Search results for: Fourier method

Authors: M. K. Balyan

Abstract:

The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: dynamical diffraction, hologram, object image, X-ray holography

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Authors: A. S. Issa, S. K. Q. AL-Omari

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In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Boehmian, Fourier integral, Fourier type integral, generalized quotient

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Authors: Balachandra Kumaraswamy, P. G. Poonacha

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Automatic Music Information Retrieval has been one of the challenging topics of research for a few decades now with several interesting approaches reported in the literature. In this paper we have developed a pitch extraction method based on a finite Fourier series approximation to the given window of samples. We then estimate pitch as the fundamental period of the finite Fourier series approximation to the given window of samples. This method uses analysis of the strength of harmonics present in the signal to reduce octave as well as harmonic errors. The performance of our method is compared with three best known methods for pitch extraction, namely, Yin, Windowed Special Normalization of the Auto-Correlation Function and Harmonic Product Spectrum methods of pitch extraction. Our study with artificially created signals as well as music files show that Fourier Approximation method gives much better estimate of pitch with less octave and harmonic errors.

Keywords: pitch, fourier series, yin, normalization of the auto- correlation function, harmonic product, mean square error

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Authors: Ramakrishna Rao Mamidi

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It is essential for Surface Mounted Permanent Magnet (SMPM) generators to determine the performance prediction and analyze the magnet’s air gap flux density wave shape. The flux density wave shape is neither a pure sine wave or square wave nor a combination. This is due to the variation of air gap reluctance between the stator and permanent magnets. The stator slot openings and the number of slots make the wave shape highly complicated. To reduce the complexity of analysis, approximations are made to the wave shape using Fourier analysis. In contrast to the traditional integration method, the Fourier coefficients, an and bn, are obtained by direct search method optimization. The wave shape with optimized coefficients gives a wave shape close to the desired wave shape. Harmonics amplitudes are worked out and compared with initial values. It can be concluded that the direct search method can be used for estimating Fourier coefficients for irregular wave shapes.

Keywords: direct search, flux plot, fourier analysis, permanent magnets

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

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Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization

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Authors: Marwa A. A. Ragab, Hadir M. Maher, Eman I. El-Kimary

Abstract:

Co-administration of methotrexate (MTX) and aspirin (ASP) can cause a pharmacokinetic interaction and a subsequent increase in blood MTX concentrations which may increase the risk of MTX toxicity. Therefore, it is important to develop a sensitive, selective, accurate and precise method for their simultaneous determination in urine. A new hybrid chemometric method has been applied to the emission response data of the two drugs. Spectrofluorimetric method for determination of MTX through measurement of its acid-degradation product, 4-amino-4-deoxy-10-methylpteroic acid (4-AMP), was developed. Moreover, the acid-catalyzed degradation reaction enables the spectrofluorimetric determination of ASP through the formation of its active metabolite salicylic acid (SA). The proposed chemometric method deals with convolution of emission data using 8-points sin xi polynomials (discrete Fourier functions) after the derivative treatment of these emission data. The first and second derivative curves (D1 & D2) were obtained first then convolution of these curves was done to obtain first and second derivative under Fourier functions curves (D1/FF) and (D2/FF). This new application was used for the resolution of the overlapped emission bands of the degradation products of both drugs to allow their simultaneous indirect determination in human urine. Not only this chemometric approach was applied to the emission data but also the obtained data were subjected to non-parametric linear regression analysis (Theil’s method). The proposed method was fully validated according to the ICH guidelines and it yielded linearity ranges as follows: 0.05-0.75 and 0.5-2.5 µg mL-1 for MTX and ASP respectively. It was found that the non-parametric method was superior over the parametric one in the simultaneous determination of MTX and ASP after the chemometric treatment of the emission spectra of their degradation products. The work combines the advantages of derivative and convolution using discrete Fourier function together with the reliability and efficacy of the non-parametric analysis of data. The achieved sensitivity along with the low values of LOD (0.01 and 0.06 µg mL-1) and LOQ (0.04 and 0.2 µg mL-1) for MTX and ASP respectively, by the second derivative under Fourier functions (D2/FF) were promising and guarantee its application for monitoring the two drugs in patients’ urine samples.

Keywords: chemometrics, emission curves, derivative, convolution, Fourier transform, human urine, non-parametric regression, Theil’s method

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Authors: A. Cherifi, B. S. Bouazza, A. O. Dahman, B. Yagoubi

Abstract:

Transmission over Optical channels will introduce inter-symbol interference (ISI) as well as inter-channel (or inter-carrier) interference (ICI). To decrease the effects of ICI, this paper proposes equalizer for the Optical OFDM system based on the fractional Fourier transform (FrFFT). In this FrFT-OFDM system, traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the data symbols. The equalizer proposed consists of sampling the received signal in the different time per time symbol. Theoretical analysis and numerical simulation are discussed.

Keywords: OFDM, fractional fourier transform, internet and information technology

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Authors: Po-Jen Su, Huann-Ming Chou

Abstract:

In this article we uses the residual correction method to deal with transient thermoelastic problems with a hollow spherical region when the continuum medium possesses spherically isotropic thermoelastic properties. Based on linear thermoelastic theory, the equations of hyperbolic heat conduction and thermoelastic motion were combined to establish the thermoelastic dynamic model with consideration of the deformation acceleration effect and non-Fourier effect under the condition of transient thermal shock. The approximate solutions of temperature and displacement distributions are obtained using the residual correction method based on the maximum principle in combination with the finite difference method, making it easier and faster to obtain upper and lower approximations of exact solutions. The proposed method is found to be an effective numerical method with satisfactory accuracy. Moreover, the result shows that the effect of transient thermal shock induced by deformation acceleration is enhanced by non-Fourier heat conduction with increased peak stress. The influence on the stress increases with the thermal relaxation time.

Keywords: maximum principle, non-Fourier heat conduction, residual correction method, thermo-elastic response

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Authors: A. Cherifi, B. Bouazza, A. O. Dahmane, B. Yagoubi

Abstract:

Transmission over Optical channels will introduce inter-symbol interference (ISI) as well as inter-channel (or inter-carrier) interference (ICI). To decrease the effects of ICI, this paper proposes equalizer for the Optical OFDM system based on the fractional Fourier transform (FrFFT). In this FrFT-OFDM system, traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the data symbols. The equalizer proposed consists of sampling the received signal in the different time per time symbol. Theoretical analysis and numerical simulation are discussed.

Keywords: OFDM, (FrFT) fractional fourier transform, optical OFDM, equalization algorithm

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Authors: Dahi Ghareab Abdelsalam Ibrahim, R. H. Bakr

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Ionizing radiation, such as gamma radiation and X-rays, has many applications in medical diagnoses and cancer treatment. In this paper, we used the windowed Fourier transform to extract the complex image of the deformed red blood cells. The real values of the complex image are used to extract the best fitting of the deformed cell boundary. Male albino rats are irradiated by γ-rays from ⁶⁰Co. The male albino rats are anesthetized with ether, and then blood samples are collected from the eye vein by heparinized capillary tubes for studying the radiation-damaging effect in-vivo by the proposed windowed Fourier transform. The peripheral blood films are prepared according to the Brown method. The peripheral blood film is photographed by using an Automatic Image Contour Analysis system (SAMICA) from ELBEK-Bildanalyse GmbH, Siegen, Germany. The SAMICA system is provided with an electronic camera connected to a computer through a built-in interface card, and the image can be magnified up to 1200 times and displayed by the computer. The images of the peripheral blood films are then analyzed by the windowed Fourier transform method to extract the precise deformation from the best fitting. Based on accurate deformation evaluation of the red blood cells, diseases can be diagnosed in their primary stages.

Keywords: windowed Fourier transform, red blood cells, phase wrapping, Image processing

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Authors: Brouri Adil, Giri Fouad

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The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent.

Keywords: Wiener-Hammerstein systems, Fourier series expansions, frequency identification, automation science

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Authors: Felix Givois, Nicolas R. Gauger, Matthias Kabel

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The efficient digital material characterization is of great interest to many fields of application. It consists of the following three steps. First, a 3D reconstruction of 2D scans must be performed. Then, the resulting gray-value image of the material sample is enhanced by image processing methods. Finally, partial differential equations (PDE) are solved on the segmented image, and by averaging the resulting solutions fields, effective properties like stiffness or conductivity can be computed. Due to the high resolution of current CT images, the latter is typically performed with matrix-free solvers. Among them, a solver that uses the explicit formula of the Green-Eshelby operator in Fourier space has been proposed by Moulinec and Suquet. Its algorithmic, most complex part is the Fast Fourier Transformation (FFT). In our talk, we will discuss the potential quantum advantage that can be obtained by replacing the FFT with the Quantum Fourier Transformation (QFT). We will especially show that the data transfer for noisy intermediate-scale quantum (NISQ) devices can be improved by using appropriate boundary conditions for the PDE, which also allows using semi-classical versions of the QFT. In the end, we will compare the results of the QFT-based algorithm for simple geometries with the results of the FFT-based homogenization method.

Keywords: most likelihood amplitude estimation (MLQAE), numerical homogenization, quantum Fourier transformation (QFT), NISQ devises

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Authors: Mohammed S. Al-Rawi, J. Bastos, J. Rodriguez

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Object detection and object recognition are essential components of every computer vision system. Despite the high computational complexity and other problems related to numerical stability and accuracy, Zernike moments of 2D images (ZMs) have shown resilience when used in object recognition and have been used in various image analysis applications. In this work, we propose a novel method for computing ZMs via Fast Fourier Transform (FFT). Notably, this is the first algorithm that can generate ZMs up to extremely high orders accurately, e.g., it can be used to generate ZMs for orders up to 1000 or even higher. Furthermore, the proposed method is also simpler and faster than the other methods due to the availability of FFT software and/or hardware. The accuracies and numerical stability of ZMs computed via FFT have been confirmed using the orthogonality property. We also introduce normalizing ZMs with Neumann factor when the image is embedded in a larger grid, and color image reconstruction based on RGB normalization of the reconstructed images. Astonishingly, higher-order image reconstruction experiments show that the proposed methods are superior, both quantitatively and subjectively, compared to the q-recursive method.

Keywords: Chebyshev polynomial, fourier transform, fast algorithms, image recognition, pseudo Zernike moments, Zernike moments

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Authors: Shahriar Farzam, Maryam Rastgarpour

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Image denoising plays extremely important role in digital image processing. Enhancement of clinical image research based on Curvelet has been developed rapidly in recent years. In this paper, we present a method for image contrast enhancement for cone beam CT (CBCT) images based on fast discrete curvelet transforms (FDCT) that work through Unequally Spaced Fast Fourier Transform (USFFT). These transforms return a table of Curvelet transform coefficients indexed by a scale parameter, an orientation and a spatial location. Accordingly, the coefficients obtained from FDCT-USFFT can be modified in order to enhance contrast in an image. Our proposed method first uses a two-dimensional mathematical transform, namely the FDCT through unequal-space fast Fourier transform on input image and then applies thresholding on coefficients of Curvelet to enhance the CBCT images. Consequently, applying unequal-space fast Fourier Transform leads to an accurate reconstruction of the image with high resolution. The experimental results indicate the performance of the proposed method is superior to the existing ones in terms of Peak Signal to Noise Ratio (PSNR) and Effective Measure of Enhancement (EME).

Keywords: curvelet transform, CBCT, image enhancement, image denoising

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Authors: Kohei Shimasaki, Tomoaki Okamura, Idaku Ishii

Abstract:

We propose a vibration imaging method for high frame rate (HFR)-video-based localization of vibrating objects with large translations. When the ratio of the translation speed of a target to its vibration frequency is large, obtaining its frequency response in image intensities becomes difficult because one or no waves are observable at the same pixel. Our method can precisely localize moving objects with vibration by virtually translating multiple image sequences for pixel-level short-time Fourier transform to observe multiple waves at the same pixel. The effectiveness of the proposed method is demonstrated by analyzing several HFR videos of flying insects in real scenarios.

Keywords: HFR video analysis, pixel-level vibration source localization, short-time Fourier transform, virtual translation

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Authors: Xianwei Zheng, Yuan Yan Tang

Abstract:

Classical window Fourier transform has been widely used in signal processing, image processing, machine learning and pattern recognition. The related Gabor transform is powerful enough to capture the texture information of any given dataset. Recently, in the emerging field of graph signal processing, researchers devoting themselves to develop a graph signal processing theory to handle the so-called graph signals. Among the new developing theory, windowed graph Fourier transform has been constructed to establish a time-frequency analysis framework of graph signals. The windowed graph Fourier transform is defined by using the translation and modulation operators of graph signals, following the similar calculations in classical windowed Fourier transform. Specifically, the translation and modulation operators of graph signals are defined by using the Laplacian eigenvectors as follows. For a given graph signal, its translation is defined by a similar manner as its definition in classical signal processing. Specifically, the translation operator can be defined by using the Fourier atoms; the graph signal translation is defined similarly by using the Laplacian eigenvectors. The modulation of the graph can also be established by using the Laplacian eigenvectors. The windowed graph Fourier transform based on these two operators has been applied to obtain time-frequency representations of graph signals. Fundamentally, the modulation operator is defined similarly to the classical modulation by multiplying a graph signal with the entries in each Fourier atom. However, a single Laplacian eigenvector entry cannot play a similar role as the Fourier atom. This definition ignored the relationship between the translation and modulation operators. In this paper, a new definition of the modulation operator is proposed and thus another time-frequency framework for graph signal is constructed. Specifically, the relationship between the translation and modulation operations can be established by the Fourier transform. Specifically, for any signal, the Fourier transform of its translation is the modulation of its Fourier transform. Thus, the modulation of any signal can be defined as the inverse Fourier transform of the translation of its Fourier transform. Therefore, similarly, the graph modulation of any graph signal can be defined as the inverse graph Fourier transform of the translation of its graph Fourier. The novel definition of the graph modulation operator established a relationship of the translation and modulation operations. The new modulation operation and the original translation operation are applied to construct a new framework of graph signal time-frequency analysis. Furthermore, a windowed graph Fourier frame theory is developed. Necessary and sufficient conditions for constructing windowed graph Fourier frames, tight frames and dual frames are presented in this paper. The novel graph signal time-frequency analysis framework is applied to signals defined on well-known graphs, e.g. Minnesota road graph and random graphs. Experimental results show that the novel framework captures new features of graph signals.

Keywords: graph signals, windowed graph Fourier transform, windowed graph Fourier frames, vertex frequency analysis

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Authors: Hare Krishna Nigam

Abstract:

In this paper, for the first time, (E,q)(C,2) product summability method is introduced and two quite new results on degree of approximation of the function f belonging to Lip (alpha,r)class and W(L(r), xi(t)) class by (E,q)(C,2) product means of Fourier series, has been obtained.

Keywords: Degree of approximation, (E, q)(C, 2) means, Fourier series, Lebesgue integral, Lip (alpha, r)class, W(L(r), xi(t))class of functions

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Authors: Kejal Khatri, Vishnu Narayan Mishra

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We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

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Authors: Manana Chumburidze

Abstract:

We have considered a non-classical model of dynamical problems for a conjugated system of differential equations arising in thermo-piezoelectricity, which was formulated by Toupin – Mindlin. The basic concepts and the general theory of solvability for isotropic homogeneous elastic media is considered. They are worked by using the methods the Laplace integral transform, potential method and singular integral equations. Approximate solutions of mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved in explicitly by using the generalized Fourier's series method.

Keywords: thermo-piezoelectricity, boundary value problems, Fourier's series, isotropic homogeneous elastic media

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Authors: Mahboobeh Eghtesad, Reza Mohseni

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We develop methods for detecting a target for orthogonal frequency division multiplexing (OFDM) based radars. As a preliminary step we introduce the target and Gaussian noise models in discrete–time form. Then, resorting to match filter (MF) we derive a detector for two different scenarios: a non-fluctuating target and a Rayleigh fluctuating target. It will be shown that a MF is not suitable for Rayleigh fluctuating targets. In this paper we propose a reduced-complexity method based on fast Fourier transfrom (FFT) for such a situation. The proposed method has better detection performance.

Keywords: constant false alarm rate (CFAR), match filter (MF), fast Fourier transform (FFT), OFDM radars, Rayleigh fluctuating target

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Authors: Xiaoyu Shen, Fang Fang, Chujun Qiu

Abstract:

Herewith we present a Fourier method for credit risk quantification and allocation in the factor-copula model framework. The key insight is that, compared to directly computing the cumulative distribution function of the portfolio loss via Monte Carlo simulation, it is, in fact, more efficient to calculate the transformation of the distribution function in the Fourier domain instead and inverting back to the real domain can be done in just one step and semi-analytically, thanks to the popular COS method (with some adjustments). We also show that the Euler risk allocation problem can be solved in the same way since it can be transformed into the problem of evaluating a conditional cumulative distribution function. Once the conditional or unconditional cumulative distribution function is known, one can easily calculate various risk metrics. The proposed method not only fills the niche in literature, to the best of our knowledge, of accurate numerical methods for risk allocation but may also serve as a much faster alternative to the Monte Carlo simulation method for risk quantification in general. It can cope with various factor-copula model choices, which we demonstrate via examples of a two-factor Gaussian copula and a two-factor Gaussian-t hybrid copula. The fast error convergence is proved mathematically and then verified by numerical experiments, in which Value-at-Risk, Expected Shortfall, and conditional Expected Shortfall are taken as examples of commonly used risk metrics. The calculation speed and accuracy are tested to be significantly superior to the MC simulation for real-sized portfolios. The computational complexity is, by design, primarily driven by the number of factors instead of the number of obligors, as in the case of Monte Carlo simulation. The limitation of this method lies in the "curse of dimension" that is intrinsic to multi-dimensional numerical integration, which, however, can be relaxed with the help of dimension reduction techniques and/or parallel computing, as we will demonstrate in a separate paper. The potential application of this method has a wide range: from credit derivatives pricing to economic capital calculation of the banking book, default risk charge and incremental risk charge computation of the trading book, and even to other risk types than credit risk.

Keywords: credit portfolio, risk allocation, factor copula model, the COS method, Fourier method

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Authors: Sonali Banrjee, Swarup Kumar Mitra, Aritra Acharyya

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A piano note recognition method has been proposed by the authors in this paper. The authors have used a comprehensive method for onset detection of each note present in a piano piece followed by segmented short-time Fourier transform (STFT) for the identification of piano notes. The performance evaluation of the proposed method has been carried out in different harsh noisy environments by adding different levels of additive white Gaussian noise (AWGN) having different signal-to-noise ratio (SNR) in the original signal and evaluating the note detection error rate (NDER) of different piano pieces consisting of different number of notes at different SNR levels. The NDER is found to be remained within 15% for all piano pieces under consideration when the SNR is kept above 8 dB.

Keywords: AWGN, onset detection, piano note, STFT

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Authors: Smita Sonker

Abstract:

Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski.

Keywords: signals, trigonometric fourier approximation, class W(L^r, \xi(t), conjugate fourier series

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Authors: Emanuel Guariglia

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In this paper we deal with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due the connection coefficients. The differential properties of Chebyshev wavelets, expressed by the connection coefficients (also called refinable integrals), are given by finite series in terms of the Kronecker delta. Moreover, we treat the p-order derivative of Chebyshev wavelets and compute its Fourier transform. Finally, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry.

Keywords: Chebyshev wavelets, Fourier transform, connection coefficients, Taylor series, local fractional derivative, Cantor set

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Authors: Royan Dawud Aldian, Endah Purwanti, Soegianto Soelistiono

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In this research we have been developed an automatic investigation to classify normal children voice or autistic by using modern computation technology that is computation based on artificial neural network. The superiority of this computation technology is its capability on processing and saving data. In this research, digital voice features are gotten from the coefficient of linear-predictive coding with auto-correlation method and have been transformed in frequency domain using fast fourier transform, which used as input of artificial neural network in back-propagation method so that will make the difference between normal children and autistic automatically. The result of back-propagation method shows that successful classification capability for normal children voice experiment data is 100% whereas, for autistic children voice experiment data is 100%. The success rate using back-propagation classification system for the entire test data is 100%.

Keywords: autism, artificial neural network, backpropagation, linier predictive coding, fast fourier transform

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

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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 (FFT), single-path delay feedback (SDF), 3GPP-LTE

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Authors: Hamdy M. Youssef, Mowffaq Oreijah, Hunaydi S. Alsharif

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In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

Keywords: thermoelasticity, thermal conductivity, Laplace transforms, Fourier transforms

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Authors: Ju-Young Choi, Ki-Il Song, Kyoung-Yul Kim

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During Tunnel Boring Machine (TBM) tunnel excavation, backfill grout should be injected after the installation of segment lining to ensure the stability of the tunnel and to minimize ground deformation. If grouting is not sufficient to fill the gap between the segments and rock mass, hydraulic pressures occur in the void, which can negatively influence the stability of the tunnel. Recently the tendency to use TBM tunnelling method to replace the drill and blast(NATM) method is increasing. However, there are only a few studies of evaluation of backfill grout. This study evaluates the TBM tunnel backfill state using Impact-Echo(IE). 3-layers, segment-grout-rock mass, are simulated by FLAC 2D, FDM-based software. The signals obtained from numerical analysis and IE test are analyzed by Short-Time Fourier Transform(STFT) in time domain, frequency domain, and time-frequency domain. The result of this study can be used to evaluate the quality of backfill grouting in tail void.

Keywords: tunnel boring machine, backfill grout, impact-echo method, time-frequency domain analysis, finite difference method

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Authors: Hamdy M. Youssef

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In this work, the usual Euler–Bernoulli nanobeam has been modeled in the context of Lord-Shulman thermoelastic theorem, which contains non-Fourier heat conduction law. The nanobeam has been subjected to a constant magnetic field and ramp-type thermal loading. The Laplace transform definition has been applied to the governing equations, and the solutions have been obtained by using a direct approach. The inversions of the Laplace transform have been calculated numerically by using Tzou approximation method. The solutions have been applied to a nanobeam made of silicon nitride. The distributions of the temperature increment, lateral deflection, strain, stress, and strain-energy density have been represented in figures with different values of the magnetic field intensity and ramp-time heat parameter. The value of the magnetic field intensity and ramp-time heat parameter have significant effects on all the studied functions, and they could be used as tuners to control the energy which has been generated through the nanobeam.

Keywords: nanobeam, vibration, constant magnetic field, ramp-type thermal loading, non-Fourier heat conduction law

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Authors: Smita Sonker, Uaday Singh

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Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

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