Search results for: Linear predictive coding
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2253

Search results for: Linear predictive coding

2193 An Analysis of Genetic Algorithm Based Test Data Compression Using Modified PRL Coding

Authors: K. S. Neelukumari, K. B. Jayanthi

Abstract:

In this paper genetic based test data compression is targeted for improving the compression ratio and for reducing the computation time. The genetic algorithm is based on extended pattern run-length coding. The test set contains a large number of X value that can be effectively exploited to improve the test data compression. In this coding method, a reference pattern is set and its compatibility is checked. For this process, a genetic algorithm is proposed to reduce the computation time of encoding algorithm. This coding technique encodes the 2n compatible pattern or the inversely compatible pattern into a single test data segment or multiple test data segment. The experimental result shows that the compression ratio and computation time is reduced.

Keywords: Backtracking, test data compression (TDC), x-filling, x-propagating and genetic algorithm.

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2192 A Predictive control based on Neural Network for Proton Exchange Membrane Fuel Cell

Authors: M. Sedighizadeh, M. Rezaei, V. Najmi

Abstract:

The Proton Exchange Membrane Fuel Cell (PEMFC) control system has an important effect on operation of cell. Traditional controllers couldn-t lead to acceptable responses because of time- change, long- hysteresis, uncertainty, strong- coupling and nonlinear characteristics of PEMFCs, so an intelligent or adaptive controller is needed. In this paper a neural network predictive controller have been designed to control the voltage of at the presence of fluctuations of temperature. The results of implementation of this designed NN Predictive controller on a dynamic electrochemical model of a small size 5 KW, PEM fuel cell have been simulated by MATLAB/SIMULINK.

Keywords: PEMFC, Neural Network, Predictive Control..

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2191 Method to Improve Channel Coding Using Cryptography

Authors: Ayyaz Mahmood

Abstract:

A new approach for the improvement of coding gain in channel coding using Advanced Encryption Standard (AES) and Maximum A Posteriori (MAP) algorithm is proposed. This new approach uses the avalanche effect of block cipher algorithm AES and soft output values of MAP decoding algorithm. The performance of proposed approach is evaluated in the presence of Additive White Gaussian Noise (AWGN). For the verification of proposed approach, computer simulation results are included.

Keywords: Advanced Encryption Standard (AES), Avalanche Effect, Maximum A Posteriori (MAP), Soft Input Decryption (SID).

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2190 Adaptive Multiple Transforms Hardware Architecture for Versatile Video Coding

Authors: T. Damak, S. Houidi, M. A. Ben Ayed, N. Masmoudi

Abstract:

The Versatile Video Coding standard (VVC) is actually under development by the Joint Video Exploration Team (or JVET). An Adaptive Multiple Transforms (AMT) approach was announced. It is based on different transform modules that provided an efficient coding. However, the AMT solution raises several issues especially regarding the complexity of the selected set of transforms. This can be an important issue, particularly for a future industrial adoption. This paper proposed an efficient hardware implementation of the most used transform in AMT approach: the DCT II. The developed circuit is adapted to different block sizes and can reach a minimum frequency of 192 MHz allowing an optimized execution time.

Keywords: AMT, DCT II, hardware, transform, VVC.

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2189 The Causation and Solution of Ringing Effect in DCT-based Video Coding

Authors: Yu Yuan, David Feng, Yu-Zhuo Zhong

Abstract:

Ringing effect is one of the most annoying visual artifacts in digital video. It is a significant factor of subjective quality deterioration. However, there is a widely-accepted misunderstanding of its cause. In this paper, we propose a reasonable interpretation of the cause of ringing effect. Based on the interpretation, we suggest further two methods to reduce ringing effect in DCT-based video coding. The methods adaptively adjust quantizers according to video features. Our experiments proved that the methods could efficiently improve subjective quality with acceptable additional computing costs.

Keywords: ringing effect, video coding, subjective quality, DCT.

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2188 Model Predictive Control with Unscented Kalman Filter for Nonlinear Implicit Systems

Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

A class of implicit systems is known as a more generalized class of systems than a class of explicit systems. To establish a control method for such a generalized class of systems, we adopt model predictive control method which is a kind of optimal feedback control with a performance index that has a moving initial time and terminal time. However, model predictive control method is inapplicable to systems whose all state variables are not exactly known. In other words, model predictive control method is inapplicable to systems with limited measurable states. In fact, it is usual that the state variables of systems are measured through outputs, hence, only limited parts of them can be used directly. It is also usual that output signals are disturbed by process and sensor noises. Hence, it is important to establish a state estimation method for nonlinear implicit systems with taking the process noise and sensor noise into consideration. To this purpose, we apply the model predictive control method and unscented Kalman filter for solving the optimization and estimation problems of nonlinear implicit systems, respectively. The objective of this study is to establish a model predictive control with unscented Kalman filter for nonlinear implicit systems.

Keywords: Model predictive control, unscented Kalman filter, nonlinear systems, implicit systems.

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2187 EZW Coding System with Artificial Neural Networks

Authors: Saudagar Abdul Khader Jilani, Syed Abdul Sattar

Abstract:

Image compression plays a vital role in today-s communication. The limitation in allocated bandwidth leads to slower communication. To exchange the rate of transmission in the limited bandwidth the Image data must be compressed before transmission. Basically there are two types of compressions, 1) LOSSY compression and 2) LOSSLESS compression. Lossy compression though gives more compression compared to lossless compression; the accuracy in retrievation is less in case of lossy compression as compared to lossless compression. JPEG, JPEG2000 image compression system follows huffman coding for image compression. JPEG 2000 coding system use wavelet transform, which decompose the image into different levels, where the coefficient in each sub band are uncorrelated from coefficient of other sub bands. Embedded Zero tree wavelet (EZW) coding exploits the multi-resolution properties of the wavelet transform to give a computationally simple algorithm with better performance compared to existing wavelet transforms. For further improvement of compression applications other coding methods were recently been suggested. An ANN base approach is one such method. Artificial Neural Network has been applied to many problems in image processing and has demonstrated their superiority over classical methods when dealing with noisy or incomplete data for image compression applications. The performance analysis of different images is proposed with an analysis of EZW coding system with Error Backpropagation algorithm. The implementation and analysis shows approximately 30% more accuracy in retrieved image compare to the existing EZW coding system.

Keywords: Accuracy, Compression, EZW, JPEG2000, Performance.

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2186 Performance Evaluation of One and Two Dimensional Prime Codes for Optical Code Division Multiple Access Systems

Authors: Gurjit Kaur, Neena Gupta

Abstract:

In this paper, we have analyzed and compared the performance of various coding schemes. The basic ID prime sequence codes are unique in only dimension, i.e. time slots, whereas 2D coding techniques are not unique by their time slots but with their wavelengths also. In this research, we have evaluated and compared the performance of 1D and 2D coding techniques constructed using prime sequence coding pattern for Optical Code Division Multiple Access (OCDMA) system on a single platform. Analysis shows that 2D prime code supports lesser number of active users than 1D codes, but they are having large code family and are the most secure codes compared to other codes. The performance of all these codes is analyzed on basis of number of active users supported at a Bit Error Rate (BER) of 10-9.

Keywords: CDMA, OCDMA, BER, OOC, PC, EPC, MPC, 2-D PC/PC, λc, λa.

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2185 Induction of Expressive Rules using the Binary Coding Method

Authors: Seyed R Mousavi

Abstract:

In most rule-induction algorithms, the only operator used against nominal attributes is the equality operator =. In this paper, we first propose the use of the inequality operator, , in addition to the equality operator, to increase the expressiveness of induced rules. Then, we present a new method, Binary Coding, which can be used along with an arbitrary rule-induction algorithm to make use of the inequality operator without any need to change the algorithm. Experimental results suggest that the Binary Coding method is promising enough for further investigation, especially in cases where the minimum number of rules is desirable.

Keywords: Data mining, Inequality operator, Number of rules, Rule-induction.

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2184 A Robust Extrapolation Method for Curtailed Aperture Reconstruction in Acoustic Imaging

Authors: R. Bremananth

Abstract:

Acoustic Imaging based sound localization using microphone array is a challenging task in digital-signal processing. Discrete Fourier transform (DFT) based near-field acoustical holography (NAH) is an important acoustical technique for sound source localization and provide an efficient solution to the ill-posed problem. However, in practice, due to the usage of small curtailed aperture and its consequence of significant spectral leakage, the DFT could not reconstruct the active-region-of-sound (AROS) effectively, especially near the edges of aperture. In this paper, we emphasize the fundamental problems of DFT-based NAH, provide a solution to spectral leakage effect by the extrapolation based on linear predictive coding and 2D Tukey windowing. This approach has been tested to localize the single and multi-point sound sources. We observe that incorporating extrapolation technique increases the spatial resolution, localization accuracy and reduces spectral leakage when small curtail aperture with a lower number of sensors accounts.

Keywords: Acoustic Imaging, Discrete Fourier Transform (DFT), k-space wavenumber, Near-Field Acoustical Holography (NAH), Source Localization, Spectral Leakage.

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2183 Neural Adaptive Switching Control of Robotic Systems

Authors: A. Denker, U. Akıncıoğlu

Abstract:

In this paper a neural adaptive control method has been developed and applied to robot control. Simulation results are presented to verify the effectiveness of the controller. These results show that the performance by using this controller is better than those which just use either direct inverse control or predictive control. In addition, they show that the resulting is a useful method which combines the advantages of both direct inverse control and predictive control.

Keywords: Neural networks, robotics, direct inverse control, predictive control.

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2182 Simplex Method for Fuzzy Variable Linear Programming Problems

Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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2181 Model Predictive Control Using Thermal Inputs for Crystal Growth Dynamics

Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

Recently, crystal growth technologies have made progress by the requirement for the high quality of crystal materials. To control the crystal growth dynamics actively by external forces is useuful for reducing composition non-uniformity. In this study, a control method based on model predictive control using thermal inputs is proposed for crystal growth dynamics of semiconductor materials. The control system of crystal growth dynamics considered here is governed by the continuity, momentum, energy, and mass transport equations. To establish the control method for such thermal fluid systems, we adopt model predictive control known as a kind of optimal feedback control in which the control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. The objective of this study is to establish a model predictive control method for crystal growth dynamics of semiconductor materials.

Keywords: Model predictive control, optimal control, crystal growth, process control.

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2180 Predictive Fuzzy Logic Controller for Agile Micro-Satellite

Authors: A. Bellar, M.K. Fellah, A.M. Si Mohammed, M. Bensaada, L. Boukhris

Abstract:

This paper presents the use of the predictive fuzzy logic controller (PFLC) applied to attitude control system for agile micro-satellite. In order to reduce the effect of unpredictable time delays and large uncertainties, the algorithm employs predictive control to predict the attitude of the satellite. Comparison of the PFLC and conventional fuzzy logic controller (FLC) is presented to evaluate the performance of the control system during attitude maneuver. The two proposed models have been analyzed with the same level of noise and external disturbances. Simulation results demonstrated the feasibility and advantages of the PFLC on the attitude determination and control system (ADCS) of agile satellite.

Keywords: Agile micro-satellite, Attitude control, fuzzy logic, predictive control

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2179 Performance Evaluation of Wavelet Based Coders on Brain MRI Volumetric Medical Datasets for Storage and Wireless Transmission

Authors: D. Dhouib, A. Naït-Ali, C. Olivier, M. S. Naceur

Abstract:

In this paper, we evaluate the performance of some wavelet based coding algorithms such as 3D QT-L, 3D SPIHT and JPEG2K. In the first step we achieve an objective comparison between three coders, namely 3D SPIHT, 3D QT-L and JPEG2K. For this purpose, eight MRI head scan test sets of 256 x 256x124 voxels have been used. Results show superior performance of 3D SPIHT algorithm, whereas 3D QT-L outperforms JPEG2K. The second step consists of evaluating the robustness of 3D SPIHT and JPEG2K coding algorithm over wireless transmission. Compressed dataset images are then transmitted over AWGN wireless channel or over Rayleigh wireless channel. Results show the superiority of JPEG2K over these two models. In fact, it has been deduced that JPEG2K is more robust regarding coding errors. Thus we may conclude the necessity of using corrector codes in order to protect the transmitted medical information.

Keywords: Image coding, medical imaging, wavelet basedcoder, wireless transmission.

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2178 Effective Context Lossless Image Coding Approach Based on Adaptive Prediction

Authors: Grzegorz Ulacha, Ryszard Stasiński

Abstract:

In the paper an effective context based lossless coding technique is presented. Three principal and few auxiliary contexts are defined. The predictor adaptation technique is an improved CoBALP algorithm, denoted CoBALP+. Cumulated predictor error combining 8 bias estimators is calculated. It is shown experimentally that indeed, the new technique is time-effective while it outperforms the well known methods having reasonable time complexity, and is inferior only to extremely computationally complex ones.

Keywords: Adaptive prediction, context coding, image losslesscoding, prediction error bias correction.

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2177 Efficient Secured Lossless Coding of Medical Images– Using Modified Runlength Coding for Character Representation

Authors: S. Annadurai, P. Geetha

Abstract:

Lossless compression schemes with secure transmission play a key role in telemedicine applications that helps in accurate diagnosis and research. Traditional cryptographic algorithms for data security are not fast enough to process vast amount of data. Hence a novel Secured lossless compression approach proposed in this paper is based on reversible integer wavelet transform, EZW algorithm, new modified runlength coding for character representation and selective bit scrambling. The use of the lifting scheme allows generating truly lossless integer-to-integer wavelet transforms. Images are compressed/decompressed by well-known EZW algorithm. The proposed modified runlength coding greatly improves the compression performance and also increases the security level. This work employs scrambling method which is fast, simple to implement and it provides security. Lossless compression ratios and distortion performance of this proposed method are found to be better than other lossless techniques.

Keywords: EZW algorithm, lifting scheme, losslesscompression, reversible integer wavelet transform, securetransmission, selective bit scrambling, modified runlength coding .

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2176 A New Fast Intra Prediction Mode Decision Algorithm for H.264/AVC Encoders

Authors: A. Elyousfi, A. Tamtaoui, E. Bouyakhf

Abstract:

The H.264/AVC video coding standard contains a number of advanced features. Ones of the new features introduced in this standard is the multiple intramode prediction. Its function exploits directional spatial correlation with adjacent block for intra prediction. With this new features, intra coding of H.264/AVC offers a considerably higher improvement in coding efficiency compared to other compression standard, but computational complexity is increased significantly when brut force rate distortion optimization (RDO) algorithm is used. In this paper, we propose a new fast intra prediction mode decision method for the complexity reduction of H.264 video coding. for luma intra prediction, the proposed method consists of two step: in the first step, we make the RDO for four mode of intra 4x4 block, based the distribution of RDO cost of those modes and the idea that the fort correlation with adjacent mode, we select the best mode of intra 4x4 block. In the second step, we based the fact that the dominating direction of a smaller block is similar to that of bigger block, the candidate modes of 8x8 blocks and 16x16 macroblocks are determined. So, in case of chroma intra prediction, the variance of the chroma pixel values is much smaller than that of luma ones, since our proposed uses only the mode DC. Experimental results show that the new fast intra mode decision algorithm increases the speed of intra coding significantly with negligible loss of PSNR.

Keywords: Intra prediction, H264/AVC, video coding, encodercomplexity.

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2175 Fuzzy Predictive Pursuit Guidance in the Homing Missiles

Authors: Mustafa Resa Becan, Ahmet Kuzucu

Abstract:

A fuzzy predictive pursuit guidance is proposed as an alternative to the conventional methods. The purpose of this scheme is to obtain a stable and fast guidance. The noise effects must be reduced in homing missile guidance to get an accurate control. An aerodynamic missile model is simulated first and a fuzzy predictive pursuit control algorithm is applied to reduce the noise effects. The performance of this algorithm is compared with the performance of the classical proportional derivative control. Stability analysis of the proposed guidance method is performed and compared with the stability properties of other guidance methods. Simulation results show that the proposed method provides the satisfying performance.

Keywords: Fuzzy, noise effect, predictive, pursuit.

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2174 Metaheuristic Algorithms for Decoding Binary Linear Codes

Authors: Hassan Berbia, Faissal Elbouanani, Rahal Romadi, Mostafa Belkasmi

Abstract:

This paper introduces two decoders for binary linear codes based on Metaheuristics. The first one uses a genetic algorithm and the second is based on a combination genetic algorithm with a feed forward neural network. The decoder based on the genetic algorithms (DAG) applied to BCH and convolutional codes give good performances compared to Chase-2 and Viterbi algorithm respectively and reach the performances of the OSD-3 for some Residue Quadratic (RQ) codes. This algorithm is less complex for linear block codes of large block length; furthermore their performances can be improved by tuning the decoder-s parameters, in particular the number of individuals by population and the number of generations. In the second algorithm, the search space, in contrast to DAG which was limited to the code word space, now covers the whole binary vector space. It tries to elude a great number of coding operations by using a neural network. This reduces greatly the complexity of the decoder while maintaining comparable performances.

Keywords: Block code, decoding, methaheuristic, genetic algorithm, neural network

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2173 An Implementation of Data Reusable MPEG Video Coding Scheme

Authors: Vasily G. Moshnyaga

Abstract:

This paper presents an optimized MPEG2 video codec implementation, which drastically reduces the number of computations and memory accesses required for video compression. Unlike traditional scheme, we reuse data stored in frame memory to omit unnecessary coding operations and memory read/writes for unchanged macroblocks. Due to dynamic memory sharing among reference frames, data-driven macroblock characterization and selective macroblock processing, we perform less than 15% of the total operations required by a conventional coder while maintaining high picture quality.

Keywords: Data reuse, adaptive processing, video coding, MPEG

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2172 Parallel-Distributed Software Implementation of Buchberger Algorithm

Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury

Abstract:

Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.

Keywords: Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation, OpenMP, MPI.

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2171 A Fuzzy Predictive Filter for Sinusoidal Signals with Time-Varying Frequencies

Authors: X. Z. Gao, S. J. Ovaska, X. Wang

Abstract:

Prediction of sinusoidal signals with time-varying frequencies has been an important research topic in power electronics systems. To solve this problem, we propose a new fuzzy predictive filtering scheme, which is based on a Finite Impulse Response (FIR) filter bank. Fuzzy logic is introduced here to provide appropriate interpolation of individual filter outputs. Therefore, instead of regular 'hard' switching, our method has the advantageous 'soft' switching among different filters. Simulation comparisons between the fuzzy predictive filtering and conventional filter bank-based approach are made to demonstrate that the new scheme can achieve an enhanced prediction performance for slowly changing sinusoidal input signals.

Keywords: Predictive filtering, fuzzy logic, sinusoidal signals, time-varying frequencies.

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2170 ATM Service Analysis Using Predictive Data Mining

Authors: S. Madhavi, S. Abirami, C. Bharathi, B. Ekambaram, T. Krishna Sankar, A. Nattudurai, N. Vijayarangan

Abstract:

The high utilization rate of Automated Teller Machine (ATM) has inevitably caused the phenomena of waiting for a long time in the queue. This in turn has increased the out of stock situations. The ATM utilization helps to determine the usage level and states the necessity of the ATM based on the utilization of the ATM system. The time in which the ATM used more frequently (peak time) and based on the predicted solution the necessary actions are taken by the bank management. The analysis can be done by using the concept of Data Mining and the major part are analyzed based on the predictive data mining. The results are predicted from the historical data (past data) and track the relevant solution which is required. Weka tool is used for the analysis of data based on predictive data mining.

Keywords: ATM, Bank Management, Data Mining, Historical data, Predictive Data Mining, Weka tool.

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2169 Colour Image Compression Method Based On Fractal Block Coding Technique

Authors: Dibyendu Ghoshal, Shimal Das

Abstract:

Image compression based on fractal coding is a lossy compression method and normally used for gray level images range and domain blocks in rectangular shape. Fractal based digital image compression technique provide a large compression ratio and in this paper, it is proposed using YUV colour space and the fractal theory which is based on iterated transformation. Fractal geometry is mainly applied in the current study towards colour image compression coding. These colour images possesses correlations among the colour components and hence high compression ratio can be achieved by exploiting all these redundancies. The proposed method utilises the self-similarity in the colour image as well as the cross-correlations between them. Experimental results show that the greater compression ratio can be achieved with large domain blocks but more trade off in image quality is good to acceptable at less than 1 bit per pixel.

Keywords: Fractal coding, Iterated Function System (IFS), Image compression, YUV colour space.

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2168 Enhanced Spectral Envelope Coding Based On NLMS for G.729.1

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

Abstract:

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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2167 Cognitive SATP for Airborne Radar Based on Slow-Time Coding

Authors: Fanqiang Kong, Jindong Zhang, Daiyin Zhu

Abstract:

Space-time adaptive processing (STAP) techniques have been motivated as a key enabling technology for advanced airborne radar applications. In this paper, the notion of cognitive radar is extended to STAP technique, and cognitive STAP is discussed. The principle for improving signal-to-clutter ratio (SCNR) based on slow-time coding is given, and the corresponding optimization algorithm based on cyclic and power-like algorithms is presented. Numerical examples show the effectiveness of the proposed method.

Keywords: Space-time adaptive processing (STAP), signal-to-clutter ratio, slow-time coding.

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2166 Bi-linear Complementarity Problem

Authors: Chao Wang, Ting-Zhu Huang Chen Jia

Abstract:

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

Keywords: Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix, M-matrix.

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2165 Recent Trends in Nonlinear Methods of HRV Analysis: A Review

Authors: Ramesh K. Sunkaria

Abstract:

The linear methods of heart rate variability analysis such as non-parametric (e.g. fast Fourier transform analysis) and parametric methods (e.g. autoregressive modeling) has become an established non-invasive tool for marking the cardiac health, but their sensitivity and specificity were found to be lower than expected with positive predictive value <30%. This may be due to considering the RR-interval series as stationary and re-sampling them prior to their use for analysis, whereas actually it is not. This paper reviews the non-linear methods of HRV analysis such as correlation dimension, largest Lyupnov exponent, power law slope, fractal analysis, detrended fluctuation analysis, complexity measure etc. which are currently becoming popular as these uses the actual RR-interval series. These methods are expected to highly accurate cardiac health prognosis.

Keywords: chaos, nonlinear dynamics, sample entropy, approximate entropy, detrended fluctuation analysis.

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2164 Two-dimensional Differential Transform Method for Solving Linear and Non-linear Goursat Problem

Authors: H. Taghvafard, G. H. Erjaee

Abstract:

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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