Anand Mohan

Abstract:

This paper deals with efficient computation of probability coefficients which offers computational simplicity as compared to spectral coefficients. It eliminates the need of inner product evaluations in determination of signature of a combinational circuit realizing given Boolean function. The method for computation of probability coefficients using transform matrix, fast transform method and using BDD is given. Theoretical relations for achievable computational advantage in terms of required additions in computing all 2n probability coefficients of n variable function have been developed. It is shown that for n ≥ 5, only 50% additions are needed to compute all probability coefficients as compared to spectral coefficients. The fault detection techniques based on spectral signature can be used with probability signature also to offer computational advantage.

Keywords: Binary Decision Diagrams, Spectral Coefficients, Fault detection

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Authors: A. Manallah, C. Meier

Abstract:

Confocal spectral interferometry (CSI) is an innovative optical method for determining microtopography of surfaces and thickness of transparent layers, based on the combination of two optical principles: confocal imaging, and spectral interferometry. Confocal optical system images at each instant a single point of the sample. The whole surface is reconstructed by plan scanning. The interference signal generated by mixing two white-light beams is analyzed using a spectrometer. In this work, five ‘rugotests’ of known standard roughnesses are investigated. The topography is then measured and illustrated, and the equivalent roughness is determined and compared with the standard values.

Keywords: Confocal spectral interferometry, Nondestructive testing, Optical metrology, Surface topography, Roughness.

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Authors: Mahamed G.H. Omran, Andries P Engelbrecht, Ayed Salman

Abstract:

An end-member selection method for spectral unmixing that is based on Particle Swarm Optimization (PSO) is developed in this paper. The algorithm uses the K-means clustering algorithm and a method of dynamic selection of end-members subsets to find the appropriate set of end-members for a given set of multispectral images. The proposed algorithm has been successfully applied to test image sets from various platforms such as LANDSAT 5 MSS and NOAA's AVHRR. The experimental results of the proposed algorithm are encouraging. The influence of different values of the algorithm control parameters on performance is studied. Furthermore, the performance of different versions of PSO is also investigated.

Keywords: End-members selection, multispectral satellite imagery, particle swarm optimization, spectral unmixing.

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Authors: Tibor Kulcsar, Gabor Sarossy, Gabor Bereznai, Robert Auer, Janos Abonyi

Abstract:

On-line (near infrared) spectroscopy is widely used to support the operation of complex process systems. Information extracted from spectral database can be used to estimate unmeasured product properties and monitor the operation of the process. These techniques are based on looking for similar spectra by nearest neighborhood algorithms and distance based searching methods. Search for nearest neighbors in the spectral space is an NP-hard problem, the computational complexity increases by the number of points in the discrete spectrum and the number of samples in the database. To reduce the calculation time some kind of indexing could be used. The main idea presented in this paper is to combine indexing and visualization techniques to reduce the computational requirement of estimation algorithms by providing a two dimensional indexing that can also be used to visualize the structure of the spectral database. This 2D visualization of spectral database does not only support application of distance and similarity based techniques but enables the utilization of advanced clustering and prediction algorithms based on the Delaunay tessellation of the mapped spectral space. This means the prediction has not to use the high dimension space but can be based on the mapped space too. The results illustrate that the proposed method is able to segment (cluster) spectral databases and detect outliers that are not suitable for instance based learning algorithms.

Keywords: indexing high dimensional databases, dimensional reduction, clustering, similarity, k-nn algorithm.

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Authors: A. Benyahia, M. Zergoug, M. Amir, M. Fodil

Abstract:

The main objective of this work is to enhance the Pulsed Eddy Current (PEC) response from the aluminum structure using signal processing. Cracks and metal loss in different structures cause changes in PEC response measurements. In this paper, time-frequency analysis is used to represent PEC response, which generates a large quantity of data and reduce the noise due to measurement. Power Spectral Density (PSD) after Wavelet Decomposition (PSD-WD) is proposed for defect detection. The experimental results demonstrate that the cracks in the surface can be extracted satisfactorily by the proposed methods. The validity of the proposed method is discussed.

Keywords: NDT, pulsed eddy current, continuous wavelet transform, Mexican hat wavelet mother, defect detection, power spectral density.

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Authors: J. P. Dubois

Abstract:

Pulse code modulation is a widespread technique in digital communication with significant impact on existing modern and proposed future communication technologies. Its widespread utilization is due to its simplicity and attractive spectral characteristics. In this paper, we present a new approach to the spectral analysis of PCM signals using Riemann-Stieltjes integrals, which is very accurate for high bit rates. This approach can serve as a model for similar spectral analysis of other competing modulation schemes.

Keywords: Coding, discrete Fourier, power spectral density, pulse code modulation, Riemann-Stieltjes integrals.

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Authors: Aritra Acharyya, Moumita Mukherjee, J. P. Banerjee

Abstract:

A generalized method for small-signal simulation of avalanche noise in Mixed Tunneling Avalanche Transit Time (MITATT) device is presented in this paper where the effect of series resistance is taken into account. The method is applied to a millimeter-wave Double Drift Region (DDR) MITATT device based on Silicon to obtain noise spectral density and noise measure as a function of frequency for different values of series resistance. It is found that noise measure of the device at the operating frequency (122 GHz) with input power density of 1010 Watt/m2 is about 35 dB for hypothetical parasitic series resistance of zero ohm (estimated junction temperature = 500 K). Results show that the noise measure increases as the value of parasitic resistance increases.

Keywords: Noise Analysis, Silicon MITATT, Admittancecharacteristics, Noise spectral density.

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Authors: Talbi Mourad, Salhi Lotfi, Chérif Adnen

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In this work, we are interested in developing a speech denoising tool by using a discrete wavelet packet transform (DWPT). This speech denoising tool will be employed for applications of recognition, coding and synthesis. For noise reduction, instead of applying the classical thresholding technique, some wavelet packet nodes are set to zero and the others are thresholded. To estimate the non stationary noise level, we employ the spectral entropy. A comparison of our proposed technique to classical denoising methods based on thresholding and spectral subtraction is made in order to evaluate our approach. The experimental implementation uses speech signals corrupted by two sorts of noise, white and Volvo noises. The obtained results from listening tests show that our proposed technique is better than spectral subtraction. The obtained results from SNR computation show the superiority of our technique when compared to the classical thresholding method using the modified hard thresholding function based on u-law algorithm.

Keywords: Enhancement, spectral subtraction, SNR, discrete wavelet packet transform, spectral entropy Histogram

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Authors: M. T. Sichani, B. J. Pedersen, S. R. K. Nielsen

Abstract:

Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper an empirical cross spectral density function for the along-wind turbulence component over the wind field area is taken as the starting point. The spectrum is spatially discretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive definite. Since the succeeding state space and ARMA modelling of the turbulence rely on the positive definiteness of the cross-spectral density matrix, the problem with the non-positive definiteness of such matrices is at first addressed and suitable treatments regarding it are proposed. From the adjusted positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.

Keywords: Turbulence, wind turbine, complex coherence, state space modelling, ARMA modelling.

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Authors: B. S. Saini, Dilbag Singh, Moin Uddin, Vinod Kumar

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The RR interval series is non-stationary and unevenly spaced in time. For estimating its power spectral density (PSD) using traditional techniques like FFT, require resampling at uniform intervals. The researchers have used different interpolation techniques as resampling methods. All these resampling methods introduce the low pass filtering effect in the power spectrum. The lomb transform is a means of obtaining PSD estimates directly from irregularly sampled RR interval series, thus avoiding resampling. In this work, the superiority of Lomb transform method has been established over FFT based approach, after applying linear and cubicspline interpolation as resampling methods, in terms of reproduction of exact frequency locations as well as the relative magnitudes of each spectral component.

Keywords: HRV, Lomb Transform, Resampling, RR-intervals.

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Authors: Hamioud Saida, Khalfallah Salah

Abstract:

In this study, a spectral element method (SEM) is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision.

Keywords: Elastically supported Euler-Bernoulli beam, free-vibration, spectral element method, Winkler foundation.

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Authors: Keigo Matsuura, Isao Tomita

Abstract:

We have studied a method to widen the spectrum of optical pulses that pass through an InGaAsP waveguide for application to broadband optical communication. In particular, we have investigated the competitive effect between spectral broadening arising from nonlinear refraction (optical Kerr effect) and shrinking due to two photon absorption in the InGaAsP waveguide with χ(3) nonlinearity. The shrunk spectrum recovers broadening by the enhancement effect of the nonlinear refractive index near the bandgap of InGaAsP with a bandgap wavelength of 1490 nm. The broadened spectral width at around 1525 nm (196.7 THz) becomes 10.7 times wider than that at around 1560 nm (192.3 THz) without the enhancement effect, where amplified optical pulses with a pulse width of ∼ 2 ps and a peak power of 10 W propagate through a 1-cm-long InGaAsP waveguide with a cross-section of 4 (μm)2.

Keywords: InGaAsP Waveguide, χ(3) Nonlinearity, Spectral Broadening.

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Authors: Keunseok Cho, Sangbae Jeong, Hyungwook Chang, Minsoo Hahn

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In this paper, a new encoding algorithm of spectral envelope based on NLMS in G.729.1 for VoIP is proposed. In the TDAC part of G.729.1, the spectral envelope and MDCT coefficients extracted in the weighted CELP coding error (lower-band) and the higher-band input signal are encoded. In order to reduce allocation bits for spectral envelope coding, a new quantization algorithm based on NLMS is proposed. Also, reduced bits are used to enhance sound quality. The performance of the proposed algorithm is evaluated by sound quality and bit reduction rates in clean and frame loss conditions.

Keywords: G.729.1, MDCT coefficient, NLMS, spectral envelope.

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Authors: Do Phuc, Nguyen Thi Kim Phung

Abstract:

In this paper, we represent protein structure by using graph. A protein structure database will become a graph database. Each graph is represented by a spectral vector. We use Jacobi rotation algorithm to calculate the eigenvalues of the normalized Laplacian representation of adjacency matrix of graph. To measure the similarity between two graphs, we calculate the Euclidean distance between two graph spectral vectors. To cluster the graphs, we use M-tree with the Euclidean distance to cluster spectral vectors. Besides, M-tree can be used for graph searching in graph database. Our proposal method was tested with graph database of 100 graphs representing 100 protein structures downloaded from Protein Data Bank (PDB) and we compare the result with the SCOP hierarchical structure.

Keywords: Eigenvalues, m-tree, graph database, protein structure, spectra graph theory.

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Authors: Nikhat Nawaz, S. Srinivasulu, P. Kesava Rao

Abstract:

Feature extraction plays an important role in many remote sensing applications. Automatic extraction of water bodies is of great significance in many remote sensing applications like change detection, image retrieval etc. This paper presents a procedure for automatic extraction of water information from remote sensing images. The algorithm uses the relative location of R color component of the chromaticity diagram. This method is then integrated with the effectiveness of the spatial scale transformation of whole method. The whole method is based on water index fitted from spectral library. Experimental results demonstrate the improved accuracy and effectiveness of the integrated method for automatic extraction of water bodies.

Keywords: Chromaticity, Feature Extraction, Remote Sensing, Spectral library, Water Index.

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