Search results for: Orthogonal Polynomials Transform

Authors: Linyu Wang, Furui Huo, Jianhong Xiang

Abstract:

The Doppler shift generated by high-speed movement and multipath effects in the channel are the main reasons for the generation of a time-frequency doubly-selective (DS) channel. There is severe inter-carrier interference (ICI) in the DS channel. Channel estimation for an orthogonal frequency division multiplexing (OFDM) system over a DS channel is very difficult. The simultaneous orthogonal matching pursuit (SOMP) algorithm under distributed compressive sensing theory (DCS-SOMP) has been used in channel estimation for OFDM systems over DS channels. However, the reconstruction accuracy of the DCS-SOMP algorithm is not high enough in the low Signal-to-Noise Ratio (SNR) stage. To solve this problem, in this paper, we propose an improved DCS-SOMP algorithm based on the inner product difference comparison operation (DCS-DCSOMP). The reconstruction accuracy is improved by increasing the number of candidate indexes and designing the comparison conditions of inner product difference. We combine the DCS-DCSOMP algorithm with the basis expansion model (BEM) to reduce the complexity of channel estimation. Simulation results show the effectiveness of the proposed algorithm and its advantages over other algorithms.

Keywords: OFDM, doubly selective, channel estimation, compressed sensing

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Authors: Harpreet Kaur, Sudipta Majumdar

Abstract:

In this paper a method for image dehazing is proposed in lifting wavelet transform domain. Lifting Daubechies (D4) wavelet has been used to obtain the approximate image and detail images.  As the haze is contained in low frequency part, only the approximate image is used for further processing. This region is processed by dehazing algorithm based on dark channel prior (DCP). The dehazed approximate image is then recombined with the detail images using inverse lifting wavelet transform. Implementation of lifting wavelet transform has the advantage of auxiliary memory saving, fast implementation and simplicity. Also, the proposed method deals with near white scene problem, blue horizon issue and localized light sources in a way to enhance image quality and makes the algorithm robust. Simulation results present improvement in terms of visual quality, parameters such as root mean square (RMS) contrast, structural similarity index (SSIM), entropy and execution time.

Keywords: Dark channel prior, image dehazing, lifting wavelet transform.

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Authors: C. Hemasundara Rao, M. Madhavi Latha

Abstract:

Image compression can improve the performance of the digital systems by reducing time and cost in image storage and transmission without significant reduction of the image quality. Furthermore, the discrete cosine transform has emerged as the new state-of-the art standard for image compression. In this paper, a hybrid image compression technique based on reversible blockade transform coding is proposed. The technique, implemented over regions of interest (ROIs), is based on selection of the coefficients that belong to different transforms, depending on the coefficients is proposed. This method allows: (1) codification of multiple kernals at various degrees of interest, (2) arbitrary shaped spectrum,and (3) flexible adjustment of the compression quality of the image and the background. No standard modification for JPEG2000 decoder was required. The method was applied over different types of images. Results show a better performance for the selected regions, when image coding methods were employed for the whole set of images. We believe that this method is an excellent tool for future image compression research, mainly on images where image coding can be of interest, such as the medical imaging modalities and several multimedia applications. Finally VLSI implementation of proposed method is shown. It is also shown that the kernal of Hartley and Cosine transform gives the better performance than any other model.

Keywords: VLSI, Discrete Cosine Transform, JPEG, Hartleytransform, Radon Transform

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Authors: Keunhong Chae, Seokho Yoon

Abstract:

We address the integer frequency offset (IFO) estimation under the influence of the timing offset (TO) in orthogonal frequency division multiplexing (OFDM) systems. Incorporating the IFO and TO into the symbol set used to represent the received OFDM symbol, we investigate the influence of the TO on the IFO, and then, propose a combining method between two consecutive OFDM correlations, reducing the influence. The proposed scheme has almost the same complexity as that of the conventional schemes, whereas it does not need the TO knowledge contrary to the conventional schemes. From numerical results it is confirmed that the proposed scheme is insensitive to the TO, consequently, yielding an improvement of the IFO estimation performance over the conventional schemes when the TO exists.

Keywords: Estimation, integer frequency offset, OFDM, timing offset.

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Authors: Chokri Jebali, Noureddine Boulejfen, Ali Gharsallah, Fadhel M. Ghannouchi

Abstract:

In this paper, a system level behavioural model for RF power amplifier, which exhibits memory effects, and based on multibranch system is proposed. When higher order terms are included, the memory polynomial model (MPM) exhibits numerical instabilities. A set of memory orthogonal polynomial model (OMPM) is introduced to alleviate the numerical instability problem associated to MPM model. A data scaling and centring algorithm was applied to improve the power amplifier modeling accuracy. Simulation results prove that the numerical instability can be greatly reduced, as well as the model precision improved with nonlinear model.

Keywords: power amplifier, orthogonal model, polynomialmodel , memory effects.

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Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

Abstract:

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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Authors: Mahdi Sharifian, Mohammad Ali Fanaei

Abstract:

Saccharomyces cerevisiae (baker-s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance models can be used to capture the dynamic behavior of such cultures. In this paper an unstructured, segregated model is used which is based on population balance equation(PBE) and then in order to simulation, the 4th order Rung-Kutta is used for time dimension and three methods, finite difference, orthogonal collocation on finite elements and Galerkin finite element are used for discretization of the cell mass domain. The results indicate that the orthogonal collocation on finite element not only is able to predict the oscillating behavior of the cell culture but also needs much little time for calculations. Therefore this method is preferred in comparison with other methods. In the next step two controllers, a globally linearizing control (GLC) and a conventional proportional-integral (PI) controller are designed for controlling the total cell mass per unit volume, and performances of these controllers are compared through simulation. The results show that although the PI controller has simpler structure, the GLC has better performance.

Keywords: Bioreactor, cell population balance, finite difference, orthogonal collocation on finite elements, Galerkin finite element, feedback linearization, PI controller.

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Authors: A. Danbaba

Abstract:

Samurai Sudoku consists of five Sudoku square designs each having nine treatments in each row (column or sub-block) only once such the five Sudoku designs overlaps. Two or more Samurai designs can be joint together to give an extended Samurai design. In addition, two Samurai designs, each containing five Sudoku square designs, are mutually orthogonal (Graeco). If we superimpose two Samurai designs and obtained a pair of Latin and Greek letters in each row (column or sub-block) of the five Sudoku designs only once, then we have Graeco Samurai design. In this paper, simple method of constructing Samurai designs and mutually orthogonal Samurai design are proposed. In addition, linear models and methods of data analysis for the designs are proposed.

Keywords: Samurai design, Graeco samurai design, sudoku design, row or column swap.

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Authors: Tong Liu, Xuan Xu, Xiaodi Wang

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Computational techniques derived from digital image processing are playing a significant role in the security and digital copyrights of multimedia and visual arts. This technology has the effect within the domain of computers. This research presents discrete M-band wavelet transform (MWT) and cosine transform (DCT) based watermarking algorithm by incorporating the principal component analysis (PCA). The proposed algorithm is expected to achieve higher perceptual transparency. Specifically, the developed watermarking scheme can successfully resist common signal processing, such as geometric distortions, and Gaussian noise. In addition, the proposed algorithm can be parameterized, thus resulting in more security. To meet these requirements, the image is transformed by a combination of MWT & DCT. In order to improve the security further, we randomize the watermark image to create three code books. During the watermark embedding, PCA is applied to the coefficients in approximation sub-band. Finally, first few component bands represent an excellent domain for inserting the watermark.

Keywords: discrete M-band wavelet transform , discrete M-band wavelet transform, randomized watermark, principal component analysis

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Authors: Masato Sasaki, Masayoshi Yamamoto

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The majority of wireless power transfer (WPT) systems transfer power in a directional manner. This paper describes a discrete exciting voltage control technique for WPT via magnetic resonant coupling with two orthogonal transmitter coils (2D omni-directional WPT system) which can maximize the power transfer efficiency in response to the change of coupling status. The theory allows the equations of the efficiency of the system to be determined at all the rate of the mutual inductance. The calculated results are included to confirm the advantage to one directional WPT system and the validity of the theory and the equations.

Keywords: Wireless power transfer, orthogonal, omni-directional, efficiency.

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Authors: Ibtihel Nouira, Asma Ben Abdallah, Ibtissem Kouaja, Mohamed Hèdi Bedoui

Abstract:

The processing of the electrocardiogram (ECG) signal consists essentially in the detection of the characteristic points of signal which are an important tool in the diagnosis of heart diseases. The most suitable are the detection of R waves. In this paper, we present various mathematical tools used for filtering ECG using digital filtering and Discreet Wavelet Transform (DWT) filtering. In addition, this paper will include two main R peak detection methods by applying a windowing process: The first method is based on calculations derived, the second is a time-frequency method based on Dyadic Wavelet Transform DyWT.

Keywords: Derived calculation methods, Electrocardiogram, R peaks, Wavelet Transform.

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Authors: B. B. M. Moasheri, S. Azadinia

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Wavelets have provided the researchers with significant positive results, by entering the texture defect detection domain. The weak point of wavelets is that they are one-dimensional by nature so they are not efficient enough to describe and analyze two-dimensional functions. In this paper we present a new method to detect the defect of texture images by using curvelet transform. Simulation results of the proposed method on a set of standard texture images confirm its correctness. Comparing the obtained results indicates the ability of curvelet transform in describing discontinuity in two-dimensional functions compared to wavelet transform

Keywords: Curvelet, Defect detection, Wavelet.

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Authors: Sergei Yendiyarov, Sergei Petrushenko

Abstract:

In this article we present a change point detection algorithm based on the continuous wavelet transform. At the beginning of the article we describe a necessary transformation of a signal which has to be made for the purpose of change detection. Then case study related to iron ore sinter production which can be solved using our proposed technique is discussed. After that we describe a probabilistic algorithm which can be used to find changes using our transformed signal. It is shown that our algorithm works well with the presence of some noise and abnormal random bursts.

Keywords: Change detection, sinter production, wavelet transform.

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Authors: Numan Unaldi, Samil Temel, Süleyman Demirci

Abstract:

A novel undecimated wavelet transform based contrast enhancement algorithmis proposed to for both gray scale andcolor images. Contrast enhancement is realized by tuning the magnitude of approximation coefficients at each level with respect to the approximation coefficients of one higher level during the inverse transform phase in a center/surround  enhancement sense.The performance of the proposed algorithm is evaluated using a statistical visual contrast measure (VCM). Experimental results on the proposed algorithm show improvement in terms of the VCM.

Keywords: Image enhancement, local contrast enhancement, visual contrast measure.

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Authors: Yang Laixia, Deng Jun, Li Dichen, Bai Yang

Abstract:

The forming process parameters of Selective Laser Sintering(SLS) directly affect the forming efficiency and forming quality. Therefore, to determine reasonable process parameters is particularly important. In this paper, the weight of each target of the forming quality and efficiency is firstly calculated with the Analytic Hierarchy Process. And then the size of each target is measured by orthogonal experiment. Finally, the sum of the product of each target with the weight is compared to the process parameters in each group and obtained the optimal molding process parameters.

Keywords: Analytic Hierarchy Process, Multi-objective optimization, Orthogonal test, Selective Laser Sintering

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Authors: Redha Benzid, Farid Marir, Nour-Eddine Bouguechal

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This paper presents a new Quality-Controlled, wavelet based, compression method for electrocardiogram (ECG) signals. Initially, an ECG signal is decomposed using the wavelet transform. Then, the resulting coefficients are iteratively thresholded to guarantee that a predefined goal percent root mean square difference (GPRD) is matched within tolerable boundaries. The quantization strategy of extracted non-zero wavelet coefficients (NZWC), according to the combination of RLE, HUFFMAN and arithmetic encoding of the NZWC and a resulting look up table, allow the accomplishment of high compression ratios with good quality reconstructed signals.

Keywords: ECG compression, Non-uniform Max-Lloydquantizer, PRD, Quality-Controlled, Wavelet transform

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Authors: Vijaya Prakash.A.M, K.S.Gurumurthy

Abstract:

In Image processing the Image compression can improve the performance of the digital systems by reducing the cost and time in image storage and transmission without significant reduction of the Image quality. This paper describes hardware architecture of low complexity Discrete Cosine Transform (DCT) architecture for image compression[6]. In this DCT architecture, common computations are identified and shared to remove redundant computations in DCT matrix operation. Vector processing is a method used for implementation of DCT. This reduction in computational complexity of 2D DCT reduces power consumption. The 2D DCT is performed on 8x8 matrix using two 1-Dimensional Discrete cosine transform blocks and a transposition memory [7]. Inverse discrete cosine transform (IDCT) is performed to obtain the image matrix and reconstruct the original image. The proposed image compression algorithm is comprehended using MATLAB code. The VLSI design of the architecture is implemented Using Verilog HDL. The proposed hardware architecture for image compression employing DCT was synthesized using RTL complier and it was mapped using 180nm standard cells. . The Simulation is done using Modelsim. The simulation results from MATLAB and Verilog HDL are compared. Detailed analysis for power and area was done using RTL compiler from CADENCE. Power consumption of DCT core is reduced to 1.027mW with minimum area[1].

Keywords: Discrete Cosine Transform (DCT), Inverse DiscreteCosine Transform (IDCT), Joint Photographic Expert Group (JPEG), Low Power Design, Very Large Scale Integration (VLSI) .

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Authors: Jaeyoon Lee, Dongweon Yoon, Hoon Yoo, Sanggoo Kim

Abstract:

Orthogonal frequency division multiplexing (OFDM) has developed into a popular scheme for wideband digital communications used in consumer applications such as digital broadcasting, wireless networking and broadband internet access. In the OFDM system, carrier frequency offset (CFO) causes intercarrier interference (ICI) which significantly degrades the system error performance. In this paper we provide an exact evaluation method for error performance analysis of arbitrary 2-D modulation OFDM systems with CFO, and analyze the effect of CFO on error performance.

Keywords: Carrier frequency offset, Probability of error, Inter-channel interference, Orthogonal frequency division multiplexing

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Authors: Farzaneh Akhavan Mahdavi, Siti Anom Ahmad, Mohd Hamiruce Marhaban, Mohammad-R. Akbarzadeh-T

Abstract:

Electromyography (EMG) signal processing has been investigated remarkably regarding various applications such as in rehabilitation systems. Specifically, wavelet transform has served as a powerful technique to scrutinize EMG signals since wavelet transform is consistent with the nature of EMG as a non-stationary signal. In this paper, the efficiency of wavelet transform in surface EMG feature extraction is investigated from four levels of wavelet decomposition and a comparative study between different mother wavelets had been done. To recognize the best function and level of wavelet analysis, two evaluation criteria, scatter plot and RES index are recruited. Hereupon, four wavelet families, namely, Daubechies, Coiflets, Symlets and Biorthogonal are studied in wavelet decomposition stage. Consequently, the results show that only features from first and second level of wavelet decomposition yields good performance and some functions of various wavelet families can lead to an improvement in separability class of different hand movements.

Keywords: Electromyography signal, feature extraction, wavelettransform, means absolute value.

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Authors: Somayeh Sadeghi, Hamid A. Jalab, Sajjad Dadkhah

Abstract:

Due to availability of powerful image processing software and improvement of human computer knowledge, it becomes easy to tamper images. Manipulation of digital images in different fields like court of law and medical imaging create a serious problem nowadays. Copy-move forgery is one of the most common types of forgery which copies some part of the image and pastes it to another part of the same image to cover an important scene. In this paper, a copy-move forgery detection method proposed based on Fourier transform to detect forgeries. Firstly, image is divided to same size blocks and Fourier transform is performed on each block. Similarity in the Fourier transform between different blocks provides an indication of the copy-move operation. The experimental results prove that the proposed method works on reasonable time and works well for gray scale and colour images. Computational complexity reduced by using Fourier transform in this method.

Keywords: Copy-Move forgery, Digital Forensics, Image Forgery.

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Authors: Abdelkader Magdy, Magdy Saeb, A. Baith Mohamed, Ahmed Khadragi

Abstract:

The Deoxyribonucleic Acid (DNA) which is a doublestranded helix of nucleotides consists of: Adenine (A), Cytosine (C), Guanine (G) and Thymine (T). In this work, we convert this genetic code into an equivalent digital signal representation. Applying a wavelet transform, such as Haar wavelet, we will be able to extract details that are not so clear in the original genetic code. We compare between different organisms using the results of the Haar wavelet Transform. This is achieved by using the trend part of the signal since the trend part bears the most energy of the digital signal representation. Consequently, we will be able to quantitatively reconstruct different biological families.

Keywords: Digital Signal, DNA, Fluctuation part, Haar wavelet, Nucleotides, Trend part.

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Authors: S. Al Wadi, Mohd Tahir Ismail, Samsul Ariffin Abdul Karim

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It is well known that during the developments in the economic sector and through the financial crises occur everywhere in the whole world, volatility measurement is the most important concept in financial time series. Therefore in this paper we discuss the volatility for Amman stocks market (Jordan) for certain period of time. Since wavelet transform is one of the most famous filtering methods and grows up very quickly in the last decade, we compare this method with the traditional technique, Fast Fourier transform to decide the best method for analyzing the volatility. The comparison will be done on some of the statistical properties by using Matlab program.

Keywords: Fast Fourier transforms, Haar wavelet transform, Matlab (Wavelet tools), stocks market, Volatility.

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Authors: M.Devakar, T.K.V.Iyengar

Abstract:

In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest.

Keywords: Couple stress fluid, Generalized Stokes’ problems, Laplace transform, Numerical inversion

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Authors: Huanjun Liu, Yaonan Wang, Feng Duan

Abstract:

This text studies glass bottle intelligent inspector based machine vision instead of manual inspection. The system structure is illustrated in detail in this paper. The text presents the method based on watershed transform methods to segment the possible defective regions and extract features of bottle wall by rules. Then wavelet transform are used to exact features of bottle finish from images. After extracting features, the fuzzy support vector machine ensemble is putted forward as classifier. For ensuring that the fuzzy support vector machines have good classification ability, the GA based ensemble method is used to combining the several fuzzy support vector machines. The experiments demonstrate that using this inspector to inspect glass bottles, the accuracy rate may reach above 97.5%.

Keywords: Intelligent Inspection, Support Vector Machines, Ensemble Methods, watershed transform, Wavelet Transform

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Authors: Xin-Yu Shih, Yue-Qu Liu, Hong-Ru Chou

Abstract:

This paper presents a low-area and fully-reconfigurable Fast Fourier Transform (FFT) hardware design for 3GPP-LTE communication standard. It can fully support 32 different FFT sizes, up to 2048 FFT points. Besides, a special processing element is developed for making reconfigurable computing characteristics possible, while first-in first-out (FIFO) scheduling scheme design technique is proposed for hardware-friendly FIFO resource arranging. In a synthesis chip realization via TSMC 40 nm CMOS technology, the hardware circuit only occupies core area of 0.2325 mm² and dissipates 233.5 mW at maximal operating frequency of 250 MHz.

Keywords: Reconfigurable, fast Fourier transform, single-path delay feedback, 3GPP-LTE.

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Authors: Shivali D. Kulkarni, Ameya K. Naik, Nitin S. Nagori

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In this paper we present simulation results for the application of a bandwidth efficient algorithm (mapping algorithm) to an image transmission system. This system considers three different real valued transforms to generate energy compact coefficients. First results are presented for gray scale and color image transmission in the absence of noise. It is seen that the system performs its best when discrete cosine transform is used. Also the performance of the system is dominated more by the size of the transform block rather than the number of coefficients transmitted or the number of bits used to represent each coefficient. Similar results are obtained in the presence of additive white Gaussian noise. The varying values of the bit error rate have very little or no impact on the performance of the algorithm. Optimum results are obtained for the system considering 8x8 transform block and by transmitting 15 coefficients from each block using 8 bits.

Keywords: Additive white Gaussian noise channel, mapping algorithm, peak signal to noise ratio, transform encoding.

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Authors: J. Prakash, K. Rajesh

Abstract:

In this paper we propose a novel method for human face segmentation using the elliptical structure of the human head. It makes use of the information present in the edge map of the image. In this approach we use the fact that the eigenvalues of covariance matrix represent the elliptical structure. The large and small eigenvalues of covariance matrix are associated with major and minor axial lengths of an ellipse. The other elliptical parameters are used to identify the centre and orientation of the face. Since an Elliptical Hough Transform requires 5D Hough Space, the Circular Hough Transform (CHT) is used to evaluate the elliptical parameters. Sparse matrix technique is used to perform CHT, as it squeeze zero elements, and have only a small number of non-zero elements, thereby having an advantage of less storage space and computational time. Neighborhood suppression scheme is used to identify the valid Hough peaks. The accurate position of the circumference pixels for occluded and distorted ellipses is identified using Bresenham-s Raster Scan Algorithm which uses the geometrical symmetry properties. This method does not require the evaluation of tangents for curvature contours, which are very sensitive to noise. The method has been evaluated on several images with different face orientations.

Keywords: Circular Hough Transform, Covariance matrix, Eigenvalues, Elliptical Hough Transform, Face segmentation, Raster Scan Algorithm.

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Authors: Morteza Moazami-Goudarzi, Mohammad H. Moradi, Ali Taheri

Abstract:

In this paper we introduce an effective ECG compression algorithm based on two dimensional multiwavelet transform. Multiwavelets offer simultaneous orthogonality, symmetry and short support, which is not possible with scalar two-channel wavelet systems. These features are known to be important in signal processing. Thus multiwavelet offers the possibility of superior performance for image processing applications. The SPIHT algorithm has achieved notable success in still image coding. We suggested applying SPIHT algorithm to 2-D multiwavelet transform of2-D arranged ECG signals. Experiments on selected records of ECG from MIT-BIH arrhythmia database revealed that the proposed algorithm is significantly more efficient in comparison with previously proposed ECG compression schemes.

Keywords: ECG signal compression, multi-rateprocessing, 2-D Multiwavelet, Prefiltering.

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Authors: Fatma H. Elfouly, Mohamed I. Mahmoud, Moawad I. M. Dessouky, Salah Deyab

Abstract:

Recently, the Field Programmable Gate Array (FPGA) technology offers the potential of designing high performance systems at low cost. The discrete wavelet transform has gained the reputation of being a very effective signal analysis tool for many practical applications. However, due to its computation-intensive nature, current implementation of the transform falls short of meeting real-time processing requirements of most application. The objectives of this paper are implement the Haar and Daubechies wavelets using FPGA technology. In addition, the Bit Error Rate (BER) between the input audio signal and the reconstructed output signal for each wavelet is calculated. From the BER, it is seen that the implementations execute the operation of the wavelet transform correctly and satisfying the perfect reconstruction conditions. The design procedure has been explained and designed using the stat-ofart Electronic Design Automation (EDA) tools for system design on FPGA. Simulation, synthesis and implementation on the FPGA target technology has been carried out.

Keywords: Daubechies wavelet, discrete wavelet transform, Haar wavelet, Xilinx FPGA.

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Authors: Chuan Li, Ming Liang

Abstract:

Oil debris signal generated from the inductive oil debris monitor (ODM) is useful information for machine condition monitoring but is often spoiled by background noise. To improve the reliability in machine condition monitoring, the high-fidelity signal has to be recovered from the noisy raw data. Considering that the noise components with large amplitude often have higher frequency than that of the oil debris signal, the integral transform is proposed to enhance the detectability of the oil debris signal. To cancel out the baseline wander resulting from the integral transform, the empirical mode decomposition (EMD) method is employed to identify the trend components. An optimal reconstruction strategy including both de-trending and de-noising is presented to detect the oil debris signal with less distortion. The proposed approach is applied to detect the oil debris signal in the raw data collected from an experimental setup. The result demonstrates that this approach is able to detect the weak oil debris signal with acceptable distortion from noisy raw data.

Keywords: Integral transform, empirical mode decomposition, oil debris, signal processing, detection.

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