A discrete dislocation–transformation model for austenitic single crystals

International Nuclear Information System (INIS)

Shi, J; Turteltaub, S; Remmers, J J C; Van der Giessen, E

2008-01-01

A discrete model for analyzing the interaction between plastic flow and martensitic phase transformations is developed. The model is intended for simulating the microstructure evolution in a single crystal of austenite that transforms non-homogeneously into martensite. The plastic flow in the untransformed austenite is simulated using a plane-strain discrete dislocation model. The phase transformation is modeled via the nucleation and growth of discrete martensitic regions embedded in the austenitic single crystal. At each instant during loading, the coupled elasto-plasto-transformation problem is solved using the superposition of analytical solutions for the discrete dislocations and discrete transformation regions embedded in an infinite homogeneous medium and the numerical solution of a complementary problem used to enforce the actual boundary conditions and the heterogeneities in the medium. In order to describe the nucleation and growth of martensitic regions, a nucleation criterion and a kinetic law suitable for discrete regions are specified. The constitutive rules used in discrete dislocation simulations are supplemented with additional evolution rules to account for the phase transformation. To illustrate the basic features of the model, simulations of specimens under plane-strain uniaxial extension and contraction are analyzed. The simulations indicate that plastic flow reduces the average stress at which transformation begins, but it also reduces the transformation rate when compared with benchmark simulations without plasticity. Furthermore, due to local stress fluctuations caused by dislocations, martensitic systems can be activated even though transformation would not appear to be favorable based on the average stress. Conversely, the simulations indicate that the plastic hardening behavior is influenced by the reduction in the effective austenitic grain size due to the evolution of transformation. During cyclic simulations, the coupled plasticity-transformation

Image Retrieval Algorithm Based on Discrete Fractional Transforms

Science.gov (United States)

Jindal, Neeru; Singh, Kulbir

2013-06-01

The discrete fractional transforms is a signal processing tool which suggests computational algorithms and solutions to various sophisticated applications. In this paper, a new technique to retrieve the encrypted and scrambled image based on discrete fractional transforms has been proposed. Two-dimensional image was encrypted using discrete fractional transforms with three fractional orders and two random phase masks placed in the two intermediate planes. The significant feature of discrete fractional transforms benefits from its extra degree of freedom that is provided by its fractional orders. Security strength was enhanced (1024!)4 times by scrambling the encrypted image. In decryption process, image retrieval is sensitive for both correct fractional order keys and scrambling algorithm. The proposed approach make the brute force attack infeasible. Mean square error and relative error are the recital parameters to verify validity of proposed method.

A Baecklund transformation between two integrable discrete hungry systems

International Nuclear Information System (INIS)

Fukuda, Akiko; Yamamoto, Yusaku; Iwasaki, Masashi; Ishiwata, Emiko; Nakamura, Yoshimasa

2011-01-01

The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.

A Baecklund transformation between two integrable discrete hungry systems

Energy Technology Data Exchange (ETDEWEB)

Fukuda, Akiko, E-mail: j1409704@ed.kagu.tus.ac.j [Department of Mathematical Information Science, Graduate School of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Yamamoto, Yusaku [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501 (Japan); Iwasaki, Masashi [Department of Informatics and Environmental Science, Kyoto Prefectural University, 1-5, Nakaragi-cho, Shimogamo, Sakyo-ku, Kyoto 606-8522 (Japan); Ishiwata, Emiko [Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Nakamura, Yoshimasa [Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)

2011-01-17

The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.

Nonlinear system modeling based on bilinear Laguerre orthonormal bases.

Science.gov (United States)

Garna, Tarek; Bouzrara, Kais; Ragot, José; Messaoud, Hassani

2013-05-01

This paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input, to the output and to the crossed product on three independent Laguerre orthonormal bases. Compared to classical bilinear model, the resulting model entitled bilinear-Laguerre model ensures a significant parameter number reduction as well as simple recursive representation. However, such reduction still constrained by an optimal choice of Laguerre pole characterizing each basis. To do so, we develop a pole optimization algorithm which constitutes an extension of that proposed by Tanguy et al.. The bilinear-Laguerre model as well as the proposed pole optimization algorithm are illustrated and tested on a numerical simulations and validated on the Continuous Stirred Tank Reactor (CSTR) System. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

The discrete Painleve II equations: Miura and auto-Baecklund transformations

International Nuclear Information System (INIS)

Carstea, A S; Ramani, A; Willox, R; Grammaticos, B

2003-01-01

We present Miura transformations for all discrete Painleve II equations known to date. We then use these Miuras to derive special solutions in terms of discrete Airy functions and to construct auto-Baecklund transformations for the discrete Painleve equations. These transformations are then used to generate rational solutions. Some new forms of d-P II and d-P 34 are obtained as well

Completeness and orthonormality of the Volkov states and the Volkov propagator in configuration space

Science.gov (United States)

Di Piazza, A.

2018-03-01

Volkov states and Volkov propagator are the basic analytical tools to investigate QED processes occurring in the presence of an intense plane-wave electromagnetic field. In the present paper we provide alternative and relatively simple proofs of the completeness and of the orthonormality at a fixed time of the Volkov states. Concerning the completeness, we exploit some known properties of the Green's function of the Dirac operator in a plane wave, whereas the orthonormality of the Volkov states is proved, relying only on a geometric argument based on the Gauss theorem in four dimensions. In relation with the completeness of the Volkov states, we also study some analytical properties of the Green's function of the Dirac operator in a plane wave, which we explicitly prove to coincide with the Volkov propagator in configuration space. In particular, a closed-form expression in terms of modified Bessel functions and Hankel functions is derived by means of the operator technique in a plane wave and different asymptotic forms are determined. Finally, the transformation properties of the Volkov propagator under general gauge transformations and a general gauge-invariant expression of the so-called dressed mass in configuration space are presented.

Geometric Representations for Discrete Fourier Transforms

Science.gov (United States)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation

International Nuclear Information System (INIS)

Shi, Ying; Zhang, Da-jun; Nimmo, Jonathan J C

2014-01-01

The Hirota–Miwa equation can be written in ‘nonlinear’ form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations. (paper)

Approximating the Analytic Fourier Transform with the Discrete Fourier Transform

OpenAIRE

Axelrod, Jeremy

2015-01-01

The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

Science.gov (United States)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Discrete transforms

CERN Document Server

Firth, Jean M

1992-01-01

The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen­ tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...

Discrete linear canonical transform computation by adaptive method.

Science.gov (United States)

Zhang, Feng; Tao, Ran; Wang, Yue

2013-07-29

The linear canonical transform (LCT) describes the effect of quadratic phase systems on a wavefield and generalizes many optical transforms. In this paper, the computation method for the discrete LCT using the adaptive least-mean-square (LMS) algorithm is presented. The computation approaches of the block-based discrete LCT and the stream-based discrete LCT using the LMS algorithm are derived, and the implementation structures of these approaches by the adaptive filter system are considered. The proposed computation approaches have the inherent parallel structures which make them suitable for efficient VLSI implementations, and are robust to the propagation of possible errors in the computation process.

Discrete wavelet transform: a tool in smoothing kinematic data.

Science.gov (United States)

Ismail, A R; Asfour, S S

1999-03-01

Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high-frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.

Lax Pairs for Discrete Integrable Equations via Darboux Transformations

International Nuclear Information System (INIS)

Cao Ce-Wen; Zhang Guang-Yao

2012-01-01

A method is developed to construct discrete Lax pairs using Darboux transformations. More kinds of Lax pairs are found for some newly appeared discrete integrable equations, including the H1, the special H3 and the Q1 models in the Adler—Bobenko—Suris list and the closely related discrete and semi-discrete pKdV, pMKdV, SG and Liouville equations. (general)

Orthonormal bases for α-modulation spaces

DEFF Research Database (Denmark)

Nielsen, Morten

We construct an orthonormal basis for the family of bi-variate a-modulation spaces. The construction is based on local trigonometric bases, and the basis elements are closely related to so-called brushlets. As an application, we show that m-term nonlinear approximation with the system in an a......-modulation space can be completely characterized....

Properties of the Simpson discrete fourier transform | Singh ...

African Journals Online (AJOL)

The Simpson discrete Fourier transform (SDFT) and its inverse are transformations relating the time and frequency domains. In this paper we state and prove the important properties of shift, circular convolution, conjugation, time reversal and Plancherel's theorem. In addition, we provide an alternative representation of the ...

Discrete cosine and sine transforms general properties, fast algorithms and integer approximations

CERN Document Server

Britanak, Vladimir; Rao, K R; Rao, K R

2006-01-01

The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhune

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

International Nuclear Information System (INIS)

Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

2014-01-01

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

Image compression-encryption algorithms by combining hyper-chaotic system with discrete fractional random transform

Science.gov (United States)

Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun

2018-07-01

Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.

A planar waveguide optical discrete Fourier transformer design for 160 Gb/s all-optical OFDM systems

Science.gov (United States)

Li, Wei; Liang, Xiaojun; Ma, Weidong; Zhou, Tianhong; Huang, Benxiong; Liu, Deming

2010-01-01

A cost-effective all-optical discrete Fourier transformer (ODFT) is designed based on a silicon planar lightwave circuit (PLC), which can be applied to all-optical orthogonal frequency division multiplexing (OFDM) transmission systems and can be achieved by current techniques. It consists of 2 × 2 directional couplers, phase shifters and optical delay lines. Metal-film heaters are used as phase shifters, according to the thermooptic effect of SiO 2. Based on the ODFT, a 160 Gb/s OFDM system is set up. Simulation results show excellent bit error rate (BER) and optical signal-to-noise ratio (OSNR) performances after 400 km transmission.

A discrete Fourier transform for virtual memory machines

Science.gov (United States)

Galant, David C.

1992-01-01

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

Elementary Baecklund transformations for a discrete Ablowitz-Ladik eigenvalue problem

International Nuclear Information System (INIS)

Rourke, David E

2004-01-01

Elementary Baecklund transformations (BTs) are described for a discretization of the Zakharov-Shabat eigenvalue problem (a special case of the Ablowitz-Ladik eigenvalue problem). Elementary BTs allow the process of adding bound states to a system (i.e., the add-one-soliton BT) to be 'factorized' to solving two simpler sub-problems. They are used to determine the effect on the scattering data when bound states are added. They are shown to provide a method of calculating discrete solitons-this is achieved by constructing a lattice of intermediate potentials, with the parameters used in the calculation of the lattice simply related to the soliton scattering data. When the potentials, S n , T n , in the system are related by S n = -T n , they enable simple derivations to be obtained of the add-one-soliton BT and the nonlinear superposition formula

An analysis of the Simpson Discrete Hartley transform | Ramsunder ...

African Journals Online (AJOL)

The relatively new Simpson Discrete Hartley Transform (SDHT) has interesting mathematical properties, which are crucial for applications. These are developed and proved in this paper. This analysis gives one a comprehensive understanding of the transform. Mathematics Subject Classication (2010): 43A32. Key words: ...

The su(2)α Hahn oscillator and a discrete Fourier-Hahn transform

International Nuclear Information System (INIS)

Jafarov, E I; Stoilova, N I; Van der Jeugt, J

2011-01-01

We define the quadratic algebra su(2) α which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2) α . We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra su(2) α . It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this so-called discrete Fourier-Hahn transform is computed explicitly. The matrix of this discrete Fourier-Hahn transform has many interesting properties, similar to those of the traditional discrete Fourier transform. (paper)

Orthonormal bases for  α-modulation spaces

DEFF Research Database (Denmark)

Nielsen, Morten

2010-01-01

We construct an orthonormal basis for the family of bi-variate α-modulation spaces. The construction is based on local trigonometric bases, and the basis elements are closely related to so-called brushlets. As an application, we show that m-term nonlinear approximation with the representing system...... in an α-modulation space can be completely characterized....

Discrete linear canonical transforms based on dilated Hermite functions.

Science.gov (United States)

Pei, Soo-Chang; Lai, Yun-Chiu

2011-08-01

Linear canonical transform (LCT) is very useful and powerful in signal processing and optics. In this paper, discrete LCT (DLCT) is proposed to approximate LCT by utilizing the discrete dilated Hermite functions. The Wigner distribution function is also used to investigate DLCT performances in the time-frequency domain. Compared with the existing digital computation of LCT, our proposed DLCT possess additivity and reversibility properties with no oversampling involved. In addition, the length of input/output signals will not be changed before and after the DLCT transformations, which is consistent with the time-frequency area-preserving nature of LCT; meanwhile, the proposed DLCT has very good approximation of continuous LCT.

Fast ghost imaging and ghost encryption based on the discrete cosine transform

International Nuclear Information System (INIS)

Tanha, Mehrdad; Ahmadi-Kandjani, Sohrab; Kheradmand, Reza

2013-01-01

We introduce the discrete cosine transform as an advanced compression tool for images in computational ghost imaging. A novel approach to fast imaging and encryption, the discrete cosine transform, promotes the security level of ghost images and reduces the image retrieval time. To discuss the advantages of this technique we compare experimental outcomes with simulated ones. (paper)

Nuclear data compression and reconstruction via discrete wavelet transform

Energy Technology Data Exchange (ETDEWEB)

Park, Young Ryong; Cho, Nam Zin [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1998-12-31

Discrete Wavelet Transforms (DWTs) are recent mathematics, and begin to be used in various fields. The wavelet transform can be used to compress the signal and image due to its inherent properties. We applied the wavelet transform compression and reconstruction to the neutron cross section data. Numerical tests illustrate that the signal compression using wavelet is very effective to reduce the data saving spaces. 7 refs., 4 figs., 3 tabs. (Author)

Nuclear data compression and reconstruction via discrete wavelet transform

Energy Technology Data Exchange (ETDEWEB)

Park, Young Ryong; Cho, Nam Zin [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1997-12-31

Discrete Wavelet Transforms (DWTs) are recent mathematics, and begin to be used in various fields. The wavelet transform can be used to compress the signal and image due to its inherent properties. We applied the wavelet transform compression and reconstruction to the neutron cross section data. Numerical tests illustrate that the signal compression using wavelet is very effective to reduce the data saving spaces. 7 refs., 4 figs., 3 tabs. (Author)

Alternatives to the discrete cosine transform for irreversible tomographic image compression

International Nuclear Information System (INIS)

Villasenor, J.D.

1993-01-01

Full-frame irreversible compression of medical images is currently being performed using the discrete cosine transform (DCT). Although the DCT is the optimum fast transform for video compression applications, the authors show here that it is out-performed by the discrete Fourier transform (DFT) and discrete Hartley transform (DHT) for images obtained using positron emission tomography (PET) and magnetic resonance imaging (MRI), and possibly for certain types of digitized radiographs. The difference occurs because PET and MRI images are characterized by a roughly circular region D of non-zero intensity bounded by a region R in which the Image intensity is essentially zero. Clipping R to its minimum extent can reduce the number of low-intensity pixels but the practical requirement that images be stored on a rectangular grid means that a significant region of zero intensity must remain an integral part of the image to be compressed. With this constraint imposed, the DCT loses its advantage over the DFT because neither transform introduces significant artificial discontinuities. The DFT and DHT have the further important advantage of requiring less computation time than the DCT

Regular Discrete Cosine Transform and its Application to Digital Images Representation

Directory of Open Access Journals (Sweden)

Yuri A. Gadzhiev

2011-11-01

Full Text Available Discrete cosine transform dct-i, unlike dct-ii, does not concentrate the energy of a transformed vector sufficiently well, so it is not used practically for the purposes of digital image compression. By performing regular normalization of the basic cosine transform matrix, we obtain a discrete cosine transform which has the same cosine basis as dct-i, coincides as dct-i with its own inverse transform, but unlike dct-i, it does not reduce the proper ability of cosine transform to the energy concentration. In this paper we consider briefly the properties of this transform, its possible integer implementation for the case of 8x8-matrix, its applications to the image itself and to the preliminary rgb colour space transformations, further more we investigate some models of quantization, perform an experiment for the estimation of the level of digital images compression and the quality achieved by use of this transform. This experiment shows that the transform can be sufficiently effective for practical use, but the question of its comparative effectiveness with respect to dct-ii remains open.

Discrete Fourier Transform in a Complex Vector Space

Science.gov (United States)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Error estimates of Lagrange interpolation and orthonormal expansions for Freud weights

Science.gov (United States)

Kwon, K. H.; Lee, D. W.

2001-08-01

Let Sn[f] be the nth partial sum of the orthonormal polynomials expansion with respect to a Freud weight. Then we obtain sufficient conditions for the boundedness of Sn[f] and discuss the speed of the convergence of Sn[f] in weighted Lp space. We also find sufficient conditions for the boundedness of the Lagrange interpolation polynomial Ln[f], whose nodal points are the zeros of orthonormal polynomials with respect to a Freud weight. In particular, if W(x)=e-(1/2)x2 is the Hermite weight function, then we obtain sufficient conditions for the inequalities to hold:andwhere and k=0,1,2...,r.

Generating Solutions to Discrete sine-Gordon Equation from Modified Baecklund Transformation

International Nuclear Information System (INIS)

Kou Xin; Zhang Dajun; Shi Ying; Zhao Songlin

2011-01-01

We modify the bilinear Baecklund transformation for the discrete sine-Gordon equation and derive variety, of solutions by freely choosing parameters from the modified Baecklund transformation. Dynamics of solutions and continuum limits are also discussed. (general)

Discrete Orthogonal Transforms and Neural Networks for Image Interpolation

Directory of Open Access Journals (Sweden)

J. Polec

1999-09-01

Full Text Available In this contribution we present transform and neural network approaches to the interpolation of images. From transform point of view, the principles from [1] are modified for 1st and 2nd order interpolation. We present several new interpolation discrete orthogonal transforms. From neural network point of view, we present interpolation possibilities of multilayer perceptrons. We use various configurations of neural networks for 1st and 2nd order interpolation. The results are compared by means of tables.

Fast parallel approach for 2-D DHT-based real-valued discrete Gabor transform.

Science.gov (United States)

Tao, Liang; Kwan, Hon Keung

2009-12-01

Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.

On the physical relevance of the discrete Fourier transform

CSIR Research Space (South Africa)

Greben, JM

1991-11-01

Full Text Available This paper originated from the author's dissatisfaction with the way the discrete Fourier transform is usually presented in the literature. Although mathematically correct, the physical meaning of the common representation is unsatisfactory...

Discretization of four types of Weyl group orbit functions

International Nuclear Information System (INIS)

Hrivnák, Jiří

2013-01-01

The discrete Fourier calculus of the four families of special functions, called C–, S–, S s – and S l -functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable — the discrete S s – and S l -transforms of the group F 4 — are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented

Infrared and visual image fusion method based on discrete cosine transform and local spatial frequency in discrete stationary wavelet transform domain

Science.gov (United States)

Jin, Xin; Jiang, Qian; Yao, Shaowen; Zhou, Dongming; Nie, Rencan; Lee, Shin-Jye; He, Kangjian

2018-01-01

In order to promote the performance of infrared and visual image fusion and provide better visual effects, this paper proposes a hybrid fusion method for infrared and visual image by the combination of discrete stationary wavelet transform (DSWT), discrete cosine transform (DCT) and local spatial frequency (LSF). The proposed method has three key processing steps. Firstly, DSWT is employed to decompose the important features of the source image into a series of sub-images with different levels and spatial frequencies. Secondly, DCT is used to separate the significant details of the sub-images according to the energy of different frequencies. Thirdly, LSF is applied to enhance the regional features of DCT coefficients, and it can be helpful and useful for image feature extraction. Some frequently-used image fusion methods and evaluation metrics are employed to evaluate the validity of the proposed method. The experiments indicate that the proposed method can achieve good fusion effect, and it is more efficient than other conventional image fusion methods.

A non-linear discrete transform for pattern recognition of discrete chaotic systems

International Nuclear Information System (INIS)

Karanikas, C.; Proios, G.

2003-01-01

It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter

A non-linear discrete transform for pattern recognition of discrete chaotic systems

CERN Document Server

Karanikas, C

2003-01-01

It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter.

Near infrared face recognition by combining Zernike moments and undecimated discrete wavelet transform

Czech Academy of Sciences Publication Activity Database

Farokhi, Sajad; Shamsuddin, S.M.; Sheikh, U.U.; Flusser, Jan; Khansari, M.; Jafari-Khouzani, K.

2014-01-01

Roč. 31, č. 1 (2014), s. 13-27 ISSN 1051-2004 R&D Projects: GA ČR GAP103/11/1552 Institutional support: RVO:67985556 Keywords : Zernike moments * Undecimated discrete wavelet transform * Decision fusion * Near infrared * Face recognition Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.256, year: 2014 http://library.utia.cas.cz/separaty/2014/ZOI/flusser-0428536.pdf

Discrete Haar transform and protein structure.

Science.gov (United States)

Morosetti, S

1997-12-01

The discrete Haar transform of the sequence of the backbone dihedral angles (phi and psi) was performed over a set of X-ray protein structures of high resolution from the Brookhaven Protein Data Bank. Afterwards, the new dihedral angles were calculated by the inverse transform, using a growing number of Haar functions, from the lower to the higher degree. New structures were obtained using these dihedral angles, with standard values for bond lengths and angles, and with omega = 0 degree. The reconstructed structures were compared with the experimental ones, and analyzed by visual inspection and statistical analysis. When half of the Haar coefficients were used, all the reconstructed structures were not yet collapsed to a tertiary folding, but they showed yet realized most of the secondary motifs. These results indicate a substantial separation of structural information in the space of Haar transform, with the secondary structural information mainly present in the Haar coefficients of lower degrees, and the tertiary one present in the higher degree coefficients. Because of this separation, the representation of the folded structures in the space of Haar transform seems a promising candidate to encompass the problem of premature convergence in genetic algorithms.

Digital Watermarks Using Discrete Wavelet Transformation and Spectrum Spreading

Directory of Open Access Journals (Sweden)

Ryousuke Takai

2003-12-01

Full Text Available In recent tears, digital media makes rapid progress through the development of digital technology. Digital media normally assures fairly high quality, nevertheless can be easily reproduced in a perfect form. This perfect reproducibility takes and advantage from a certain point of view, while it produces an essential disadvantage, since digital media is frequently copied illegally. Thus the problem of the copyright protection becomes a very important issue. A solution of this problem is to embed digital watermarks that is not perceived clearly by usual people, but represents the proper right of original product. In our method, the images data in the frequency domain are transformed by the Discrete Wavelet Transform and analyzed by the multi resolution approximation, [1]. Further, the spectrum spreading is executed by using PN-sequences. Choi and Aizawa [7] embed watermarks by using block correlation of DCT coefficients. Thus, we apply Discrete Cosine Transformation, abbreviated to DCT, instead of the Fourier transformation in order to embed watermarks.If the value of this variance is high then we decide that the block has bigger magnitude for visual fluctuations. Henceforth, we may embed stronger watermarks, which gives resistance for images processing, such as attacks and/or compressions.

Discrete Fourier and wavelet transforms an introduction through linear algebra with applications to signal processing

CERN Document Server

Goodman, Roe W

2016-01-01

This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

Fast Algorithm for Computing the Discrete Hartley Transform of Type-II

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Mounir Taha Hamood

2016-06-01

Full Text Available The generalized discrete Hartley transforms (GDHTs have proved to be an efficient alternative to the generalized discrete Fourier transforms (GDFTs for real-valued data applications. In this paper, the development of direct computation of radix-2 decimation-in-time (DIT algorithm for the fast calculation of the GDHT of type-II (DHT-II is presented. The mathematical analysis and the implementation of the developed algorithm are derived, showing that this algorithm possesses a regular structure and can be implemented in-place for efficient memory utilization.The performance of the proposed algorithm is analyzed and the computational complexity is calculated for different transform lengths. A comparison between this algorithm and existing DHT-II algorithms shows that it can be considered as a good compromise between the structural and computational complexities.

Invariant object recognition based on the generalized discrete radon transform

Science.gov (United States)

Easley, Glenn R.; Colonna, Flavia

2004-04-01

We introduce a method for classifying objects based on special cases of the generalized discrete Radon transform. We adjust the transform and the corresponding ridgelet transform by means of circular shifting and a singular value decomposition (SVD) to obtain a translation, rotation and scaling invariant set of feature vectors. We then use a back-propagation neural network to classify the input feature vectors. We conclude with experimental results and compare these with other invariant recognition methods.

Discrete-continuous bispectral operators and rational Darboux transformations

International Nuclear Information System (INIS)

Boyallian, Carina; Portillo, Sofia

2010-01-01

In this Letter we construct examples of discrete-continuous bispectral operators obtained by rational Darboux transformations applied to a regular pseudo-difference operator with constant coefficients. Moreover, we give an explicit procedure to write down the differential operators involved in the bispectral situation corresponding to the pseudo-difference operator obtained by the Darboux process.

Discrete Fourier transform in nanostructures using scattering

International Nuclear Information System (INIS)

Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.

2004-01-01

In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed

The spectral transform as a tool for solving nonlinear discrete evolution equations

International Nuclear Information System (INIS)

Levi, D.

1979-01-01

In this contribution we study nonlinear differential difference equations which became important to the description of an increasing number of problems in natural science. Difference equations arise for instance in the study of electrical networks, in statistical problems, in queueing problems, in ecological problems, as computer models for differential equations and as models for wave excitation in plasma or vibrations of particles in an anharmonic lattice. We shall first review the passages necessary to solve linear discrete evolution equations by the discrete Fourier transfrom, then, starting from the Zakharov-Shabat discretized eigenvalue, problem, we shall introduce the spectral transform. In the following part we obtain the correlation between the evolution of the potentials and scattering data through the Wronskian technique, giving at the same time many other properties as, for example, the Baecklund transformations. Finally we recover some of the important equations belonging to this class of nonlinear discrete evolution equations and extend the method to equations with n-dependent coefficients. (HJ)

Orthonormal Wavelet Bases for Quantum Molecular Dynamics

International Nuclear Information System (INIS)

Tymczak, C.; Wang, X.

1997-01-01

We report on the use of compactly supported, orthonormal wavelet bases for quantum molecular-dynamics (Car-Parrinello) algorithms. A wavelet selection scheme is developed and tested for prototypical problems, such as the three-dimensional harmonic oscillator, the hydrogen atom, and the local density approximation to atomic and molecular systems. Our method shows systematic convergence with increased grid size, along with improvement on compression rates, thereby yielding an optimal grid for self-consistent electronic structure calculations. copyright 1997 The American Physical Society

Use of switched capacitor filters to implement the discrete wavelet transform

Science.gov (United States)

Kaiser, Kraig E.; Peterson, James N.

1993-01-01

This paper analyzes the use of IIR switched capacitor filters to implement the discrete wavelet transform and the inverse transform, using quadrature mirror filters (QMF) which have the necessary symmetry for reconstruction of the data. This is done by examining the sensitivity of the QMF transforms to the manufacturing variance in the desired capacitances. The performance is evaluated at the outputs of the separate filter stages and the error in the reconstruction of the inverse transform is compared with the desired results.

A Laplace transform method for energy multigroup hybrid discrete ordinates

International Nuclear Information System (INIS)

Segatto, C.F.; Vilhena, M.T.; Barros, R.C.

2010-01-01

In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this work we describe a hybrid discrete ordinates (S N) method for energy multigroup slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. The idea is based on the fact that in weakly absorbing media whose physical size is several neutron mean free paths in extent, even the S 2 method (P 1 approximation), leads to an accurate result. We use special fuel-moderator interface conditions and the Laplace transform (LTS N ) analytical numerical method to calculate the two-energy group neutron flux distributions and the thermal disadvantage factor. We present numerical results for a range of typical model problems.

Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations

International Nuclear Information System (INIS)

Clarkson, Peter A

2013-01-01

We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations. It is shown that the coefficients in these recurrence relations can be expressed in terms of Wronskians of modified Bessel functions and confluent hypergeometric functions, respectively for the generalized Charlier and generalized Meixner polynomials. These Wronskians arise in the description of special function solutions of the third and fifth Painlevé equations. (paper)

Oblique projections and standard-form transformations for discrete inverse problems

DEFF Research Database (Denmark)

Hansen, Per Christian

2013-01-01

This tutorial paper considers a specific computational tool for the numerical solution of discrete inverse problems, known as the standard-form transformation, by which we can treat general Tikhonov regularization problems efficiently. In the tradition of B. N. Datta's expositions of numerical li...... linear algebra, we use the close relationship between oblique projections, pseudoinverses, and matrix computations to derive a simple geometric motivation and algebraic formulation of the standard-form transformation....

Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules

International Nuclear Information System (INIS)

Dong Ping; Yang Ming; Cao Zhuoliang

2008-01-01

In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system

Novel Iris Biometric Watermarking Based on Singular Value Decomposition and Discrete Cosine Transform

Directory of Open Access Journals (Sweden)

Jinyu Lu

2014-01-01

Full Text Available A novel iris biometric watermarking scheme is proposed focusing on iris recognition instead of the traditional watermark for increasing the security of the digital products. The preprocess of iris image is to be done firstly, which generates the iris biometric template from person's eye images. And then the templates are to be on discrete cosine transform; the value of the discrete cosine is encoded to BCH error control coding. The host image is divided into four areas equally correspondingly. The BCH codes are embedded in the singular values of each host image's coefficients which are obtained through discrete cosine transform (DCT. Numerical results reveal that proposed method can extract the watermark effectively and illustrate its security and robustness.

Discrete Hadamard transformation algorithm's parallelism analysis and achievement

Science.gov (United States)

Hu, Hui

2009-07-01

With respect to Discrete Hadamard Transformation (DHT) wide application in real-time signal processing while limitation in operation speed of DSP. The article makes DHT parallel research and its parallel performance analysis. Based on multiprocessor platform-TMS320C80 programming structure, the research is carried out to achieve two kinds of parallel DHT algorithms. Several experiments demonstrated the effectiveness of the proposed algorithms.

Efficient Algorithms for the Discrete Gabor Transform with a Long Fir Window

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2012-01-01

The Discrete Gabor Transform (DGT) is the most commonly used signal transform for signal analysis and synthesis using a linear frequency scale. The development of the Linear Time-Frequency Analysis Toolbox (LTFAT) has been based on a detailed study of many variants of the relevant algorithms. As ...

Homogeneous hierarchies: A discrete analogue to the wavelet-based multiresolution approximation

Energy Technology Data Exchange (ETDEWEB)

Mirkin, B. [Rutgers Univ., Piscataway, NJ (United States)

1996-12-31

A correspondence between discrete binary hierarchies and some orthonormal bases of the n-dimensional Euclidean space can be applied to such problems as clustering, ordering, identifying/testing in very large data bases, or multiresolution image/signal processing. The latter issue is considered in the paper. The binary hierarchy based multiresolution theory is expected to lead to effective methods for data processing because of relaxing the regularity restrictions of the classical theory.

Discrete Fourier Transform Analysis in a Complex Vector Space

Science.gov (United States)

Dean, Bruce H.

2009-01-01

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Discrete Ramanujan transform for distinguishing the protein coding regions from other regions.

Science.gov (United States)

Hua, Wei; Wang, Jiasong; Zhao, Jian

2014-01-01

Based on the study of Ramanujan sum and Ramanujan coefficient, this paper suggests the concepts of discrete Ramanujan transform and spectrum. Using Voss numerical representation, one maps a symbolic DNA strand as a numerical DNA sequence, and deduces the discrete Ramanujan spectrum of the numerical DNA sequence. It is well known that of discrete Fourier power spectrum of protein coding sequence has an important feature of 3-base periodicity, which is widely used for DNA sequence analysis by the technique of discrete Fourier transform. It is performed by testing the signal-to-noise ratio at frequency N/3 as a criterion for the analysis, where N is the length of the sequence. The results presented in this paper show that the property of 3-base periodicity can be only identified as a prominent spike of the discrete Ramanujan spectrum at period 3 for the protein coding regions. The signal-to-noise ratio for discrete Ramanujan spectrum is defined for numerical measurement. Therefore, the discrete Ramanujan spectrum and the signal-to-noise ratio of a DNA sequence can be used for distinguishing the protein coding regions from the noncoding regions. All the exon and intron sequences in whole chromosomes 1, 2, 3 and 4 of Caenorhabditis elegans have been tested and the histograms and tables from the computational results illustrate the reliability of our method. In addition, we have analyzed theoretically and gotten the conclusion that the algorithm for calculating discrete Ramanujan spectrum owns the lower computational complexity and higher computational accuracy. The computational experiments show that the technique by using discrete Ramanujan spectrum for classifying different DNA sequences is a fast and effective method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Orthonormal filters for identification in active control systems

International Nuclear Information System (INIS)

Mayer, Dirk

2015-01-01

Many active noise and vibration control systems require models of the control paths. When the controlled system changes slightly over time, adaptive digital filters for the identification of the models are useful. This paper aims at the investigation of a special class of adaptive digital filters: orthonormal filter banks possess the robust and simple adaptation of the widely applied finite impulse response (FIR) filters, but at a lower model order, which is important when considering implementation on embedded systems. However, the filter banks require prior knowledge about the resonance frequencies and damping of the structure. This knowledge can be supposed to be of limited precision, since in many practical systems, uncertainties in the structural parameters exist. In this work, a procedure using a number of training systems to find the fixed parameters for the filter banks is applied. The effect of uncertainties in the prior knowledge on the model error is examined both with a basic example and in an experiment. Furthermore, the possibilities to compensate for the imprecise prior knowledge by a higher filter order are investigated. Also comparisons with FIR filters are implemented in order to assess the possible advantages of the orthonormal filter banks. Numerical and experimental investigations show that significantly lower computational effort can be reached by the filter banks under certain conditions. (paper)

Integrable discretization s of derivative nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2002-01-01

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)

Towards discrete wavelet transform-based human activity recognition

Science.gov (United States)

Khare, Manish; Jeon, Moongu

2017-06-01

Providing accurate recognition of human activities is a challenging problem for visual surveillance applications. In this paper, we present a simple and efficient algorithm for human activity recognition based on a wavelet transform. We adopt discrete wavelet transform (DWT) coefficients as a feature of human objects to obtain advantages of its multiresolution approach. The proposed method is tested on multiple levels of DWT. Experiments are carried out on different standard action datasets including KTH and i3D Post. The proposed method is compared with other state-of-the-art methods in terms of different quantitative performance measures. The proposed method is found to have better recognition accuracy in comparison to the state-of-the-art methods.

On the discrete version of Gabor's signal expansion, the Gabor transform, and the Zak transform

NARCIS (Netherlands)

Bastiaans, M.J.; Veen, J.P.

1996-01-01

Gabors expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or synthesis window is introduced, along with the inverse operation, i.e., the Gabor transform, which uses an analysis window that is related to the synthesis window and with the help of

Surface Design Based on Discrete Conformal Transformations

Science.gov (United States)

Duque, Carlos; Santangelo, Christian; Vouga, Etienne

Conformal transformations are angle-preserving maps from one domain to another. Although angles are preserved, the lengths between arbitrary points are not generally conserved. As a consequence there is always a given amount of distortion associated to any conformal map. Different uses of such transformations can be found in various fields, but have been used by us to program non-uniformly swellable gel sheets to buckle into prescribed three dimensional shapes. In this work we apply circle packings as a kind of discrete conformal map in order to find conformal maps from the sphere to the plane that can be used as nearly uniform swelling patterns to program non-Euclidean sheets to buckle into spheres. We explore the possibility of tuning the area distortion to fit the experimental range of minimum and maximum swelling by modifying the boundary of the planar domain through the introduction of different cutting schemes.

A difference tracking algorithm based on discrete sine transform

Science.gov (United States)

Liu, HaoPeng; Yao, Yong; Lei, HeBing; Wu, HaoKun

2018-04-01

Target tracking is an important field of computer vision. The template matching tracking algorithm based on squared difference matching (SSD) and standard correlation coefficient (NCC) matching is very sensitive to the gray change of image. When the brightness or gray change, the tracking algorithm will be affected by high-frequency information. Tracking accuracy is reduced, resulting in loss of tracking target. In this paper, a differential tracking algorithm based on discrete sine transform is proposed to reduce the influence of image gray or brightness change. The algorithm that combines the discrete sine transform and the difference algorithm maps the target image into a image digital sequence. The Kalman filter predicts the target position. Using the Hamming distance determines the degree of similarity between the target and the template. The window closest to the template is determined the target to be tracked. The target to be tracked updates the template. Based on the above achieve target tracking. The algorithm is tested in this paper. Compared with SSD and NCC template matching algorithms, the algorithm tracks target stably when image gray or brightness change. And the tracking speed can meet the read-time requirement.

Multirate-based fast parallel algorithms for 2-D DHT-based real-valued discrete Gabor transform.

Science.gov (United States)

Tao, Liang; Kwan, Hon Keung

2012-07-01

Novel algorithms for the multirate and fast parallel implementation of the 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented in this paper. A 2-D multirate-based analysis convolver bank is designed for the 2-D RDGT, and a 2-D multirate-based synthesis convolver bank is designed for the 2-D inverse RDGT. The parallel channels in each of the two convolver banks have a unified structure and can apply the 2-D fast DHT algorithm to speed up their computations. The computational complexity of each parallel channel is low and is independent of the Gabor oversampling rate. All the 2-D RDGT coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process. The computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2-D discrete Gabor transforms. The results indicate that the proposed algorithms are the fastest, which make them attractive for real-time image processing.

Analytical form of the orthonormal basis of the decomposition SU(3) is contained in O(3) is contained in O(2) for some (lambda, μ) multiplets

International Nuclear Information System (INIS)

Alisauskas, S.; Raychev, P.; Roussev, R.

1981-01-01

An analytical formula for the overlap integrals in the case of the non-canonical basis of Bargmann and Moshinsky (Nucl. Phys.; 23:177 (1961)) has been obtained. These integrals are tabulated for μ = O, 1, 2, 3, 4 and lambda > μ. The overlap integrals are used for the construction (by means of the Hilbert-Schmidt procedure) of an orthonormal basis. The transformation coefficients are tabulated for μ = O, 1, 2, 3 and lambda > μ. (author)

Construction of Orthonormal Piecewise Polynomial Scaling and Wavelet Bases on Non-Equally Spaced Knots

Directory of Open Access Journals (Sweden)

Jean Pierre Astruc

2007-01-01

Full Text Available This paper investigates the mathematical framework of multiresolution analysis based on irregularly spaced knots sequence. Our presentation is based on the construction of nested nonuniform spline multiresolution spaces. From these spaces, we present the construction of orthonormal scaling and wavelet basis functions on bounded intervals. For any arbitrary degree of the spline function, we provide an explicit generalization allowing the construction of the scaling and wavelet bases on the nontraditional sequences. We show that the orthogonal decomposition is implemented using filter banks where the coefficients depend on the location of the knots on the sequence. Examples of orthonormal spline scaling and wavelet bases are provided. This approach can be used to interpolate irregularly sampled signals in an efficient way, by keeping the multiresolution approach.

Discrete Multiwavelet Critical-Sampling Transform-Based OFDM System over Rayleigh Fading Channels

Directory of Open Access Journals (Sweden)

Sameer A. Dawood

2015-01-01

Full Text Available Discrete multiwavelet critical-sampling transform (DMWCST has been proposed instead of fast Fourier transform (FFT in the realization of the orthogonal frequency division multiplexing (OFDM system. The proposed structure further reduces the level of interference and improves the bandwidth efficiency through the elimination of the cyclic prefix due to the good orthogonality and time-frequency localization properties of the multiwavelet transform. The proposed system was simulated using MATLAB to allow various parameters of the system to be varied and tested. The performance of DMWCST-based OFDM (DMWCST-OFDM was compared with that of the discrete wavelet transform-based OFDM (DWT-OFDM and the traditional FFT-based OFDM (FFT-OFDM over flat fading and frequency-selective fading channels. Results obtained indicate that the performance of the proposed DMWCST-OFDM system achieves significant improvement compared to those of DWT-OFDM and FFT-OFDM systems. DMWCST improves the performance of the OFDM system by a factor of 1.5–2.5 dB and 13–15.5 dB compared with the DWT and FFT, respectively. Therefore the proposed system offers higher data rate in wireless mobile communications.

3-D discrete shearlet transform and video processing.

Science.gov (United States)

Negi, Pooran Singh; Labate, Demetrio

2012-06-01

In this paper, we introduce a digital implementation of the 3-D shearlet transform and illustrate its application to problems of video denoising and enhancement. The shearlet representation is a multiscale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional multiscale systems in dealing with multidimensional data. While the shearlet approach shares the general philosophy of curvelets and surfacelets, it is based on a very different mathematical framework, which is derived from the theory of affine systems and uses shearing matrices rather than rotations. This allows a natural transition from the continuous setting to the digital setting and a more flexible mathematical structure. The 3-D digital shearlet transform algorithm presented in this paper consists in a cascade of a multiscale decomposition and a directional filtering stage. The filters employed in this decomposition are implemented as finite-length filters, and this ensures that the transform is local and numerically efficient. To illustrate its performance, the 3-D discrete shearlet transform is applied to problems of video denoising and enhancement, and compared against other state-of-the-art multiscale techniques, including curvelets and surfacelets.

Moment-based method for computing the two-dimensional discrete Hartley transform

Science.gov (United States)

Dong, Zhifang; Wu, Jiasong; Shu, Huazhong

2009-10-01

In this paper, we present a fast algorithm for computing the two-dimensional (2-D) discrete Hartley transform (DHT). By using kernel transform and Taylor expansion, the 2-D DHT is approximated by a linear sum of 2-D geometric moments. This enables us to use the fast algorithms developed for computing the 2-D moments to efficiently calculate the 2-D DHT. The proposed method achieves a simple computational structure and is suitable to deal with any sequence lengths.

Soliton solutions of the mixed discrete modified Korteweg-de Vries hierarchy via the inverse scattering transform

International Nuclear Information System (INIS)

Li Qi; Duan Qiuyuan; Zhang Jianbing

2012-01-01

The mixed discrete modified Korteweg-de Vries (mKdV) hierarchy and the Lax pair are derived. The hierarchy related to the Ablowitz-Ladik spectral problem is reduced to the isospectral discrete mKdV hierarchy and to the non-isospectral discrete mKdV hierarchy. N-soliton solutions of the hierarchies are obtained through inverse scattering transform.

Transformation of nonlinear discrete-time system into the extended observer form

Science.gov (United States)

Kaparin, V.; Kotta, Ü.

2018-04-01

The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input-output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.

Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States

Directory of Open Access Journals (Sweden)

D. Marcus Appleby

2014-03-01

Full Text Available Recently there has been much effort in the quantum information community to prove (or disprove the existence of symmetric informationally complete (SIC sets of quantum states in arbitrary finite dimension. This paper strengthens the urgency of this question by showing that if SIC-sets exist: (1 by a natural measure of orthonormality, they are as close to being an orthonormal basis for the space of density operators as possible; and (2 in prime dimensions, the standard construction for complete sets of mutually unbiased bases and Weyl-Heisenberg covariant SIC-sets are intimately related: The latter represent minimum uncertainty states for the former in the sense of Wootters and Sussman. Finally, we contribute to the question of existence by conjecturing a quadratic redundancy in the equations for Weyl-Heisenberg SIC-sets.

The discrete Fourier transform theory, algorithms and applications

CERN Document Server

Sundaraajan, D

2001-01-01

This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and

Time dependent and asymptotic neutron number probability distribution calculation using discrete Fourier transform

International Nuclear Information System (INIS)

Humbert, Ph.

2005-01-01

In this paper we consider the probability distribution of neutrons in a multiplying assembly. The problem is studied using a space independent one group neutron point reactor model without delayed neutrons. We recall the generating function methodology and analytical results obtained by G.I. Bell when the c 2 approximation is used and we present numerical solutions in the general case, without this approximation. The neutron source induced distribution is calculated using the single initial neutron distribution which satisfies a master (Kolmogorov backward) equation. This equation is solved using the generating function method. The generating function satisfies a differential equation and the probability distribution is derived by inversion of the generating function. Numerical results are obtained using the same methodology where the generating function is the Fourier transform of the probability distribution. Discrete Fourier transforms are used to calculate the discrete time dependent distributions and continuous Fourier transforms are used to calculate the asymptotic continuous probability distributions. Numerical applications are presented to illustrate the method. (author)

Investigation of magneto-hemodynamic flow in a semi-porous channel using orthonormal Bernstein polynomials

Science.gov (United States)

Hosseini, E.; Loghmani, G. B.; Heydari, M.; Rashidi, M. M.

2017-07-01

In this paper, the problem of the magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field is investigated numerically. Using a Berman's similarity transformation, the two-dimensional momentum conservation partial differential equations can be written as a system of nonlinear ordinary differential equations incorporating Lorentizian magneto-hydrodynamic body force terms. A new computational method based on the operational matrix of derivative of orthonormal Bernstein polynomials for solving the resulting differential systems is introduced. Moreover, by using the residual correction process, two types of error estimates are provided and reported to show the strength of the proposed method. Graphical and tabular results are presented to investigate the influence of the Hartmann number ( Ha) and the transpiration Reynolds number ( Re on velocity profiles in the channel. The results are compared with those obtained by previous works to confirm the accuracy and efficiency of the proposed scheme.

Meixner-like functions having a rational z-transform

NARCIS (Netherlands)

Brinker, den A.C.

1995-01-01

Square-summable causal functions can be expressed in a Meixner series. In principle, approximate filter synthesis is thus possible. However, Meixner filters are not realizable since the Meixner functions do not have a rational z-transform. A set of orthonormal functions is constructed with the

Experimental demonstration of an OFDM receiver based on a silicon-nanophot onic discrete Fourier transform filter

DEFF Research Database (Denmark)

Da Ros, Francesco; Nolle, Markus; Meuer, C.

2014-01-01

We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit.......We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit....

Full-frame compression of discrete wavelet and cosine transforms

Science.gov (United States)

Lo, Shih-Chung B.; Li, Huai; Krasner, Brian; Freedman, Matthew T.; Mun, Seong K.

1995-04-01

At the foreground of computerized radiology and the filmless hospital are the possibilities for easy image retrieval, efficient storage, and rapid image communication. This paper represents the authors' continuous efforts in compression research on full-frame discrete wavelet (FFDWT) and full-frame discrete cosine transforms (FFDCT) for medical image compression. Prior to the coding, it is important to evaluate the global entropy in the decomposed space. It is because of the minimum entropy, that a maximum compression efficiency can be achieved. In this study, each image was split into the top three most significant bit (MSB) and the remaining remapped least significant bit (RLSB) images. The 3MSB image was compressed by an error-free contour coding and received an average of 0.1 bit/pixel. The RLSB image was either transformed to a multi-channel wavelet or the cosine transform domain for entropy evaluation. Ten x-ray chest radiographs and ten mammograms were randomly selected from our clinical database and were used for the study. Our results indicated that the coding scheme in the FFDCT domain performed better than in FFDWT domain for high-resolution digital chest radiographs and mammograms. From this study, we found that decomposition efficiency in the DCT domain for relatively smooth images is higher than that in the DWT. However, both schemes worked just as well for low resolution digital images. We also found that the image characteristics of the `Lena' image commonly used in the compression literature are very different from those of radiological images. The compression outcome of the radiological images can not be extrapolated from the compression result based on the `Lena.'

The Pegg–Barnett phase operator and the discrete Fourier transform

International Nuclear Information System (INIS)

Perez-Leija, Armando; Szameit, Alexander; Andrade-Morales, Luis A; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

2016-01-01

In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg–Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London–Susskind–Glogower phase operator, whose natural logarithm gives rise to the Pegg–Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties. (invited comment)

An Efficient Algorithm for the Discrete Gabor Transform using full length Windows

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2007-01-01

This paper extends the efficient factorization of the Gabor frame operator developed by Strohmer in [1] to the Gabor analysis/synthesis operator. This provides a fast method for computing the discrete Gabor transform (DGT) and several algorithms associated with it. The algorithm is used...

Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor Transform

Directory of Open Access Journals (Sweden)

Rui Li

2018-01-01

Full Text Available The long-periodic/infinite discrete Gabor transform (DGT is more effective than the periodic/finite one in many applications. In this paper, a fast and effective approach is presented to efficiently compute the Gabor analysis window for arbitrary given synthesis window in DGT of long-periodic/infinite sequences, in which the new orthogonality constraint between analysis window and synthesis window in DGT for long-periodic/infinite sequences is derived and proved to be equivalent to the completeness condition of the long-periodic/infinite DGT. By using the property of delta function, the original orthogonality can be expressed as a certain number of linear equation sets in both the critical sampling case and the oversampling case, which can be fast and efficiently calculated by fast discrete Fourier transform (FFT. The computational complexity of the proposed approach is analyzed and compared with that of the existing canonical algorithms. The numerical results indicate that the proposed approach is efficient and fast for computing Gabor analysis window in both the critical sampling case and the oversampling case in comparison to existing algorithms.

Implementation of 2D Discrete Wavelet Transform by Number Theoretic Transform and 2D Overlap-Save Method

Directory of Open Access Journals (Sweden)

Lina Yang

2014-01-01

Full Text Available To reduce the computation complexity of wavelet transform, this paper presents a novel approach to be implemented. It consists of two key techniques: (1 fast number theoretic transform(FNTT In the FNTT, linear convolution is replaced by the circular one. It can speed up the computation of 2D discrete wavelet transform. (2 In two-dimensional overlap-save method directly calculating the FNTT to the whole input sequence may meet two difficulties; namely, a big modulo obstructs the effective implementation of the FNTT and a long input sequence slows the computation of the FNTT down. To fight with such deficiencies, a new technique which is referred to as 2D overlap-save method is developed. Experiments have been conducted. The fast number theoretic transform and 2D overlap-method have been used to implement the dyadic wavelet transform and applied to contour extraction in pattern recognition.

Image processing tensor transform and discrete tomography with Matlab

CERN Document Server

Grigoryan, Artyom M

2012-01-01

Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB(R) introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan. The book presents several new ideas, concepts, and methods, many of which have not been published elsewhere. New co

Discrete canonical transforms that are Hadamard matrices

International Nuclear Information System (INIS)

Healy, John J; Wolf, Kurt Bernardo

2011-01-01

The group Sp(2,R) of symplectic linear canonical transformations has an integral kernel which has quadratic and linear phases, and which is realized by the geometric paraxial optical model. The discrete counterpart of this model is a finite Hamiltonian system that acts on N-point signals through N x N matrices whose elements also have a constant absolute value, although they do not form a representation of that group. Those matrices that are also unitary are Hadamard matrices. We investigate the manifolds of these N x N matrices under the Sp(2,R) equivalence imposed by the model, and find them to be on two-sided cosets. By means of an algorithm we determine representatives that lead to collections of mutually unbiased bases.

A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals

Directory of Open Access Journals (Sweden)

Pablo Soto-Quiros

2015-01-01

Full Text Available This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT: the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.

Use of orthonormal polynomials to fit energy spectrum data for water transported through membrane

International Nuclear Information System (INIS)

Bogdanova, N.; Todorova, L.

2001-01-01

A new application of our approach with orthonormal polynomials to curve fitting is given when both variables have errors. We approximate and describe data of a new effect due to change of water energy spectrum as a result of water transport in a porous membrane

An integrable semi-discretization of the Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yingnan, E-mail: ynzhang@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Tian, Lixin, E-mail: tianlixin@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, Jiangsu (China)

2016-10-23

Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

Uniform sparse bounds for discrete quadratic phase Hilbert transforms

Science.gov (United States)

Kesler, Robert; Arias, Darío Mena

2017-09-01

For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.

Simulasi Unjuk Kerja Discrete Wavelet Transform (DWT dan Discrete Cosine Transform (DCT untuk Pengolahan Sinyal Radar di Daerah yang Ber-Noise Tinggi

Directory of Open Access Journals (Sweden)

Raisah Hayati

2014-03-01

Full Text Available Detection of low signal and determination target locations is the basis and important in the system radar. Performance of radar can enhanced with enhancement signal-to-noise ratio in the receiver. In this research, will show a algorithm in radar signal processing, that is for extract the signal target in the place of noise. Discrete Cosine Transform (DCT and Discrete Wavelet Transform (DWT is the success full mathematic function in the signal processing in the last twenty years. In this research will simulate signal with DCT and DWT, analysis his performance in radar signal processing. DWT signal processing will analysis and compare with mother wavelet Haar, Daubechies-12, Coiflet-5 and Symlet-8. DCT signal processing will analysis and compare with same of window function with use in signal restrictions. Window function have influence signal resolution in domain frequency. Window function that use in this research Rectangular, Hamming, Hanning and Dolph-Chebyshev. The result of simulation and analysis Is: mother wavelet with DWT, wavelet Daubechies-12 and Symlet-8 give the best performance and mother wavelet Haar give bad performance. Wavelet Daubechies-12 give the biggest signal to noise ratio that is 32,0603 dB. Mother wavelet Symlet-8 give 32,6589 dB. Mother wavelet Haar give 14,6692 dB. Testing window function DCT, window Dolph-Chebyshev give the best performance, with give the best separation of signal. Analysis of signal reflection that accept of radar give the result that DWT is better performance than DCT in breaking of noise.

Improved FHT Algorithms for Fast Computation of the Discrete Hartley Transform

Directory of Open Access Journals (Sweden)

M. T. Hamood

2013-05-01

Full Text Available In this paper, by using the symmetrical properties of the discrete Hartley transform (DHT, an improved radix-2 fast Hartley transform (FHT algorithm with arithmetic complexity comparable to that of the real-valued fast Fourier transform (RFFT is developed. It has a simple and regular butterfly structure and possesses the in-place computation property. Furthermore, using the same principles, the development can be extended to more efficient radix-based FHT algorithms. An example for the improved radix-4 FHT algorithm is given to show the validity of the presented method. The arithmetic complexity for the new algorithms are computed and then compared with the existing FHT algorithms. The results of these comparisons have shown that the developed algorithms reduce the number of multiplications and additions considerably.

A novel method for computation of the discrete Fourier transform over characteristic two finite field of even extension degree

OpenAIRE

Fedorenko, Sergei V.

2011-01-01

A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of constructing for a cyclic convolution over a finite field is introduced.

Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painleve equations

International Nuclear Information System (INIS)

Dzhamay, Anton

2009-01-01

We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painleve equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D Arinkin and A Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.

The parallel algorithm for the 2D discrete wavelet transform

Science.gov (United States)

Barina, David; Najman, Pavel; Kleparnik, Petr; Kula, Michal; Zemcik, Pavel

2018-04-01

The discrete wavelet transform can be found at the heart of many image-processing algorithms. Until now, the transform on general-purpose processors (CPUs) was mostly computed using a separable lifting scheme. As the lifting scheme consists of a small number of operations, it is preferred for processing using single-core CPUs. However, considering a parallel processing using multi-core processors, this scheme is inappropriate due to a large number of steps. On such architectures, the number of steps corresponds to the number of points that represent the exchange of data. Consequently, these points often form a performance bottleneck. Our approach appropriately rearranges calculations inside the transform, and thereby reduces the number of steps. In other words, we propose a new scheme that is friendly to parallel environments. When evaluating on multi-core CPUs, we consistently overcome the original lifting scheme. The evaluation was performed on 61-core Intel Xeon Phi and 8-core Intel Xeon processors.

Sparse kernel orthonormalized PLS for feature extraction in large datasets

DEFF Research Database (Denmark)

Arenas-García, Jerónimo; Petersen, Kaare Brandt; Hansen, Lars Kai

2006-01-01

In this paper we are presenting a novel multivariate analysis method for large scale problems. Our scheme is based on a novel kernel orthonormalized partial least squares (PLS) variant for feature extraction, imposing sparsity constrains in the solution to improve scalability. The algorithm...... is tested on a benchmark of UCI data sets, and on the analysis of integrated short-time music features for genre prediction. The upshot is that the method has strong expressive power even with rather few features, is clearly outperforming the ordinary kernel PLS, and therefore is an appealing method...

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

Science.gov (United States)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

Design of the Coordinate Transformation Function for Cylindrical Acoustic Cloaks with a Quantity of Discrete Layers

International Nuclear Information System (INIS)

Cai Li; Wen Ji-Hong; Yu Dian-Long; Lu Zhi-Miao; Wen Xi-Sen

2014-01-01

Acoustic cloak based on coordinate transformation is of great topical interest and has promise in potential applications such as sound transparency and insulation. The frequency response of acoustic cloaks with a quantity of discrete homogeneous layers is analyzed by the acoustic scattering theory. The effect of coordinate transformation function on the acoustic total scattering cross section is discussed to achieve low scattering with only a few layers of anisotropic metamaterials. Also, the physics of acoustic wave interaction with the interfaces between the discrete layers inside the cloak shell is discussed. These results provide a better way of designing a multilayered acoustic cloak with fewer layers. (fundamental areas of phenomenology(including applications))

Design of the Coordinate Transformation Function for Cylindrical Acoustic Cloaks with a Quantity of Discrete Layers

Science.gov (United States)

Cai, Li; Wen, Ji-Hong; Yu, Dian-Long; Lu, Zhi-Miao; Wen, Xi-Sen

2014-09-01

Acoustic cloak based on coordinate transformation is of great topical interest and has promise in potential applications such as sound transparency and insulation. The frequency response of acoustic cloaks with a quantity of discrete homogeneous layers is analyzed by the acoustic scattering theory. The effect of coordinate transformation function on the acoustic total scattering cross section is discussed to achieve low scattering with only a few layers of anisotropic metamaterials. Also, the physics of acoustic wave interaction with the interfaces between the discrete layers inside the cloak shell is discussed. These results provide a better way of designing a multilayered acoustic cloak with fewer layers.

A discrete spherical X-ray transform of orientation distribution functions using bounding cubes

DEFF Research Database (Denmark)

Kazantsev, Ivan G; Schmidt, Søren; Poulsen, Henning Friis

2009-01-01

We investigate a cubed sphere parametrization of orientation space with the aim of constructing a discrete voxelized version of the spherical x-ray transform. For tracing the propagation of a unit great circle through the partition subsets, the frustums of the cubed sphere, a fast procedure...

State transformations and Hamiltonian structures for optimal control in discrete systems

Science.gov (United States)

Sieniutycz, S.

2006-04-01

Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.

A 16X16 Discrete Cosine Transform Chip

Science.gov (United States)

Sun, M. T.; Chen, T. C.; Gottlieb, A.; Wu, L.; Liou, M. L.

1987-10-01

Among various transform coding techniques for image compression the Discrete Cosine Transform (DCT) is considered to be the most effective method and has been widely used in the laboratory as well as in the market, place. DCT is computationally intensive. For video application at 14.3 MHz sample rate, a direct implementation of a 16x16 DCT requires a throughput, rate of approximately half a billion multiplications per second. In order to reduce the cost of hardware implementation, a single chip DCT implementation is highly desirable. In this paper, the implementation of a 16x16 DCT chip using a concurrent architecture will be presented. The chip is designed for real-time processing of 14.3 MHz sampled video data. It uses row-column decomposition to implement the two-dimensional transform. Distributed arithmetic combined with hit-serial and hit-parallel structures is used to implement the required vector inner products concurrently. Several schemes are utilized to reduce the size of required memory. The resultant circuit only uses memory, shift registers, and adders. No multipliers are required. It achieves high speed performance with a very regular and efficient integrated circuit realization. The chip accepts 0-bit input and produces 14-bit DCT coefficients. 12 bits are maintained after the first one-dimensional transform. The circuit has been laid out using a 2-μm CMOS technology with a symbolic design tool MULGA. The core contains approximately 73,000 transistors in an area of 7.2 x 7.0

Design and application of discrete wavelet packet transform based multiresolution controller for liquid level system.

Science.gov (United States)

Paul, Rimi; Sengupta, Anindita

2017-11-01

A new controller based on discrete wavelet packet transform (DWPT) for liquid level system (LLS) has been presented here. This controller generates control signal using node coefficients of the error signal which interprets many implicit phenomena such as process dynamics, measurement noise and effect of external disturbances. Through simulation results on LLS problem, this controller is shown to perform faster than both the discrete wavelet transform based controller and conventional proportional integral controller. Also, it is more efficient in terms of its ability to provide better noise rejection. To overcome the wind up phenomenon by considering the saturation due to presence of actuator, anti-wind up technique is applied to the conventional PI controller and compared to the wavelet packet transform based controller. In this case also, packet controller is found better than the other ones. This similar work has been extended for analogous first order RC plant as well as second order plant also. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Discrete Hilbert transformation and its application to estimate the wind speed in Hong Kong

Energy Technology Data Exchange (ETDEWEB)

Zhu, Zuojin [Department of Thermal Science and Energy Engineering, Institute of Engineering Science, University of Science and Technology of China, Hefei, Anhui (China); Yang, Hongxing [Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong (Hong Kong)

2002-01-01

Discrete Hilbert Transform (DHT) has been applied to estimate the wind speed with the sample data sequence selected from the data record observed by the observatory in Hong Kong in June 1989, during which the data pertain to deep valleys and sharp crests due to manifold weather conditions in this region. To confirm the performance of the discrete Hilbert transformer, two harmonic input sequences were used to inspect the output signals, whether good agreement with the theoretical results is obtained. It was found that the energy spectrum and the outputs for the two different harmonic discrete waves are certainly correct. After the inspection of the DHT filter, the sample data for wind speed in Hong Kong were used for wind speed forecasting. For zero mean input sequence, the variance of the output is the same as that of the input signals, and so is the energy spectrum. The DHT of an individual input sample can really reflect the local variation performance, since it is the convolution with the reciprocal of time and the input data sequence, but there exists phase shift. For harmonic signals, the output signal holds a 90 phase delay.

Stabilizing the discrete vortex of topological charge S=2

International Nuclear Information System (INIS)

Kevrekidis, P.G.; Frantzeskakis, D.J.

2005-01-01

We study the instability of the discrete vortex with topological charge S=2 in a prototypical lattice model and observe its mediation through the central lattice site. Motivated by this finding, we analyze the model with the central site being inert. We identify analytically and observe numerically the existence of a range of linearly stable discrete vortices with S=2 in the latter model. The range of stability is comparable to that of the recently observed experimentally S=1 discrete vortex, suggesting the potential for observation of such higher charge discrete vortices

Low-power hardware implementation of movement decoding for brain computer interface with reduced-resolution discrete cosine transform.

Science.gov (United States)

Minho Won; Albalawi, Hassan; Xin Li; Thomas, Donald E

2014-01-01

This paper describes a low-power hardware implementation for movement decoding of brain computer interface. Our proposed hardware design is facilitated by two novel ideas: (i) an efficient feature extraction method based on reduced-resolution discrete cosine transform (DCT), and (ii) a new hardware architecture of dual look-up table to perform discrete cosine transform without explicit multiplication. The proposed hardware implementation has been validated for movement decoding of electrocorticography (ECoG) signal by using a Xilinx FPGA Zynq-7000 board. It achieves more than 56× energy reduction over a reference design using band-pass filters for feature extraction.

Generalized reciprocity principle for discrete symplectic systems

Directory of Open Access Journals (Sweden)

Julia Elyseeva

2015-12-01

Full Text Available This paper studies transformations for conjoined bases of symplectic difference systems $Y_{i+1}=\\mathcal S_{i}Y_{i}$ with the symplectic coefficient matrices $\\mathcal S_i.$ For an arbitrary symplectic transformation matrix $P_{i}$ we formulate most general sufficient conditions for $\\mathcal S_{i},\\, P_{i}$ which guarantee that $P_{i}$ preserves oscillatory properties of conjoined bases $Y_{i}.$ We present examples which show that our new results extend the applicability of the discrete transformation theory.

Ambiguity attacks on robust blind image watermarking scheme based on redundant discrete wavelet transform and singular value decomposition

Directory of Open Access Journals (Sweden)

Khaled Loukhaoukha

2017-12-01

Full Text Available Among emergent applications of digital watermarking are copyright protection and proof of ownership. Recently, Makbol and Khoo (2013 have proposed for these applications a new robust blind image watermarking scheme based on the redundant discrete wavelet transform (RDWT and the singular value decomposition (SVD. In this paper, we present two ambiguity attacks on this algorithm that have shown that this algorithm fails when used to provide robustness applications like owner identification, proof of ownership, and transaction tracking. Keywords: Ambiguity attack, Image watermarking, Singular value decomposition, Redundant discrete wavelet transform

Medical images storage using discrete cosine transform

International Nuclear Information System (INIS)

Arhouma, Ali M.; Ajaal, Tawfik; Marghani, Khaled

2010-01-01

The advances in technology during the last decades have made the use of digital images as one of the common things in everyday life. While the application of digital images in communicating information is very important, the cost of storing and transmitting images is much larger compared to storage and transmission of text. The main problem with all of the images was the fact that they take large size of memory space, large transmission bandwidth and long transmission time. Image data compression is needed to reduce the storage space,transmission bandwidth and transmission time. Medical image compression plays a key role as hospitals move towards filmless imaging and go completely digital. Image compression allows Picture Archiving and Communication Systems (PACS) to reduce the file size on their storage requirements while maintaining relevant diagnostic information. The reduced image file size yield reduced transmission times. Even as the capacity of storage media continues to increase, it is expected that the volume of uncompressed data produced by hospitals will exceed capacity of storage and drive up costs. This paper proposes a Discrete Cosine Transform (DCT) algorithm which can help to solve the image storage and transmission time problem in hospitals. Discrete cosine transform (DCT) has become the most popular technique for image compression over the past several years. One of the major reasons for its popularity is its selection as the standard for JPEG. DCTs are most commonly used for non-analytical applications such as image processing and digital signal-processing (DSP) applications such as video conferencing, fax systems, video disks, and high-definition television HDTV. They also can be used on a matrix of practically any dimension. The proposed (DCT) algorithm improves the performance of medical image compression while satisfying both the medical image quality, and the high compression ratio. Application of DCT coding algorithm to actual still images

Implementation in an FPGA circuit of Edge detection algorithm based on the Discrete Wavelet Transforms

Science.gov (United States)

Bouganssa, Issam; Sbihi, Mohamed; Zaim, Mounia

2017-07-01

The 2D Discrete Wavelet Transform (DWT) is a computationally intensive task that is usually implemented on specific architectures in many imaging systems in real time. In this paper, a high throughput edge or contour detection algorithm is proposed based on the discrete wavelet transform. A technique for applying the filters on the three directions (Horizontal, Vertical and Diagonal) of the image is used to present the maximum of the existing contours. The proposed architectures were designed in VHDL and mapped to a Xilinx Sparten6 FPGA. The results of the synthesis show that the proposed architecture has a low area cost and can operate up to 100 MHz, which can perform 2D wavelet analysis for a sequence of images while maintaining the flexibility of the system to support an adaptive algorithm.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

Science.gov (United States)

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

Novel structures for Discrete Hartley Transform based on first-order moments

Science.gov (United States)

Xiong, Jun; Zheng, Wenjuan; Wang, Hao; Liu, Jianguo

2018-03-01

Discrete Hartley Transform (DHT) is an important tool in digital signal processing. In the present paper, the DHT is firstly transformed into the first-order moments-based form, then a new fast algorithm is proposed to calculate the first-order moments without multiplication. Based on the algorithm theory, the corresponding hardware architecture for DHT is proposed, which only contains shift operations and additions with no need for multipliers and large memory. To verify the availability and effectiveness, the proposed design is implemented with hardware description language and synthesized by Synopsys Design Compiler with 0.18-μm SMIC library. A series of experiments have proved that the proposed architecture has better performance in terms of the product of the hardware consumption and computation time.

Feature Extraction Using Discrete Wavelet Transform for Gear Fault Diagnosis of Wind Turbine Gearbox

DEFF Research Database (Denmark)

Bajric, Rusmir; Zuber, Ninoslav; Skrimpas, Georgios Alexandros

2016-01-01

, the vibration signals are decomposed into a series of subbands signals with the use of amultiresolution analytical property of the discrete wavelet transform.Then, 22 condition indicators are extracted fromthe TSA signal, residual signal, and difference signal.Through the case study analysis, a new approach...

Algebraic manipulation of the states associated with the U(5)containsO(5)containsO(3) chain of groups: Orthonormalization and matrix elements

International Nuclear Information System (INIS)

Yannouleas, C.; Pacheco, J.M.

1989-01-01

A collection of procedures able to perform algebraic manipulations for the orthonormalization and for the calculation of matrix elements between the states associated with the U(5)containsO(5)containsO(3) chain of groups is presented. These procedures combine both the exact- and the bigfloat-arithmetic modes and thus return arbitrarily accurate results; this is particulary relevant to the Gram-Schmidt orthonormalization, where strong cancellations usually pose serious problems in all floating-point implementations. (orig.)

A novel algorithm for discrimination between inrush current and internal faults in power transformer differential protection based on discrete wavelet transform

Energy Technology Data Exchange (ETDEWEB)

Eldin, A.A. Hossam; Refaey, M.A. [Electrical Engineering Department, Alexandria University, Alexandria (Egypt)

2011-01-15

This paper proposes a novel methodology for transformer differential protection, based on wave shape recognition of the discriminating criterion extracted of the instantaneous differential currents. Discrete wavelet transform has been applied to the differential currents due to internal fault and inrush currents. The diagnosis criterion is based on median absolute deviation (MAD) of wavelet coefficients over a specified frequency band. The proposed algorithm is examined using various simulated inrush and internal fault current cases on a power transformer that has been modeled using electromagnetic transients program EMTDC software. Results of evaluation study show that, proposed wavelet based differential protection scheme can discriminate internal faults from inrush currents. (author)

Iterative normalization technique for reference sequence generation for zero-tail discrete fourier transform spread orthogonal frequency division multiplexing

DEFF Research Database (Denmark)

2017-01-01

Systems, methods, apparatuses, and computer program products for generating sequences for zero-tail discrete fourier transform (DFT)-spread-orthogonal frequency division multiplexing (OFDM) (ZT DFT-s-OFDM) reference signals. One method includes adding a zero vector to an input sequence...... of each of the elements, converting the sequence to time domain, generating a zero-padded sequence by forcing a zero head and tail of the sequence, and repeating the steps until a final sequence with zero-tail and flat frequency response is obtained....

Animation Strategies for Smooth Transformations Between Discrete Lods of 3d Building Models

Science.gov (United States)

Kada, Martin; Wichmann, Andreas; Filippovska, Yevgeniya; Hermes, Tobias

2016-06-01

The cartographic 3D visualization of urban areas has experienced tremendous progress over the last years. An increasing number of applications operate interactively in real-time and thus require advanced techniques to improve the quality and time response of dynamic scenes. The main focus of this article concentrates on the discussion of strategies for smooth transformation between two discrete levels of detail (LOD) of 3D building models that are represented as restricted triangle meshes. Because the operation order determines the geometrical and topological properties of the transformation process as well as its visual perception by a human viewer, three different strategies are proposed and subsequently analyzed. The simplest one orders transformation operations by the length of the edges to be collapsed, while the other two strategies introduce a general transformation direction in the form of a moving plane. This plane either pushes the nodes that need to be removed, e.g. during the transformation of a detailed LOD model to a coarser one, towards the main building body, or triggers the edge collapse operations used as transformation paths for the cartographic generalization.

Distributed mean curvature on a discrete manifold for Regge calculus

International Nuclear Information System (INIS)

Conboye, Rory; Miller, Warner A; Ray, Shannon

2015-01-01

The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector. (paper)

Distributed mean curvature on a discrete manifold for Regge calculus

Science.gov (United States)

Conboye, Rory; Miller, Warner A.; Ray, Shannon

2015-09-01

The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector.

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

Science.gov (United States)

Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.

1977-01-01

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.

Transformed number states from a generalized Bogoliubov transformation and their relationships to the eigenstates of the Kossakowski-Lindblad equation

International Nuclear Information System (INIS)

Tay, B A

2011-01-01

We use a generalized Bogoliubov transformation to construct a set of transformed occupation number states of the harmonic oscillator in the Liouville space. General expressions for the expansion coefficients of these states in the bare number basis are obtained and the properties of these states investigated. The transformation is non-dynamical in nature and divides the transformed basis into disconnected correlation subspaces under the transformation. The basis is complete and orthonormal. Elements of the basis are in general mixed states, and the state with the lowest number indices is the thermal vacuum. Since the Kossakowski-Lindblad (KL) equation remains form invariant under the same transformation, the transformation parameter can be identified to the thermal parameter of the master equation. The transformed states then acquire thermal property through this connection. We also work out the explicit expressions of the transformation matrices between the transformed states and the eigenstates of the KL equation for different temperatures.

Estimation of Interchannel Time Difference in Frequency Subbands Based on Nonuniform Discrete Fourier Transform

Directory of Open Access Journals (Sweden)

Qiu Bo

2008-01-01

Full Text Available Binaural cue coding (BCC is an efficient technique for spatial audio rendering by using the side information such as interchannel level difference (ICLD, interchannel time difference (ICTD, and interchannel correlation (ICC. Of the side information, the ICTD plays an important role to the auditory spatial image. However, inaccurate estimation of the ICTD may lead to the audio quality degradation. In this paper, we develop a novel ICTD estimation algorithm based on the nonuniform discrete Fourier transform (NDFT and integrate it with the BCC approach to improve the decoded auditory image. Furthermore, a new subjective assessment method is proposed for the evaluation of auditory image widths of decoded signals. The test results demonstrate that the NDFT-based scheme can achieve much wider and more externalized auditory image than the existing BCC scheme based on the discrete Fourier transform (DFT. It is found that the present technique, regardless of the image width, does not deteriorate the sound quality at the decoder compared to the traditional scheme without ICTD estimation.

ANIMATION STRATEGIES FOR SMOOTH TRANSFORMATIONS BETWEEN DISCRETE LODS OF 3D BUILDING MODELS

Directory of Open Access Journals (Sweden)

M. Kada

2016-06-01

Full Text Available The cartographic 3D visualization of urban areas has experienced tremendous progress over the last years. An increasing number of applications operate interactively in real-time and thus require advanced techniques to improve the quality and time response of dynamic scenes. The main focus of this article concentrates on the discussion of strategies for smooth transformation between two discrete levels of detail (LOD of 3D building models that are represented as restricted triangle meshes. Because the operation order determines the geometrical and topological properties of the transformation process as well as its visual perception by a human viewer, three different strategies are proposed and subsequently analyzed. The simplest one orders transformation operations by the length of the edges to be collapsed, while the other two strategies introduce a general transformation direction in the form of a moving plane. This plane either pushes the nodes that need to be removed, e.g. during the transformation of a detailed LOD model to a coarser one, towards the main building body, or triggers the edge collapse operations used as transformation paths for the cartographic generalization.

Discrete Wavelet Transform for Fault Locations in Underground Distribution System

Science.gov (United States)

Apisit, C.; Ngaopitakkul, A.

2010-10-01

In this paper, a technique for detecting faults in underground distribution system is presented. Discrete Wavelet Transform (DWT) based on traveling wave is employed in order to detect the high frequency components and to identify fault locations in the underground distribution system. The first peak time obtained from the faulty bus is employed for calculating the distance of fault from sending end. The validity of the proposed technique is tested with various fault inception angles, fault locations and faulty phases. The result is found that the proposed technique provides satisfactory result and will be very useful in the development of power systems protection scheme.

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

Science.gov (United States)

Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua

2016-07-01

On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.

Application of Discrete Fourier Transform in solving the inverse problem in gamma-ray logging

International Nuclear Information System (INIS)

Zorski, T.

1980-01-01

A new approach to the solution of inverse problem in gamma-ray logging is presented. The equation: I(z) = ∫sup(+infinite)sub(-infinite) phi (z-z')Isub(infinite)(z')dz', which relates the measured intensity I(z) with the intensity Isub(infinite)(z) not disturbed by finite thickness of an elementary layer, is solved for Isub(infinite)(z). Discrete Fourier Transform and convolution theorem are used. As a result of our solution discrete values of Isub(infinite)(z) given at a step of Δh are obtained. Examples of application of this method for Δh <= 4.5 cm and for the curves I(z) theoretically calculated are also discussed. (author)

FAST DISCRETE CURVELET TRANSFORM BASED ANISOTROPIC FEATURE EXTRACTION FOR IRIS RECOGNITION

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Amol D. Rahulkar

2010-11-01

Full Text Available The feature extraction plays a very important role in iris recognition. Recent researches on multiscale analysis provide good opportunity to extract more accurate information for iris recognition. In this work, a new directional iris texture features based on 2-D Fast Discrete Curvelet Transform (FDCT is proposed. The proposed approach divides the normalized iris image into six sub-images and the curvelet transform is applied independently on each sub-image. The anisotropic feature vector for each sub-image is derived using the directional energies of the curvelet coefficients. These six feature vectors are combined to create the resultant feature vector. During recognition, the nearest neighbor classifier based on Euclidean distance has been used for authentication. The effectiveness of the proposed approach has been tested on two different databases namely UBIRIS and MMU1. Experimental results show the superiority of the proposed approach.

A study of renal blood flow regulation using the discrete wavelet transform

Science.gov (United States)

Pavlov, Alexey N.; Pavlova, Olga N.; Mosekilde, Erik; Sosnovtseva, Olga V.

2010-02-01

In this paper we provide a way to distinguish features of renal blood flow autoregulation mechanisms in normotensive and hypertensive rats based on the discrete wavelet transform. Using the variability of the wavelet coefficients we show distinctions that occur between the normal and pathological states. A reduction of this variability in hypertension is observed on the microscopic level of the blood flow in efferent arteriole of single nephrons. This reduction is probably associated with higher flexibility of healthy cardiovascular system.

Use of the Discrete Cosine Transform for the restoration of an image sequence

International Nuclear Information System (INIS)

Acheroy, M.P.J.

1985-01-01

The Discrete Cosine Transform (DCT) is recognized as an important tool for image compression techniques. Its use in image restoration is, however, not well known. It is the aim of this paper to provide a restoration method for a sequence of images using the DCT as well for the deblurring as for the noise reduction. It is shown that the DCT can play an interesting role in the deconvolution problem for linear imaging systems with finite, invariant and symmetric impulse response. It is further shown that the noise reduction can be performed onto an image sequence using a time adaptive Kalman filter in the domain of the Karhunen-Loeve transform which is approximated by the DCT

The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

Energy Technology Data Exchange (ETDEWEB)

Kingsbury, J Ng and N G [Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ (United Kingdom)

2004-02-06

This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar

Sato's Baecklund transformations, additional symmetries and ASvM formula for the discrete KP hierarchy

International Nuclear Information System (INIS)

Liu Shaowei; Cheng Yi

2010-01-01

Two kinds of symmetries, Sato's Baecklund transformations and additional symmetries, for the discrete KP (dKP) hierarchy are introduced, and the ASvM formula which demonstrates the equivalence of these two kinds of symmetries is obtained. In this process the Fay identity and the difference Fay identity of the dKP hierarchy are introduced and the ASvM formula in the form of tau function is calculated.

Lattice functions, wavelet aliasing, and SO(3) mappings of orthonormal filters

Science.gov (United States)

John, Sarah

1998-01-01

A formulation of multiresolution in terms of a family of dyadic lattices {Sj;j∈Z} and filter matrices Mj⊂U(2)⊂GL(2,C) illuminates the role of aliasing in wavelets and provides exact relations between scaling and wavelet filters. By showing the {DN;N∈Z+} collection of compactly supported, orthonormal wavelet filters to be strictly SU(2)⊂U(2), its representation in the Euler angles of the rotation group SO(3) establishes several new results: a 1:1 mapping of the {DN} filters onto a set of orbits on the SO(3) manifold; an equivalence of D∞ to the Shannon filter; and a simple new proof for a criterion ruling out pathologically scaled nonorthonormal filters.

Wiener discrete cosine transform-based image filtering

Science.gov (United States)

Pogrebnyak, Oleksiy; Lukin, Vladimir V.

2012-10-01

A classical problem of additive white (spatially uncorrelated) Gaussian noise suppression in grayscale images is considered. The main attention is paid to discrete cosine transform (DCT)-based denoising, in particular, to image processing in blocks of a limited size. The efficiency of DCT-based image filtering with hard thresholding is studied for different sizes of overlapped blocks. A multiscale approach that aggregates the outputs of DCT filters having different overlapped block sizes is proposed. Later, a two-stage denoising procedure that presumes the use of the multiscale DCT-based filtering with hard thresholding at the first stage and a multiscale Wiener DCT-based filtering at the second stage is proposed and tested. The efficiency of the proposed multiscale DCT-based filtering is compared to the state-of-the-art block-matching and three-dimensional filter. Next, the potentially reachable multiscale filtering efficiency in terms of output mean square error (MSE) is studied. The obtained results are of the same order as those obtained by Chatterjee's approach based on nonlocal patch processing. It is shown that the ideal Wiener DCT-based filter potential is usually higher when noise variance is high.

Adaptive discrete cosine transform coding algorithm for digital mammography

Science.gov (United States)

Baskurt, Atilla M.; Magnin, Isabelle E.; Goutte, Robert

1992-09-01

The need for storage, transmission, and archiving of medical images has led researchers to develop adaptive and efficient data compression techniques. Among medical images, x-ray radiographs of the breast are especially difficult to process because of their particularly low contrast and very fine structures. A block adaptive coding algorithm based on the discrete cosine transform to compress digitized mammograms is described. A homogeneous repartition of the degradation in the decoded images is obtained using a spatially adaptive threshold. This threshold depends on the coding error associated with each block of the image. The proposed method is tested on a limited number of pathological mammograms including opacities and microcalcifications. A comparative visual analysis is performed between the original and the decoded images. Finally, it is shown that data compression with rather high compression rates (11 to 26) is possible in the mammography field.

Group-theoretical aspects of the discrete sine-Gordon equation

International Nuclear Information System (INIS)

Orfanidis, S.J.

1980-01-01

The group-theoretical interpretation of the sine-Gordon equation in terms of connection forms on fiber bundles is extended to the discrete case. Solutions of the discrete sine-Gordon equation induce surfaces on a lattice in the SU(2) group space. The inverse scattering representation, expressing the parallel transport of fibers, is implemented by means of finite rotations. Discrete Baecklund transformations are realized as gauge transformations. The three-dimensional inverse scattering representation is used to derive a discrete nonlinear sigma model, and the corresponding Baecklund transformation and Pohlmeyer's R transformation are constructed

Psychoacoustic Music Analysis Based on the Discrete Wavelet Packet Transform

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Xing He

2008-01-01

Full Text Available Psychoacoustical computational models are necessary for the perceptual processing of acoustic signals and have contributed significantly in the development of highly efficient audio analysis and coding. In this paper, we present an approach for the psychoacoustic analysis of musical signals based on the discrete wavelet packet transform. The proposed method mimics the multiresolution properties of the human ear closer than other techniques and it includes simultaneous and temporal auditory masking. Experimental results show that this method provides better masking capabilities and it reduces the signal-to-masking ratio substantially more than other approaches, without introducing audible distortion. This model can lead to greater audio compression by permitting further bit rate reduction and more secure watermarking by providing greater signal space for information hiding.

Privacy Data Decomposition and Discretization Method for SaaS Services

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Changbo Ke

2017-01-01

Full Text Available In cloud computing, user functional requirements are satisfied through service composition. However, due to the process of interaction and sharing among SaaS services, user privacy data tends to be illegally disclosed to the service participants. In this paper, we propose a privacy data decomposition and discretization method for SaaS services. First, according to logic between the data, we classify the privacy data into discrete privacy data and continuous privacy data. Next, in order to protect the user privacy information, continuous data chains are decomposed into discrete data chain, and discrete data chains are prevented from being synthesized into continuous data chains. Finally, we propose a protection framework for privacy data and demonstrate its correctness and feasibility with experiments.

International Conference eXtended Discretization MethodS

CERN Document Server

Benvenuti, Elena

2016-01-01

This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.

Cuspidal discrete series for projective hyperbolic spaces

DEFF Research Database (Denmark)

Andersen, Nils Byrial; Flensted-Jensen, Mogens

2013-01-01

Abstract. We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces G/H, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an infinite number of cuspidal discrete series......, and at most finitely many non-cuspidal discrete series, including in particular the spherical discrete series. For the projective spaces, the spherical discrete series are the only non-cuspidal discrete series. Below, we extend these results to the other hyperbolic spaces, and we also study the question...

Numerical computation of the discrete Fourier transform and its applications in the statistic processing of experimental data

International Nuclear Information System (INIS)

Marinescu, D.C.; Radulescu, T.G.

1977-06-01

The Integral Fourier Transform has a large range of applications in such areas as communication theory, circuit theory, physics, etc. In order to perform discrete Fourier Transform the Finite Fourier Transform is defined; it operates upon N samples of a uniformely sampled continuous function. All the properties known in the continuous case can be found in the discrete case also. The first part of the paper presents the relationship between the Finite Fourier Transform and the Integral one. The computing of a Finite Fourier Transform is a problem in itself since in order to transform a set of N data we have to perform N 2 ''operations'' if the transformation relations are used directly. An algorithm known as the Fast Fourier Transform (FFT) reduces this figure from N 2 to a more reasonable Nlog 2 N, when N is a power of two. The original Cooley and Tuckey algorithm for FFT can be further improved when higher basis are used. The price to be paid in this case is the increase in complexity of such algorithms. The recurrence relations and a comparation among such algorithms are presented. The key point in understanding the application of FFT resides in the convolution theorem which states that the convolution (an N 2 type procedure) of the primitive functions is equivalent to the ordinar multiplication of their transforms. Since filtering is actually a convolution process we present several procedures to perform digital filtering by means of FFT. The best is the one using the segmentation of records and the transformation of pairs of records. In the digital processing of signals, besides digital filtering a special attention is paid to the estimation of various statistical characteristics of a signal as: autocorrelation and correlation functions, periodiograms, density power sepctrum, etc. We give several algorithms for the consistent and unbiased estimation of such functions, by means of FFT. (author)

Long memory analysis by using maximal overlapping discrete wavelet transform

Science.gov (United States)

Shafie, Nur Amalina binti; Ismail, Mohd Tahir; Isa, Zaidi

2015-05-01

Long memory process is the asymptotic decay of the autocorrelation or spectral density around zero. The main objective of this paper is to do a long memory analysis by using the Maximal Overlapping Discrete Wavelet Transform (MODWT) based on wavelet variance. In doing so, stock market of Malaysia, China, Singapore, Japan and United States of America are used. The risk of long term and short term investment are also being looked into. MODWT can be analyzed with time domain and frequency domain simultaneously and decomposing wavelet variance to different scales without loss any information. All countries under studied show that they have long memory. Subprime mortgage crisis in 2007 is occurred in the United States of America are possible affect to the major trading countries. Short term investment is more risky than long term investment.

Closing Gaps in Geometrically Frustrated Symmetric Clusters: Local Equivalence between Discrete Curvature and Twist Transformations

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Fang Fang

2018-05-01

Full Text Available In geometrically frustrated clusters of polyhedra, gaps between faces can be closed without distorting the polyhedra by the long established method of discrete curvature, which consists of curving the space into a fourth dimension, resulting in a dihedral angle at the joint between polyhedra in 4D. An alternative method—the twist method—has been recently suggested for a particular case, whereby the gaps are closed by twisting the cluster in 3D, resulting in an angular offset of the faces at the joint between adjacent polyhedral. In this paper, we show the general applicability of the twist method, for local clusters, and present the surprising result that both the required angle of the twist transformation and the consequent angle at the joint are the same, respectively, as the angle of bending to 4D in the discrete curvature and its resulting dihedral angle. The twist is therefore not only isomorphic, but isogonic (in terms of the rotation angles to discrete curvature. Our results apply to local clusters, but in the discussion we offer some justification for the conjecture that the isomorphism between twist and discrete curvature can be extended globally. Furthermore, we present examples for tetrahedral clusters with three-, four-, and fivefold symmetry.

SECURE VISUAL SECRET SHARING BASED ON DISCRETE WAVELET TRANSFORM

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S. Jyothi Lekshmi

2015-08-01

Full Text Available Visual Cryptography Scheme (VCS is an encryption method to encode secret written materials. This method converts the secret written material into an image. Then encode this secret image into n shadow images called shares. For the recreation of the original secret, all or some selected subsets of shares are needed; individual shares are of no use on their own. The secret image can be recovered simply by selecting some subset of these n shares, makes transparencies of them and stacking on top of each other. Nowadays, the data security has an important role. The shares can be altered by an attacker. So providing security to the shares is important. This paper proposes a method of adding security to cryptographic shares. This method uses two dimensional discrete wavelet transform to hide visual secret shares. Then the hidden secrets are distributed among participants through the internet. All hidden shares are extracted to reconstruct the secret.

Post-processing of EPR spectrum from dosimetric substances through filtering of Discrete Fourier Transform

International Nuclear Information System (INIS)

Vieira, Fabio P.B.; Bevilacqua, Joyce S.

2014-01-01

The use of electron paramagnetic resonance spectrometers - EPR - in radiation dosimetry is known for more than four decades. It is an important tool in the retrospective determination of doses absorbed. To estimate the dose absorbed by the sample, it is necessary to know the amplitude of the peak to peak signature of the substance in its EPR spectrum. This information can be compromised by the presence of spurious information: noise - of random and low intensity nature; and the behavior of the baseline - coming from the coupling between the resonator tube and the sample analyzed. Due to the intrinsic characteristics of the three main components of the signal, i.e. signature, noise, and baseline - the analysis in the frequency domain allows, through post-processing techniques to filter spurious information. In this work, an algorithm that retrieves the signature of a substance has been implemented. The Discrete Fourier Transform is applied to the signal and without user intervention, the noise is filtered. From the filtered signal, recovers the signature by Inverse Discrete Fourier Transform. The peak to peak amplitude, and the absorbed dose is calculated with an error of less than 1% for signals wherein the base line is linearized. Some more general cases are under investigation and with little user intervention, you can get the same error

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2012-01-01

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation. (paper)

A new stationary gridline artifact suppression method based on the 2D discrete wavelet transform

International Nuclear Information System (INIS)

Tang, Hui; Tong, Dan; Dong Bao, Xu; Dillenseger, Jean-Louis

2015-01-01

Purpose: In digital x-ray radiography, an antiscatter grid is inserted between the patient and the image receptor to reduce scattered radiation. If the antiscatter grid is used in a stationary way, gridline artifacts will appear in the final image. In most of the gridline removal image processing methods, the useful information with spatial frequencies close to that of the gridline is usually lost or degraded. In this study, a new stationary gridline suppression method is designed to preserve more of the useful information. Methods: The method is as follows. The input image is first recursively decomposed into several smaller subimages using a multiscale 2D discrete wavelet transform. The decomposition process stops when the gridline signal is found to be greater than a threshold in one or several of these subimages using a gridline detection module. An automatic Gaussian band-stop filter is then applied to the detected subimages to remove the gridline signal. Finally, the restored image is achieved using the corresponding 2D inverse discrete wavelet transform. Results: The processed images show that the proposed method can remove the gridline signal efficiently while maintaining the image details. The spectra of a 1D Fourier transform of the processed images demonstrate that, compared with some existing gridline removal methods, the proposed method has better information preservation after the removal of the gridline artifacts. Additionally, the performance speed is relatively high. Conclusions: The experimental results demonstrate the efficiency of the proposed method. Compared with some existing gridline removal methods, the proposed method can preserve more information within an acceptable execution time

A new stationary gridline artifact suppression method based on the 2D discrete wavelet transform

Energy Technology Data Exchange (ETDEWEB)

Tang, Hui, E-mail: corinna@seu.edu.cn [Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University, Nanjing 210096 (China); Key Laboratory of Computer Network and Information Integration (Southeast University), Ministry of Education, Nanjing 210000 (China); Centre de Recherche en Information Biomédicale sino-français, Laboratoire International Associé, Inserm, Université de Rennes 1, Rennes 35000 (France); Southeast University, Nanjing 210000 (China); Tong, Dan; Dong Bao, Xu [Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University, Nanjing 210096 (China); Dillenseger, Jean-Louis [INSERM, U1099, Rennes F-35000 (France); Université de Rennes 1, LTSI, Rennes F-35000 (France); Centre de Recherche en Information Biomédicale sino-français, Laboratoire International Associé, Inserm, Université de Rennes 1, Rennes 35000 (France); Southeast University, Nanjing 210000 (China)

2015-04-15

Purpose: In digital x-ray radiography, an antiscatter grid is inserted between the patient and the image receptor to reduce scattered radiation. If the antiscatter grid is used in a stationary way, gridline artifacts will appear in the final image. In most of the gridline removal image processing methods, the useful information with spatial frequencies close to that of the gridline is usually lost or degraded. In this study, a new stationary gridline suppression method is designed to preserve more of the useful information. Methods: The method is as follows. The input image is first recursively decomposed into several smaller subimages using a multiscale 2D discrete wavelet transform. The decomposition process stops when the gridline signal is found to be greater than a threshold in one or several of these subimages using a gridline detection module. An automatic Gaussian band-stop filter is then applied to the detected subimages to remove the gridline signal. Finally, the restored image is achieved using the corresponding 2D inverse discrete wavelet transform. Results: The processed images show that the proposed method can remove the gridline signal efficiently while maintaining the image details. The spectra of a 1D Fourier transform of the processed images demonstrate that, compared with some existing gridline removal methods, the proposed method has better information preservation after the removal of the gridline artifacts. Additionally, the performance speed is relatively high. Conclusions: The experimental results demonstrate the efficiency of the proposed method. Compared with some existing gridline removal methods, the proposed method can preserve more information within an acceptable execution time.

Reactive scattering with row-orthonormal hyperspherical coordinates. 4. Four-dimensional-space Wigner rotation function for pentaatomic systems.

Science.gov (United States)

Kuppermann, Aron

2011-05-14

The row-orthonormal hyperspherical coordinate (ROHC) approach to calculating state-to-state reaction cross sections and bound state levels of N-atom systems requires the use of angular momentum tensors and Wigner rotation functions in a space of dimension N - 1. The properties of those tensors and functions are discussed for arbitrary N and determined for N = 5 in terms of the 6 Euler angles involved in 4-dimensional space.

On organizing principles of discrete differential geometry. Geometry of spheres

International Nuclear Information System (INIS)

Bobenko, Alexander I; Suris, Yury B

2007-01-01

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

Inverse Problem for Two-Dimensional Discrete Schr`dinger Equation

CERN Document Server

Serdyukova, S I

2000-01-01

For two-dimensional discrete Schroedinger equation the boundary-value problem in rectangle M times N with zero boundary conditions is solved. It's stated in this work, that inverse problem reduces to reconstruction of C symmetric five-diagonal matrix with given spectrum and given first k(M,N), 1<-korthonormality conditions coupled with relations determining elements of C matrix by eigenvalues and components of basic eigenvectors. We succeeded to clear the statement of the problem to the end in the process of concrete calculations. Deriving and solving the huge polynomial systems had been perfor...

BOOK REVIEW: The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

Science.gov (United States)

Ng, J.; Kingsbury, N. G.

2004-02-01

This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar

Discrete symmetries for spinor field in de Sitter space

International Nuclear Information System (INIS)

Moradi, S.; Rouhani, S.; Takook, M.V.

2005-01-01

Discrete symmetries, parity, time reversal, antipodal, and charge conjugation transformations for spinor field in de Sitter space, are presented in the ambient space notation, i.e., in a coordinate independent way. The PT and PCT transformations are also discussed in this notation. The five-current density is studied and their transformation under the discrete symmetries is discussed

Damage Detection on Sudden Stiffness Reduction Based on Discrete Wavelet Transform

Directory of Open Access Journals (Sweden)

Bo Chen

2014-01-01

Full Text Available The sudden stiffness reduction in a structure may cause the signal discontinuity in the acceleration responses close to the damage location at the damage time instant. To this end, the damage detection on sudden stiffness reduction of building structures has been actively investigated in this study. The signal discontinuity of the structural acceleration responses of an example building is extracted based on the discrete wavelet transform. It is proved that the variation of the first level detail coefficients of the wavelet transform at damage instant is linearly proportional to the magnitude of the stiffness reduction. A new damage index is proposed and implemented to detect the damage time instant, location, and severity of a structure due to a sudden change of structural stiffness. Numerical simulation using a five-story shear building under different types of excitation is carried out to assess the effectiveness and reliability of the proposed damage index for the building at different damage levels. The sensitivity of the damage index to the intensity and frequency range of measurement noise is also investigated. The made observations demonstrate that the proposed damage index can accurately identify the sudden damage events if the noise intensity is limited.

Detection of short-term anomaly using parasitic discrete wavelet transform

International Nuclear Information System (INIS)

Nagamatsu, Takashi; Gofuku, Akio

2013-01-01

A parasitic discrete wavelet transform (P-DWT) that has a large flexibility in design of the mother wavelet (MW) and a high processing speed was applied for simulation and measured anomalies. First, we applied the P-DWT to detection of the short-term anomalies. Second, we applied the P-DWT to detection of the collision of pump using the pump diagnostic experiment equipment that was designed taking into consideration the structure of the pump used for the water-steam system of the fast breeder reactor 'Monju'. The vibration signals were measured by the vibration sensor attached to the pump when injecting four types of small objects (sphere, small sphere, cube, and rectangular parallelepiped). Anomaly detection was performed by calculating the fast wavelet instantaneous correlation using the parasitic filter that was constructed on the basis of the measured signals. The results suggested that the anomalies could be detected for all types of the supposed anomalies. (author)

Feature Extraction on Brain Computer Interfaces using Discrete Dyadic Wavelet Transform: Preliminary Results

International Nuclear Information System (INIS)

Gareis, I; Gentiletti, G; Acevedo, R; Rufiner, L

2011-01-01

The purpose of this work is to evaluate different feature extraction alternatives to detect the event related evoked potential signal on brain computer interfaces, trying to minimize the time employed and the classification error, in terms of sensibility and specificity of the method, looking for alternatives to coherent averaging. In this context the results obtained performing the feature extraction using discrete dyadic wavelet transform using different mother wavelets are presented. For the classification a single layer perceptron was used. The results obtained with and without the wavelet decomposition were compared; showing an improvement on the classification rate, the specificity and the sensibility for the feature vectors obtained using some mother wavelets.

Some Notes on the Use of theWindowed Fourier Transform for Spectral Analysis of Discretely Sampled Data

Directory of Open Access Journals (Sweden)

Robert W. Johnson

2013-06-01

Full Text Available The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can satisfy numerically the energy and reconstruction theorems; however, transform pairs based on a variable window or nonuniform frequency sampling in general do not. Instead of selecting the shape of the window as some function of the central frequency, we propose constructing a single window with unit energy from an arbitrary set of windows that is applied over the entire frequency axis. By virtue of using a fixed window with uniform frequency sampling, such a transform satisfies the energy and reconstruction theorems. The shape of the window can be tailored to meet the requirements of the investigator in terms of time/frequency resolution. The algorithm extends naturally to the case of nonuniform signal sampling without modification beyond identification of the Nyquist interval.

Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

International Nuclear Information System (INIS)

Ding Qing

2007-01-01

We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model

A new Watermarking System based on Discrete Cosine Transform (DCT) in color biometric images.

Science.gov (United States)

Dogan, Sengul; Tuncer, Turker; Avci, Engin; Gulten, Arif

2012-08-01

This paper recommend a biometric color images hiding approach An Watermarking System based on Discrete Cosine Transform (DCT), which is used to protect the security and integrity of transmitted biometric color images. Watermarking is a very important hiding information (audio, video, color image, gray image) technique. It is commonly used on digital objects together with the developing technology in the last few years. One of the common methods used for hiding information on image files is DCT method which used in the frequency domain. In this study, DCT methods in order to embed watermark data into face images, without corrupting their features.

An integrable semi-discretization of the Boussinesq equation

International Nuclear Information System (INIS)

Zhang, Yingnan; Tian, Lixin

2016-01-01

Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

Warped Discrete Cosine Transform-Based Low Bit-Rate Block Coding Using Image Downsampling

Directory of Open Access Journals (Sweden)

Ertürk Sarp

2007-01-01

Full Text Available This paper presents warped discrete cosine transform (WDCT-based low bit-rate block coding using image downsampling. While WDCT aims to improve the performance of conventional DCT by frequency warping, the WDCT has only been applicable to high bit-rate coding applications because of the overhead required to define the parameters of the warping filter. Recently, low bit-rate block coding based on image downsampling prior to block coding followed by upsampling after the decoding process is proposed to improve the compression performance for low bit-rate block coders. This paper demonstrates that a superior performance can be achieved if WDCT is used in conjunction with image downsampling-based block coding for low bit-rate applications.

High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform.

Science.gov (United States)

Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A

2017-08-21

In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.

Difference Discrete Variational Principles, Euler-Lagrange Cohomology and Symplectic, Multisymplectic Structures I: Difference Discrete Variational Principle

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying,; LI Yu-Qi; WU Ke1; WANG Shi-Kun

2002-01-01

In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.

Fast Fourier and discrete wavelet transforms applied to sensorless vector control induction motor for rotor bar faults diagnosis.

Science.gov (United States)

Talhaoui, Hicham; Menacer, Arezki; Kessal, Abdelhalim; Kechida, Ridha

2014-09-01

This paper presents new techniques to evaluate faults in case of broken rotor bars of induction motors. Procedures are applied with closed-loop control. Electrical and mechanical variables are treated using fast Fourier transform (FFT), and discrete wavelet transform (DWT) at start-up and steady state. The wavelet transform has proven to be an excellent mathematical tool for the detection of the faults particularly broken rotor bars type. As a performance, DWT can provide a local representation of the non-stationary current signals for the healthy machine and with fault. For sensorless control, a Luenberger observer is applied; the estimation rotor speed is analyzed; the effect of the faults in the speed pulsation is compensated; a quadratic current appears and used for fault detection. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Discrete wavelet transform-based denoising technique for advanced state-of-charge estimator of a lithium-ion battery in electric vehicles

International Nuclear Information System (INIS)

Lee, Seongjun; Kim, Jonghoon

2015-01-01

Sophisticated data of the experimental DCV (discharging/charging voltage) of a lithium-ion battery is required for high-accuracy SOC (state-of-charge) estimation algorithms based on the state-space ECM (electrical circuit model) in BMSs (battery management systems). However, when sensing noisy DCV signals, erroneous SOC estimation (which results in low BMS performance) is inevitable. Therefore, this manuscript describes the design and implementation of a DWT (discrete wavelet transform)-based denoising technique for DCV signals. The steps for denoising a noisy DCV measurement in the proposed approach are as follows. First, using MRA (multi-resolution analysis), the noise-riding DCV signal is decomposed into different frequency sub-bands (low- and high-frequency components, A n and D n ). Specifically, signal processing of the high frequency component D n that focuses on a short-time interval is necessary to reduce noise in the DCV measurement. Second, a hard-thresholding-based denoising rule is applied to adjust the wavelet coefficients of the DWT to achieve a clear separation between the signal and the noise. Third, the desired de-noised DCV signal is reconstructed by taking the IDWT (inverse discrete wavelet transform) of the filtered detailed coefficients. Finally, this signal is sent to the ECM-based SOC estimation algorithm using an EKF (extended Kalman filter). Experimental results indicate the robustness of the proposed approach for reliable SOC estimation. - Highlights: • Sophisticated data of the experimental DCV is required for high-accuracy SOC. • DWT (discrete wavelet transform)-based denoising technique is newly investigated. • Three steps for denoising a noisy DCV measurement in this work are implemented. • Experimental results indicate the robustness of the proposed work for reliable SOC

Shift-invariant discrete wavelet transform analysis for retinal image classification.

Science.gov (United States)

Khademi, April; Krishnan, Sridhar

2007-12-01

This work involves retinal image classification and a novel analysis system was developed. From the compressed domain, the proposed scheme extracts textural features from wavelet coefficients, which describe the relative homogeneity of localized areas of the retinal images. Since the discrete wavelet transform (DWT) is shift-variant, a shift-invariant DWT was explored to ensure that a robust feature set was extracted. To combat the small database size, linear discriminant analysis classification was used with the leave one out method. 38 normal and 48 abnormal (exudates, large drusens, fine drusens, choroidal neovascularization, central vein and artery occlusion, histoplasmosis, arteriosclerotic retinopathy, hemi-central retinal vein occlusion and more) were used and a specificity of 79% and sensitivity of 85.4% were achieved (the average classification rate is 82.2%). The success of the system can be accounted to the highly robust feature set which included translation, scale and semi-rotational, features. Additionally, this technique is database independent since the features were specifically tuned to the pathologies of the human eye.

A Fast Mellin and Scale Transform

Directory of Open Access Journals (Sweden)

Davide Rocchesso

2007-01-01

Full Text Available A fast algorithm for the discrete-scale (and β-Mellin transform is proposed. It performs a discrete-time discrete-scale approximation of the continuous-time transform, with subquadratic asymptotic complexity. The algorithm is based on a well-known relation between the Mellin and Fourier transforms, and it is practical and accurate. The paper gives some theoretical background on the Mellin, β-Mellin, and scale transforms. Then the algorithm is presented and analyzed in terms of computational complexity and precision. The effects of different interpolation procedures used in the algorithm are discussed.

A Fast Mellin and Scale Transform

Directory of Open Access Journals (Sweden)

Rocchesso Davide

2007-01-01

Full Text Available A fast algorithm for the discrete-scale (and -Mellin transform is proposed. It performs a discrete-time discrete-scale approximation of the continuous-time transform, with subquadratic asymptotic complexity. The algorithm is based on a well-known relation between the Mellin and Fourier transforms, and it is practical and accurate. The paper gives some theoretical background on the Mellin, -Mellin, and scale transforms. Then the algorithm is presented and analyzed in terms of computational complexity and precision. The effects of different interpolation procedures used in the algorithm are discussed.

Discrete SLn-connections and self-adjoint difference operators on 2-dimensional manifolds

International Nuclear Information System (INIS)

Grinevich, P G; Novikov, S P

2013-01-01

The programme of discretization of famous completely integrable systems and associated linear operators was launched in the 1990s. In particular, the properties of second-order difference operators on triangulated manifolds and equilateral triangular lattices have been studied by Novikov and Dynnikov since 1996. This study included Laplace transformations, new discretizations of complex analysis, and new discretizations of GL n -connections on triangulated n-dimensional manifolds. A general theory of discrete GL n -connections 'of rank one' has been developed (see the Introduction for definitions). The problem of distinguishing the subclass of SL n -connections (and unimodular SL n ± -connections, which satisfy detA = ±1) has not been solved. In the present paper it is shown that these connections play an important role (which is similar to the role of magnetic fields in the continuous case) in the theory of self-adjoint Schrödinger difference operators on equilateral triangular lattices in ℝ 2 . In Appendix 1 a complete characterization is given of unimodular SL n ± -connections of rank 1 for all n > 1, thus correcting a mistake (it was wrongly claimed that they reduce to a canonical connection for n > 2). With the help of a communication from Korepanov, a complete clarification is provided of how the classical theory of electrical circuits and star-triangle transformations is connected with the discrete Laplace transformations on triangular lattices. Bibliography: 29 titles

High-capacity method for hiding data in the discrete cosine transform domain

Science.gov (United States)

Qazanfari, Kazem; Safabakhsh, Reza

2013-10-01

Steganography is the art and science of hiding data in different media such as texts, audios, images, and videos. Data hiding techniques are generally divided into two groups: spatial and frequency domain techniques. Spatial domain methods generally have low security and, as a result, are less attractive to researchers. Discrete cosine transform (DCT) is the most common transform domain used in steganography and JPEG compression. Since a large number of the DCT coefficients of JPEG images are zero, the capacity of DCT domain-based steganography methods is not very high. We present a high-capacity method for hiding messages in the DCT domain. We describe the method in two classes where the receiver has and where the receiver does not have the cover image. In each class, we consider three cases for each coefficient. By considering n coefficients, there are 3n different situations. The method embeds ⌊log2 3n⌋ bits in these n coefficients. We show that the maximum reachable capacity by our method is 58% higher than the other general steganography methods. Experimental results show that the histogram-based steganalysis methods cannot detect the stego images produced by the proposed method while the capacity is increased significantly.

A new time-adaptive discrete bionic wavelet transform for enhancing speech from adverse noise environment

Science.gov (United States)

Palaniswamy, Sumithra; Duraisamy, Prakash; Alam, Mohammad Showkat; Yuan, Xiaohui

2012-04-01

Automatic speech processing systems are widely used in everyday life such as mobile communication, speech and speaker recognition, and for assisting the hearing impaired. In speech communication systems, the quality and intelligibility of speech is of utmost importance for ease and accuracy of information exchange. To obtain an intelligible speech signal and one that is more pleasant to listen, noise reduction is essential. In this paper a new Time Adaptive Discrete Bionic Wavelet Thresholding (TADBWT) scheme is proposed. The proposed technique uses Daubechies mother wavelet to achieve better enhancement of speech from additive non- stationary noises which occur in real life such as street noise and factory noise. Due to the integration of human auditory system model into the wavelet transform, bionic wavelet transform (BWT) has great potential for speech enhancement which may lead to a new path in speech processing. In the proposed technique, at first, discrete BWT is applied to noisy speech to derive TADBWT coefficients. Then the adaptive nature of the BWT is captured by introducing a time varying linear factor which updates the coefficients at each scale over time. This approach has shown better performance than the existing algorithms at lower input SNR due to modified soft level dependent thresholding on time adaptive coefficients. The objective and subjective test results confirmed the competency of the TADBWT technique. The effectiveness of the proposed technique is also evaluated for speaker recognition task under noisy environment. The recognition results show that the TADWT technique yields better performance when compared to alternate methods specifically at lower input SNR.

On E-discretization of tori of compact simple Lie groups. II

Science.gov (United States)

Hrivnák, Jiří; Juránek, Michal

2017-10-01

Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

A Complete Video Coding Chain Based on Multi-Dimensional Discrete Cosine Transform

Directory of Open Access Journals (Sweden)

T. Fryza

2010-09-01

Full Text Available The paper deals with a video compression method based on the multi-dimensional discrete cosine transform. In the text, the encoder and decoder architectures including the definitions of all mathematical operations like the forward and inverse 3-D DCT, quantization and thresholding are presented. According to the particular number of currently processed pictures, the new quantization tables and entropy code dictionaries are proposed in the paper. The practical properties of the 3-D DCT coding chain compared with the modern video compression methods (such as H.264 and WebM and the computing complexity are presented as well. It will be proved the best compress properties could be achieved by complex H.264 codec. On the other hand the computing complexity - especially on the encoding side - is lower for the 3-D DCT method.

Manifestly gauge invariant discretizations of the Schrödinger equation

International Nuclear Information System (INIS)

Halvorsen, Tore Gunnar; Kvaal, Simen

2012-01-01

Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice gauge theory, and the process defined is applicable to a large class of discretized differential operators. In particular, popular discretizations such as pseudospectral discretizations using the fast Fourier transform can be transformed to gauge invariant schemes. Also generic gauge invariant versions of generic time integration methods are considered, enabling completely gauge invariant calculations of the time dependent Schrödinger equation. Numerical examples illuminating the differences between a gauge invariant discretization and conventional discretization procedures are also presented. -- Highlights: ► We investigate the Schrödinger equation coupled to an external magnetic field. ► Any grid-based discretization is made trivially gauge invariant. ► An extension of classical lattice gauge theory.

Noether symmetries of discrete mechanico–electrical systems

International Nuclear Information System (INIS)

Fu Jingli; Xie Fengping; Chen Benyong

2008-01-01

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange–Maxwell equations, the discrete analogue of Noether theorems for Lagrange–Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results. (general)

The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

International Nuclear Information System (INIS)

Kingsbury, J Ng and N G

2004-01-01

This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar

Fourier transformation for engineering and natural science

International Nuclear Information System (INIS)

Klingen, B.

2001-01-01

The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)

A multidimensionally consistent version of Hirota’s discrete KdV equation

International Nuclear Information System (INIS)

Atkinson, James

2012-01-01

A multidimensionally consistent generalization of Hirota’s discrete KdV equation is proposed, it is a quad equation defined by a polynomial that is quadratic in each variable. Soliton solutions and interpretation of the model as superposition principle are given. It is discussed how an important property of the defining polynomial, a factorization of discriminants, appears also in the few other known discrete integrable multi-quadratic models. (fast track communication)

Discrete Chebyshev nets and a universal permutability theorem

International Nuclear Information System (INIS)

Schief, W K

2007-01-01

The Pohlmeyer-Lund-Regge system which was set down independently in the contexts of Lagrangian field theories and the relativistic motion of a string and which played a key role in the development of a geometric interpretation of soliton theory is known to appear in a variety of important guises such as the vectorial Lund-Regge equation, the O(4) nonlinear σ-model and the SU(2) chiral model. Here, it is demonstrated that these avatars may be discretized in such a manner that both integrability and equivalence are preserved. The corresponding discretization procedure is geometric and algebraic in nature and based on discrete Chebyshev nets and generalized discrete Lelieuvre formulae. In connection with the derivation of associated Baecklund transformations, it is shown that a generalized discrete Lund-Regge equation may be interpreted as a universal permutability theorem for integrable equations which admit commuting matrix Darboux transformations acting on su(2) linear representations. Three-dimensional coordinate systems and lattices of 'Lund-Regge' type related to particular continuous and discrete Zakharov-Manakov systems are obtained as a by-product of this analysis

ISAR Imaging of Maneuvering Targets Based on the Modified Discrete Polynomial-Phase Transform

Directory of Open Access Journals (Sweden)

Yong Wang

2015-09-01

Full Text Available Inverse synthetic aperture radar (ISAR imaging of a maneuvering target is a challenging task in the field of radar signal processing. The azimuth echo can be characterized as a multi-component polynomial phase signal (PPS after the translational compensation, and the high quality ISAR images can be obtained by the parameters estimation of it combined with the Range-Instantaneous-Doppler (RID technique. In this paper, a novel parameters estimation algorithm of the multi-component PPS with order three (cubic phase signal-CPS based on the modified discrete polynomial-phase transform (MDPT is proposed, and the corresponding new ISAR imaging algorithm is presented consequently. This algorithm is efficient and accurate to generate a focused ISAR image, and the results of real data demonstrate the effectiveness of it.

Transforming between discrete and continuous angle distribution models: application to protein χ1 torsions

International Nuclear Information System (INIS)

Schmidt, Jürgen M.

2012-01-01

Two commonly employed angular-mobility models for describing amino-acid side-chain χ 1 torsion conformation, the staggered-rotamer jump and the normal probability density, are discussed and performance differences in applications to scalar-coupling data interpretation highlighted. Both models differ in their distinct statistical concepts, representing discrete and continuous angle distributions, respectively. Circular statistics, introduced for describing torsion-angle distributions by using a universal circular order parameter central to all models, suggest another distribution of the continuous class, here referred to as the elliptic model. Characteristic of the elliptic model is that order parameter and circular variance form complementary moduli. Transformations between the parameter sets that describe the probability density functions underlying the different models are provided. Numerical aspects of parameter optimization are considered. The issues are typified by using a set of χ 1 related 3 J coupling constants available for FK506-binding protein. The discrete staggered-rotamer model is found generally to produce lower order parameters, implying elevated rotatory variability in the amino-acid side chains, whereas continuous models tend to give higher order parameters that suggest comparatively less variation in angle conformations. The differences perceived regarding angular mobility are attributed to conceptually different features inherent to the models.

Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme

International Nuclear Information System (INIS)

Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.

2007-01-01

We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schroedinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R 3

Simulation study and experimental results for detection and classification of the transient capacitor inrush current using discrete wavelet transform and artificial intelligence

Directory of Open Access Journals (Sweden)

Patcharoen Theerasak

2018-04-01

Full Text Available This paper describes the combination of discrete wavelet transforms (DWT and artificial intelligence (AI, which are efficient techniques to identify the type of inrush current, analyze the origin and possible cause on the capacitor bank switching. The experiment setup used to verify the proposed techniques can be detected and classified the transient inrush current from normal capacitor rated current. The discrete wavelet transforms are used to detect and classify the inrush current. Then, output from wavelet is acted as input of fuzzy inference system for discriminating the type of switching transient inrush current. The proposed technique shows enhanced performance with a discrimination accuracy of 90.57%. Both simulation study and experimental results are quite satisfactory with providing the high accuracy and reliability which can be developed and implemented into a numerical overcurrent (50/51 and unbalanced current (60C protection relay for an application of shunt capacitor bank protection in the future.

Simulation study and experimental results for detection and classification of the transient capacitor inrush current using discrete wavelet transform and artificial intelligence

Science.gov (United States)

Patcharoen, Theerasak; Yoomak, Suntiti; Ngaopitakkul, Atthapol; Pothisarn, Chaichan

2018-04-01

This paper describes the combination of discrete wavelet transforms (DWT) and artificial intelligence (AI), which are efficient techniques to identify the type of inrush current, analyze the origin and possible cause on the capacitor bank switching. The experiment setup used to verify the proposed techniques can be detected and classified the transient inrush current from normal capacitor rated current. The discrete wavelet transforms are used to detect and classify the inrush current. Then, output from wavelet is acted as input of fuzzy inference system for discriminating the type of switching transient inrush current. The proposed technique shows enhanced performance with a discrimination accuracy of 90.57%. Both simulation study and experimental results are quite satisfactory with providing the high accuracy and reliability which can be developed and implemented into a numerical overcurrent (50/51) and unbalanced current (60C) protection relay for an application of shunt capacitor bank protection in the future.

Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas.

Science.gov (United States)

Yan, Xin-Zhong

2011-07-01

The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency with several orders without losing accuracy. As an example, we apply the algorithm to study the three-dimensional interacting electron gas under the renormalized-ring-diagram approximation where the Green's function needs to be self-consistently solved. We present the results for the chemical potential, compressibility, free energy, entropy, and specific heat of the system. The ground-state energy obtained by the present calculation is compared with the existing results of Monte Carlo simulation and random-phase approximation.

From the continuous PV to discrete Painleve equations

International Nuclear Information System (INIS)

Tokihiro, T.; Grammaticos, B.; Ramani, A.

2002-01-01

We study the discrete transformations that are associated with the auto-Baecklund of the (continuous) P V equation. We show that several two-parameter discrete Painleve equations can be obtained as contiguity relations of P V . Among them we find the asymmetric d-P II equation which is a well-known form of discrete P III . The relation between the ternary P I (previously obtained through the discrete dressing approach) and P V is also established. A new discrete Painleve equation is also derived. (author)

Painleve test and discrete Boltzmann equations

International Nuclear Information System (INIS)

Euler, N.; Steeb, W.H.

1989-01-01

The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs

Symmetries in discrete-time mechanics

International Nuclear Information System (INIS)

Khorrami, M.

1996-01-01

Based on a general formulation for discrete-time quantum mechanics, introduced by M. Khorrami (Annals Phys. 224 (1995), 101), symmetries in discrete-time quantum mechanics are investigated. It is shown that any classical continuous symmetry leads to a conserved quantity in classical mechanics, as well as quantum mechanics. The transformed wave function, however, has the correct evolution if and only if the symmetry is nonanomalous. Copyright copyright 1996 Academic Press, Inc

A quantum search algorithm of two entangled registers to realize quantum discrete Fourier transform of signal processing

International Nuclear Information System (INIS)

Pang Chaoyang; Hu Benqiong

2008-01-01

The discrete Fourier transform (DFT) is the base of modern signal processing. 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N 2 log N) respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT (ID QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, ID and 2D QDFT have time complexity O(√N) and O (N) respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible. (general)

Fault location in underground cables using ANFIS nets and discrete wavelet transform

Directory of Open Access Journals (Sweden)

Shimaa Barakat

2014-12-01

Full Text Available This paper presents an accurate algorithm for locating faults in a medium voltage underground power cable using a combination of Adaptive Network-Based Fuzzy Inference System (ANFIS and discrete wavelet transform (DWT. The proposed method uses five ANFIS networks and consists of 2 stages, including fault type classification and exact fault location. In the first part, an ANFIS is used to determine the fault type, applying four inputs, i.e., the maximum detailed energy of three phase and zero sequence currents. Other four ANFIS networks are utilized to pinpoint the faults (one for each fault type. Four inputs, i.e., the maximum detailed energy of three phase and zero sequence currents, are used to train the neuro-fuzzy inference systems in order to accurately locate the faults on the cable. The proposed method is evaluated under different fault conditions such as different fault locations, different fault inception angles and different fault resistances.

Digital double random amplitude image encryption method based on the symmetry property of the parametric discrete Fourier transform

Science.gov (United States)

Bekkouche, Toufik; Bouguezel, Saad

2018-03-01

We propose a real-to-real image encryption method. It is a double random amplitude encryption method based on the parametric discrete Fourier transform coupled with chaotic maps to perform the scrambling. The main idea behind this method is the introduction of a complex-to-real conversion by exploiting the inherent symmetry property of the transform in the case of real-valued sequences. This conversion allows the encrypted image to be real-valued instead of being a complex-valued image as in all existing double random phase encryption methods. The advantage is to store or transmit only one image instead of two images (real and imaginary parts). Computer simulation results and comparisons with the existing double random amplitude encryption methods are provided for peak signal-to-noise ratio, correlation coefficient, histogram analysis, and key sensitivity.

Quantum statistical properties of orthonormalized eigenstates of the operator (a-circumflex f (n-circumflex))k

International Nuclear Information System (INIS)

Wang Jisuo; Jian Feng; Liu Tangkun

2002-01-01

The completeness of the k orthonormalized eigenstates of the operator (a-circumflex f (n-circumflex)) k (k≥3) is investigated. We introduce a new kind of higher-order squeezing and an antibunching. The properties of the Mth-order squeezing and the antibunching effect of the k states are studied. The result shows that these states may form a complete Hilbert space, and the Mth-order (M=(n+1/2)k; n=0,1,...) squeezing effects exist in all of the k states when k is even. There is an antibunching effect in all of the states. An alternative method for constructing the k states is proposed, and the result shows that all of them can be generated by linear superposition of the time-dependent nonlinear coherent states at different instants. (author)

An asymptotic formula for polynomials orthonormal with respect to a varying weight. II

International Nuclear Information System (INIS)

Komlov, A V; Suetin, S P

2014-01-01

This paper gives a proof of the theorem announced by the authors in the preceding paper with the same title. The theorem states that asymptotically the behaviour of the polynomials which are orthonormal with respect to the varying weight e −2nQ(x) p g (x)/√(∏ j=1 2p (x−e j )) coincides with the asymptotic behaviour of the Nuttall psi-function, which solves a special boundary-value problem on the relevant hyperelliptic Riemann surface of genus g=p−1. Here e 1

Laplacians on discrete and quantum geometries

International Nuclear Information System (INIS)

Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

2013-01-01

We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries. (paper)

Decompositions of bubbly flow PIV velocity fields using discrete wavelets multi-resolution and multi-section image method

International Nuclear Information System (INIS)

Choi, Je-Eun; Takei, Masahiro; Doh, Deog-Hee; Jo, Hyo-Jae; Hassan, Yassin A.; Ortiz-Villafuerte, Javier

2008-01-01

Currently, wavelet transforms are widely used for the analyses of particle image velocimetry (PIV) velocity vector fields. This is because the wavelet provides not only spatial information of the velocity vectors, but also of the time and frequency domains. In this study, a discrete wavelet transform is applied to real PIV images of bubbly flows. The vector fields obtained by a self-made cross-correlation PIV algorithm were used for the discrete wavelet transform. The performances of the discrete wavelet transforms were investigated by changing the level of power of discretization. The images decomposed by wavelet multi-resolution showed conspicuous characteristics of the bubbly flows for the different levels. A high spatial bubble concentrated area could be evaluated by the constructed discrete wavelet transform algorithm, in which high-leveled wavelets play dominant roles in revealing the flow characteristics

The Discrete Wavelet Transform and Its Application for Noise Removal in Localized Corrosion Measurements

Directory of Open Access Journals (Sweden)

Rogelio Ramos

2017-01-01

Full Text Available The present work discusses the problem of induced external electrical noise as well as its removal from the electrical potential obtained from Scanning Vibrating Electrode Technique (SVET in the pitting corrosion process of aluminum alloy A96061 in 3.5% NaCl. An accessible and efficient solution of this problem is presented with the use of virtual instrumentation (VI, embedded systems, and the discrete wavelet transform (DWT. The DWT is a computational algorithm for digital processing that allows obtaining electrical noise with Signal to Noise Ratio (SNR superior to those obtained with Lock-In Amplifier equipment. The results show that DWT and the threshold method are efficient and powerful alternatives to carry out electrical measurements of potential signals from localized corrosion processes measured by SVET.

Techniques for computing the discrete Fourier transform using the quadratic residue Fermat number systems

Science.gov (United States)

Truong, T. K.; Chang, J. J.; Hsu, I. S.; Pei, D. Y.; Reed, I. S.

1986-01-01

The complex integer multiplier and adder over the direct sum of two copies of finite field developed by Cozzens and Finkelstein (1985) is specialized to the direct sum of the rings of integers modulo Fermat numbers. Such multiplication over the rings of integers modulo Fermat numbers can be performed by means of two integer multiplications, whereas the complex integer multiplication requires three integer multiplications. Such multiplications and additions can be used in the implementation of a discrete Fourier transform (DFT) of a sequence of complex numbers. The advantage of the present approach is that the number of multiplications needed to compute a systolic array of the DFT can be reduced substantially. The architectural designs using this approach are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

COMPARATIVE ANALYSIS OF APPLICATION EFFICIENCY OF ORTHOGONAL TRANSFORMATIONS IN FREQUENCY ALGORITHMS FOR DIGITAL IMAGE WATERMARKING

Directory of Open Access Journals (Sweden)

Vladimir A. Batura

2014-11-01

Full Text Available The efficiency of orthogonal transformations application in the frequency algorithms of the digital watermarking of still images is examined. Discrete Hadamard transform, discrete cosine transform and discrete Haar transform are selected. Their effectiveness is determined by the invisibility of embedded in digital image watermark and its resistance to the most common image processing operations: JPEG-compression, noising, changing of the brightness and image size, histogram equalization. The algorithm for digital watermarking and its embedding parameters remain unchanged at these orthogonal transformations. Imperceptibility of embedding is defined by the peak signal to noise ratio, watermark stability– by Pearson's correlation coefficient. Embedding is considered to be invisible, if the value of the peak signal to noise ratio is not less than 43 dB. Embedded watermark is considered to be resistant to a specific attack, if the Pearson’s correlation coefficient is not less than 0.5. Elham algorithm based on the image entropy is chosen for computing experiment. Computing experiment is carried out according to the following algorithm: embedding of a digital watermark in low-frequency area of the image (container by Elham algorithm, exposure to a harmful influence on the protected image (cover image, extraction of a digital watermark. These actions are followed by quality assessment of cover image and watermark on the basis of which efficiency of orthogonal transformation is defined. As a result of computing experiment it was determined that the choice of the specified orthogonal transformations at identical algorithm and parameters of embedding doesn't influence the degree of imperceptibility for a watermark. Efficiency of discrete Hadamard transform and discrete cosine transformation in relation to the attacks chosen for experiment was established based on the correlation indicators. Application of discrete Hadamard transform increases

Evaluation of cardiac signals using discrete wavelet transform with MATLAB graphical user interface.

Science.gov (United States)

John, Agnes Aruna; Subramanian, Aruna Priyadharshni; Jaganathan, Saravana Kumar; Sethuraman, Balasubramanian

2015-01-01

To process the electrocardiogram (ECG) signals using MATLAB-based graphical user interface (GUI) and to classify the signals based on heart rate. The subject condition was identified using R-peak detection based on discrete wavelet transform followed by a Bayes classifier that classifies the ECG signals. The GUI was designed to display the ECG signal plot. Obtained from MIT database 18 patients had normal heart rate and 9 patients had abnormal heart rate; 14.81% of the patients suffered from tachycardia and 18.52% of the patients have bradycardia. The proposed GUI display was found useful to analyze the digitized ECG signal by a non-technical user and may help in diagnostics. Further improvement can be done by employing field programmable gate array for the real time processing of cardiac signals. Copyright © 2015 Cardiological Society of India. Published by Elsevier B.V. All rights reserved.

A New Approach to Rational Discrete-Time Approximations to Continuous-Time Fractional-Order Systems

OpenAIRE

Matos , Carlos; Ortigueira , Manuel ,

2012-01-01

Part 10: Signal Processing; International audience; In this paper a new approach to rational discrete-time approximations to continuous fractional-order systems of the form 1/(sα+p) is proposed. We will show that such fractional-order LTI system can be decomposed into sub-systems. One has the classic behavior and the other is similar to a Finite Impulse Response (FIR) system. The conversion from continuous-time to discrete-time systems will be done using the Laplace transform inversion integr...

A semi-discrete integrable multi-component coherently coupled nonlinear Schrödinger system

International Nuclear Information System (INIS)

Zhao, Hai-qiong; Yuan, Jinyun

2016-01-01

A new integrable semi-discrete version is proposed for the multi-component coherently coupled nonlinear Schrödinger equation. The integrability of the semi-discrete system is confirmed by existence of Lax pair and infinite number of conservation laws. With the aid of gauge transformations, explicit formulas for N -fold Darboux transformations are derived whereby some physically important solutions of the system are presented. Furthermore, the theory of the semi-discrete system including Lax pair, Darboux transformations, exact solutions and infinite number of conservation laws are shown for their continuous counterparts in the continuous limit. (paper)

Discrimination Between Inrush and Short Circuit Currents in Differential Protection of Power Transformer Based on Correlation Method Using the Wavelet Transform

OpenAIRE

M. Rasoulpoor; M. Banejad; A. Ahmadyfard

2011-01-01

This paper presents a novel technique for transformer differential protection to prevent incorrect operation due to inrush current. The proposed method in this paper is based on time-frequency transform known as the Wavelet transform. The discrete Wavelet transform is used for analysis the differential current signals in time and frequency domains. The investigation on the energy distribution of the signal on the discrete Wavelet transform components shows the difference distribution between ...

A robust image watermarking in contourlet transform domain

Science.gov (United States)

Sharma, Rajat; Gupta, Abhishek Kumar; Singh, Deepak; Verma, Vivek Singh; Bhardwaj, Anuj

2017-10-01

A lot of work has been done in the field of image watermarking to overcome the problems of rightful ownership, copyright protection etc. In order to provide a robust solution of such issues, the authors propose a hybrid approach that involves contourlet, lifting wavelet, and discrete cosine transform. The first level coefficients of the original image which are obtained using contourlet transform are further decomposed using one level lifting wavelet transform. After that, these coefficients are modified using discrete cosine transform. Whereas, second level subband of contourlet transform coefficients are used to obtain block wise modification parameter based on edge detection and entropy calculations. Watermark bits are embedded by quantizing the discrete cosine transform coefficient blocks obtained using HL sub-band of first level lifting wavelet transform coefficients. The experimental results reveal that the proposed scheme has high robustness and imperceptibility.

Integrable discretizations of the (2+1)-dimensional sinh-Gordon equation

International Nuclear Information System (INIS)

Hu, Xing-Biao; Yu, Guo-Fu

2007-01-01

In this paper, we propose two semi-discrete equations and one fully discrete equation and study them by Hirota's bilinear method. These equations have continuum limits into a system which admits the (2+1)-dimensional generalization of the sinh-Gordon equation. As a result, two integrable semi-discrete versions and one fully discrete version for the sinh-Gordon equation are found. Baecklund transformations, nonlinear superposition formulae, determinant solution and Lax pairs for these discrete versions are presented

Intrusion Detection in NEAR System by Anti-denoising Traffic Data Series using Discrete Wavelet Transform

Directory of Open Access Journals (Sweden)

VANCEA, F.

2014-11-01

Full Text Available The paper presents two methods for detecting anomalies in data series derived from network traffic. Intrusion detection systems based on network traffic analysis are able to respond to incidents never seen before by detecting anomalies in data series extracted from the traffic. Some anomalies manifest themselves as pulses of various sizes and shapes, superimposed on series corresponding to normal traffic. In order to detect those impulses we propose two methods based on discrete wavelet transformation. Their effectiveness expressed in relative thresholds on pulse amplitude for no false negatives and no false positives is then evaluated against pulse duration and Hurst characteristic of original series. Different base functions are also evaluated for efficiency in the context of the proposed methods.

Spread spectrum image data hiding in the encrypted discrete cosine transform coefficients

Science.gov (United States)

Zhang, Xiaoqiang; Wang, Z. Jane

2013-10-01

Digital watermarking and data hiding are important tools for digital rights protection of media data. Spread spectrum (SS)-based watermarking and data-hiding approaches are popular due to their outstanding robustness, but their security might not be sufficient. To improve the security of SS, a SS-based image data-hiding approach is proposed by encrypting the discrete cosine transform coefficients of the host image with the piecewise linear chaotic map, before the operation of watermark embedding. To evaluate the performance of the proposed approach, simulations and analyses of its robustness and security are carried out. The average bit-error-rate values on 100 real images from the Berkeley segmentation dataset under the JPEG compression, additive Gaussian noise, salt and pepper noise, and cropping attacks are reported. Experimental results show that the proposed approach can maintain the high robustness of traditional SS schemes and, meanwhile, also improve the security. The proposed approach can extend the key space of traditional SS schemes from 10 to 10 and thus can resist brute-force attack and unauthorized detection watermark attack.

Designing an Algorithm for Cancerous Tissue Segmentation Using Adaptive K-means Cluttering and Discrete Wavelet Transform.

Science.gov (United States)

Rezaee, Kh; Haddadnia, J

2013-09-01

Breast cancer is currently one of the leading causes of death among women worldwide. The diagnosis and separation of cancerous tumors in mammographic images require accuracy, experience and time, and it has always posed itself as a major challenge to the radiologists and physicians. This paper proposes a new algorithm which draws on discrete wavelet transform and adaptive K-means techniques to transmute the medical images implement the tumor estimation and detect breast cancer tumors in mammograms in early stages. It also allows the rapid processing of the input data. In the first step, after designing a filter, the discrete wavelet transform is applied to the input images and the approximate coefficients of scaling components are constructed. Then, the different parts of image are classified in continuous spectrum. In the next step, by using adaptive K-means algorithm for initializing and smart choice of clusters' number, the appropriate threshold is selected. Finally, the suspicious cancerous mass is separated by implementing the image processing techniques. We Received 120 mammographic images in LJPEG format, which had been scanned in Gray-Scale with 50 microns size, 3% noise and 20% INU from clinical data taken from two medical databases (mini-MIAS and DDSM). The proposed algorithm detected tumors at an acceptable level with an average accuracy of 92.32% and sensitivity of 90.24%. Also, the Kappa coefficient was approximately 0.85, which proved the suitable reliability of the system performance. The exact positioning of the cancerous tumors allows the radiologist to determine the stage of disease progression and suggest an appropriate treatment in accordance with the tumor growth. The low PPV and high NPV of the system is a warranty of the system and both clinical specialists and patients can trust its output.

Analysis of the pathological severity degree of aortic stenosis (AS) and mitral stenosis (MS) using the discrete wavelet transform (DWT).

Science.gov (United States)

Meziani, F; Debbal, S M; Atbi, A

2013-01-01

The heart is the principal organ that circulates blood. In normal conditions it produces four sounds for each cardiac cycle. However, most often only two sounds appear essential: S1 and S2. Two other sounds: S3 and S4, with lower amplitude than S1 or S2, appear occasionally in the cardiac cycle by the effect of disease or age. The presence of abnormal sounds in one cardiac cycle provide valuable information on various diseases. The aortic stenosis (AS), as being a valvular pathology, is characterized by a systolic murmur due to a narrowing of the aortic valve. The mitral stenosis (MS) is characterized by a diastolic murmur due to a reduction in the mitral valve. Early screening of these diseases is necessary; it's done by a simple technique known as: phonocardiography. Analysis of phonocardiograms signals using signal processing techniques can provide for clinicians useful information considered as a platform for significant decisions in their medical diagnosis. In this work two types of diseases were studied: aortic stenosis (AS) and mitral stenosis (MS). Each one presents six different cases. The application of the discrete wavelet transform (DWT) to analyse pathological severity of the (AS and MS was presented. Then, the calculation of various parameters was performed for each patient. This study examines the possibility of using the DWT in the analysis of pathological severity of AS and MS.

Application of wavelet transform in seismic signal processing

International Nuclear Information System (INIS)

Ghasemi, M. R.; Mohammadzadeh, A.; Salajeghe, E.

2005-01-01

Wavelet transform is a new tool for signal analysis which can perform a simultaneous signal time and frequency representations. Under Multi Resolution Analysis, one can quickly determine details for signals and their properties using Fast Wavelet Transform algorithms. In this paper, for a better physical understanding of a signal and its basic algorithms, Multi Resolution Analysis together with wavelet transforms in a form of Digital Signal Processing will be discussed. For a Seismic Signal Processing, sets of Orthonormal Daubechies Wavelets are suggested. when dealing with the application of wavelets in SSP, one may discuss about denoising from the signal and data compression existed in the signal, which is important in seismic signal data processing. Using this techniques, EL-Centro and Nagan signals were remodeled with a 25% of total points, resulted in a satisfactory results with an acceptable error drift. Thus a total of 1559 and 2500 points for EL-centro and Nagan seismic curves each, were reduced to 389 and 625 points respectively, with a very reasonable error drift, details of which are recorded in the paper. Finally, the future progress in signal processing, based on wavelet theory will be appointed

Discrete coherent and squeezed states of many-qudit systems

International Nuclear Information System (INIS)

Klimov, Andrei B.; Munoz, Carlos; Sanchez-Soto, Luis L.

2009-01-01

We consider the phase space for n identical qudits (each one of dimension d, with d a primer number) as a grid of d n xd n points and use the finite Galois field GF(d n ) to label the corresponding axes. The associated displacement operators permit to define s-parametrized quasidistributions on this grid, with properties analogous to their continuous counterparts. These displacements allow also for the construction of finite coherent states, once a fiducial state is fixed. We take this reference as one eigenstate of the discrete Fourier transform and study the factorization properties of the resulting coherent states. We extend these ideas to include discrete squeezed states, and show their intriguing relation with entangled states of different qudits.

Characterizing a discrete-to-discrete X-ray transform for iterative image reconstruction with limited angular-range scanning in CT

DEFF Research Database (Denmark)

Sidky, Emil; Jørgensen, Jakob Heide; Pan, Xiaochuan

2012-01-01

Iterative image reconstruction in computed tomography often employs a discrete-to-discrete (DD) linear data model, and many of the aspects of the image recovery relate directly to the properties of this linear model. While much is known about the properties of the continuous X-ray, the correspond...

Use of orthonormal polynomial expansion method to the description of the energy spectra of biological liquids

International Nuclear Information System (INIS)

Bogdanova, N.B.; Todorov, S.T.; Ososkov, G.A.

2015-01-01

Orthonormal polynomial expansion method (OPEM) is applied to the data obtained by the method of energy spectra to the liquid of the biomass of wheat in the case when herbicides are used. Since the biomass of a biological object contains liquid composed mainly of water, the method of water spectra is applicable to this case as well. For comparison, the similar data obtained from control sample consisting of wheat liquid without the application of herbicides are shown. The total variance OPEM is involved including errors in both dependent and independent variables. Special criteria are used for evaluating the optimal polynomial degree and the number of iterations. The presented numerical results show good agreement with the experimental data. The developed analysis frame is of interest for future analysis in theoretical ecology.

Discrete systems and integrability

CERN Document Server

Hietarinta, J; Nijhoff, F W

2016-01-01

This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...

Application of complex discrete wavelet transform in classification of Doppler signals using complex-valued artificial neural network.

Science.gov (United States)

Ceylan, Murat; Ceylan, Rahime; Ozbay, Yüksel; Kara, Sadik

2008-09-01

In biomedical signal classification, due to the huge amount of data, to compress the biomedical waveform data is vital. This paper presents two different structures formed using feature extraction algorithms to decrease size of feature set in training and test data. The proposed structures, named as wavelet transform-complex-valued artificial neural network (WT-CVANN) and complex wavelet transform-complex-valued artificial neural network (CWT-CVANN), use real and complex discrete wavelet transform for feature extraction. The aim of using wavelet transform is to compress data and to reduce training time of network without decreasing accuracy rate. In this study, the presented structures were applied to the problem of classification in carotid arterial Doppler ultrasound signals. Carotid arterial Doppler ultrasound signals were acquired from left carotid arteries of 38 patients and 40 healthy volunteers. The patient group included 22 males and 16 females with an established diagnosis of the early phase of atherosclerosis through coronary or aortofemoropopliteal (lower extremity) angiographies (mean age, 59 years; range, 48-72 years). Healthy volunteers were young non-smokers who seem to not bear any risk of atherosclerosis, including 28 males and 12 females (mean age, 23 years; range, 19-27 years). Sensitivity, specificity and average detection rate were calculated for comparison, after training and test phases of all structures finished. These parameters have demonstrated that training times of CVANN and real-valued artificial neural network (RVANN) were reduced using feature extraction algorithms without decreasing accuracy rate in accordance to our aim.

Polyphase-discrete Fourier transform spectrum analysis for the Search for Extraterrestrial Intelligence sky survey

Science.gov (United States)

Zimmerman, G. A.; Gulkis, S.

1991-01-01

The sensitivity of a matched filter-detection system to a finite-duration continuous wave (CW) tone is compared with the sensitivities of a windowed discrete Fourier transform (DFT) system and an ideal bandpass filter-bank system. These comparisons are made in the context of the NASA Search for Extraterrestrial Intelligence (SETI) microwave observing project (MOP) sky survey. A review of the theory of polyphase-DFT filter banks and its relationship to the well-known windowed-DFT process is presented. The polyphase-DFT system approximates the ideal bandpass filter bank by using as few as eight filter taps per polyphase branch. An improvement in sensitivity of approx. 3 dB over a windowed-DFT system can be obtained by using the polyphase-DFT approach. Sidelobe rejection of the polyphase-DFT system is vastly superior to the windowed-DFT system, thereby improving its performance in the presence of radio frequency interference (RFI).

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Notes on discrete subgroups of Möbius transformations

Indian Academy of Sciences (India)

Abstract. Jørgensen's inequality gives a necessary condition for a nonelementary two generator subgroup of SL(2, C) to be discrete. By embedding SL(2, C) into. ˆU(1, 1; H), we obtain a new type of Jørgensen's inequality, which is in terms of the coefficients of involved isometries. We provide an example to show that this ...

Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz—Ladik—Lattice system

International Nuclear Information System (INIS)

Fu Jing-Li; He Yu-Fang; Hong Fang-Yu; Song Duan; Fu Hao

2013-01-01

In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz—Ladik—Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz—Ladik—Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz—Ladik—Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz—Ladik—Lattice method is verified. (general)

Spatially localized, temporally quasiperiodic, discrete nonlinear excitations

International Nuclear Information System (INIS)

Cai, D.; Bishop, A.R.; Gronbech-Jensen, N.

1995-01-01

In contrast to the commonly discussed discrete breather, which is a spatially localized, time-periodic solution, we present an exact solution of a discrete nonlinear Schroedinger breather which is a spatially localized, temporally quasiperiodic nonlinear coherent excitation. This breather is a multiple-soliton solution in the sense of the inverse scattering transform. A discrete breather of multiple frequencies is conceptually important in studies of nonlinear lattice systems. We point out that, for this breather, the incommensurability of its frequencies is a discrete lattice effect and these frequencies become commensurate in the continuum limit. To understand the dynamical properties of the breather, we also discuss its stability and its behavior in the presence of an external potential. Finally, we indicate how to obtain an exact N-soliton breather as a discrete generalization of the continuum multiple-soliton solution

Calculation Scheme Based on a Weighted Primitive: Application to Image Processing Transforms

Directory of Open Access Journals (Sweden)

Gregorio de Miguel Casado

2007-01-01

Full Text Available This paper presents a method to improve the calculation of functions which specially demand a great amount of computing resources. The method is based on the choice of a weighted primitive which enables the calculation of function values under the scope of a recursive operation. When tackling the design level, the method shows suitable for developing a processor which achieves a satisfying trade-off between time delay, area costs, and stability. The method is particularly suitable for the mathematical transforms used in signal processing applications. A generic calculation scheme is developed for the discrete fast Fourier transform (DFT and then applied to other integral transforms such as the discrete Hartley transform (DHT, the discrete cosine transform (DCT, and the discrete sine transform (DST. Some comparisons with other well-known proposals are also provided.

The geometric phase analysis method based on the local high resolution discrete Fourier transform for deformation measurement

International Nuclear Information System (INIS)

Dai, Xianglu; Xie, Huimin; Wang, Huaixi; Li, Chuanwei; Wu, Lifu; Liu, Zhanwei

2014-01-01

The geometric phase analysis (GPA) method based on the local high resolution discrete Fourier transform (LHR-DFT) for deformation measurement, defined as LHR-DFT GPA, is proposed to improve the measurement accuracy. In the general GPA method, the fundamental frequency of the image plays a crucial role. However, the fast Fourier transform, which is generally employed in the general GPA method, could make it difficult to locate the fundamental frequency accurately when the fundamental frequency is not located at an integer pixel position in the Fourier spectrum. This study focuses on this issue and presents a LHR-DFT algorithm that can locate the fundamental frequency with sub-pixel precision in a specific frequency region for the GPA method. An error analysis is offered and simulation is conducted to verify the effectiveness of the proposed method; both results show that the LHR-DFT algorithm can accurately locate the fundamental frequency and improve the measurement accuracy of the GPA method. Furthermore, typical tensile and bending tests are carried out and the experimental results verify the effectiveness of the proposed method. (paper)

Multiresolution analysis (discrete wavelet transform) through Daubechies family for emotion recognition in speech.

Science.gov (United States)

Campo, D.; Quintero, O. L.; Bastidas, M.

2016-04-01

We propose a study of the mathematical properties of voice as an audio signal. This work includes signals in which the channel conditions are not ideal for emotion recognition. Multiresolution analysis- discrete wavelet transform - was performed through the use of Daubechies Wavelet Family (Db1-Haar, Db6, Db8, Db10) allowing the decomposition of the initial audio signal into sets of coefficients on which a set of features was extracted and analyzed statistically in order to differentiate emotional states. ANNs proved to be a system that allows an appropriate classification of such states. This study shows that the extracted features using wavelet decomposition are enough to analyze and extract emotional content in audio signals presenting a high accuracy rate in classification of emotional states without the need to use other kinds of classical frequency-time features. Accordingly, this paper seeks to characterize mathematically the six basic emotions in humans: boredom, disgust, happiness, anxiety, anger and sadness, also included the neutrality, for a total of seven states to identify.

Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation

Directory of Open Access Journals (Sweden)

Hongwei Yang

2012-01-01

Full Text Available We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.

Fast numerical algorithm for the linear canonical transform.

Science.gov (United States)

Hennelly, Bryan M; Sheridan, John T

2005-05-01

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.

Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization

International Nuclear Information System (INIS)

Novitsky, Andrey; Qiu, C-W; Zouhdi, Said

2009-01-01

Based on the concept of the cloak generating function, we propose an implicit transformation-independent method for the required parameters of spherical cloaks without knowing the needed coordinate transformation beforehand. A non-ideal discrete model is used to calculate and optimize the total scattering cross-sections of different profiles of the generating function. A bell-shaped quadratic spherical cloak is found to be the best candidate, which is further optimized by controlling the design parameters involved. Such improved invisibility is steady even when the model is highly discretized.

Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

International Nuclear Information System (INIS)

Common, Alan K; Hone, Andrew N W

2008-01-01

The Yablonskii-Vorob'ev polynomials y n (t), which are defined by a second-order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painleve equation (P II ). Here we define two-variable polynomials Y n (t, h) on a lattice with spacing h, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when h = 0. They also provide rational solutions for a particular discretization of P II , namely the so-called alternate discrete P II , and this connection leads to an expression in terms of the Umemura polynomials for the third Painleve equation (P III ). It is shown that the Baecklund transformation for the alternate discrete Painleve equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete P II , which recovers Jimbo and Miwa's Lax pair for P II in the continuum limit h → 0

From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry

Energy Technology Data Exchange (ETDEWEB)

Latini, D., E-mail: latini@fis.uniroma3.it [Department of Mathematics and Physics and INFN, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy); Riglioni, D. [Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy)

2016-10-14

The coalgebraic structure of the harmonic oscillator is used to underline possible connections between continuous and discrete superintegrable models which can be described in terms of SUSY discrete quantum mechanics. A set of 1-parameter algebraic transformations is introduced in order to generate a discrete representation for the coalgebraic harmonic oscillator. This set of transformations is shown to play a role in the generalization of classical orthogonal polynomials to the realm of discrete orthogonal polynomials in the Askey scheme. As an explicit example the connection between Hermite and Charlier oscillators, that share the same coalgebraic structure, is presented and a two-dimensional maximally superintegrable version of the Charlier oscillator is constructed. - Highlights: • We construct a discrete quantum version of the harmonic oscillator. • We solve the spectral problem on the lattice. • We introduce the coalgebra symmetry in real discrete Quantum Mechanics (rdQM). • The coalgebra is used to extend the system to higher dimensions preserving its superintegrability. • We explicitly write down a discrete version of both the angular momentum and the Demkov–Fradkin Tensor.

Application of the Sumudu Transform to Discrete Dynamic Systems

Science.gov (United States)

Asiru, Muniru Aderemi

2003-01-01

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

A new discrete dipole kernel for quantitative susceptibility mapping.

Science.gov (United States)

Milovic, Carlos; Acosta-Cabronero, Julio; Pinto, José Miguel; Mattern, Hendrik; Andia, Marcelo; Uribe, Sergio; Tejos, Cristian

2018-09-01

Most approaches for quantitative susceptibility mapping (QSM) are based on a forward model approximation that employs a continuous Fourier transform operator to solve a differential equation system. Such formulation, however, is prone to high-frequency aliasing. The aim of this study was to reduce such errors using an alternative dipole kernel formulation based on the discrete Fourier transform and discrete operators. The impact of such an approach on forward model calculation and susceptibility inversion was evaluated in contrast to the continuous formulation both with synthetic phantoms and in vivo MRI data. The discrete kernel demonstrated systematically better fits to analytic field solutions, and showed less over-oscillations and aliasing artifacts while preserving low- and medium-frequency responses relative to those obtained with the continuous kernel. In the context of QSM estimation, the use of the proposed discrete kernel resulted in error reduction and increased sharpness. This proof-of-concept study demonstrated that discretizing the dipole kernel is advantageous for QSM. The impact on small or narrow structures such as the venous vasculature might by particularly relevant to high-resolution QSM applications with ultra-high field MRI - a topic for future investigations. The proposed dipole kernel has a straightforward implementation to existing QSM routines. Copyright © 2018 Elsevier Inc. All rights reserved.

Discrete variable representation for singular Hamiltonians

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2004-01-01

We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...

A new twist to fourier transforms

CERN Document Server

Meikle, Hamish D

2004-01-01

Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs

Discrete Fourier transformation processor based on complex radix (−1 + j number system

Directory of Open Access Journals (Sweden)

Anidaphi Shadap

2017-02-01

Full Text Available Complex radix (−1 + j allows the arithmetic operations of complex numbers to be done without treating the divide and conquer rules, which offers the significant speed improvement of complex numbers computation circuitry. Design and hardware implementation of complex radix (−1 + j converter has been introduced in this paper. Extensive simulation results have been incorporated and an application of this converter towards the implementation of discrete Fourier transformation (DFT processor has been presented. The functionality of the DFT processor have been verified in Xilinx ISE design suite version 14.7 and performance parameters like propagation delay and dynamic switching power consumption have been calculated by Virtuoso platform in Cadence. The proposed DFT processor has been implemented through conversion, multiplication and addition. The performance parameter matrix in terms of delay and power consumption offered a significant improvement over other traditional implementation of DFT processor.

A NEW DISCRETE HARTLEY TRANSFORM PRECODING BASED INTERLEAVED-OFDMA UPLINK SYSTEM WITH REDUCED PAPR FOR 4G CELLULAR NETWORKS

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VARUN JEOTI

2011-12-01

Full Text Available High peak-to-average power ratio (PAPR reduction is one of the major challenges in orthogonal frequency division multiple access (OFDMA systems since last decades. High PAPR increases the complexity of analogue-to-digital (A/D and digital-to-analogue (D/A convertors and also reduces the efficiency of RF high-power-amplifier (HPA. In this paper, we present a new Discrete- Hartley transform (DHT precoding based interleaved-OFDMA uplink system for PAPR reduction in the upcoming 4G cellular networks. Extensive computer simulations have been performed to analyze the PAPR of the proposed system with root-raised-cosine (RRC pulse shaping. We also compare simulation results of the proposed system with the conventional interleaved-OFDMA uplink systems and the Walsh-Hadamard transform (WHT precoding based interleaved-OFDMA uplink systems. It is concluded from the computer simulations that the proposed system has low PAPR as compared to the conventional interleaved-OFDMA uplink systems and the WHT precoded interleaved-OFDMA uplink systems.

A comparison of orthogonal transformations for digital speech processing.

Science.gov (United States)

Campanella, S. J.; Robinson, G. S.

1971-01-01

Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals. To rate their effectiveness in accomplishing this goal the quantizing error (or noise) resulting for each transformation method at various bit rates is computed and compared with that for conventional companded PCM processing. Based on this comparison, it is found that Karhunen-Loeve provides a reduction in bit rate of 13.5 kbits/s, Fourier 10 kbits/s, and Hadamard 7.5 kbits/s as compared with the bit rate required for companded PCM. These bit-rate reductions are shown to be somewhat independent of the transmission bit rate.

String constraints on discrete symmetries in MSSM type II quivers

Energy Technology Data Exchange (ETDEWEB)

Anastasopoulos, Pascal [Technische Univ. Wien (Austria). Inst. fur Theor. Phys.; Cvetic, Mirjam [Univ. of Pennsylvania, Philadelphia PA (United States). Dept. of Physics and Astronomy; Univ. of Maribor (Slovenia). Center for Applied Mathematics and Theoretical Physics; Richter, Robert [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2012-11-15

We study the presence of discrete gauge symmetries in D-brane semirealistic compactifications. After establishing the constraints on the transformation behaviour of the chiral matter for the presence of a discrete gauge symmetry we perform a systematic search for discrete gauge symmetries within semi-realistic D-brane realizations, based on four D-brane stacks, of the MSSM and the MSSM with three right-handed neutrinos. The systematic search reveals that Proton hexality, a discrete symmetry which ensures the absence of R-parity violating terms as well as the absence of dangerous dimension 5 proton decay operators, is only rarely realized. Moreover, none of the semi-realistic local D-brane configurations exhibit any family dependent discrete gauge symmetry.

Hybridization, agency discretion, and implementation of the U.S. Endangered Species Act.

Science.gov (United States)

Lind-Riehl, Jennifer F; Mayer, Audrey L; Wellstead, Adam M; Gailing, Oliver

2016-12-01

The U.S. Endangered Species Act (ESA) requires that the "best available scientific and commercial data" be used to protect imperiled species from extinction and preserve biodiversity. However, it does not provide specific guidance on how to apply this mandate. Scientific data can be uncertain and controversial, particularly regarding species delineation and hybridization issues. The U.S. Fish and Wildlife Service (FWS) had an evolving hybrid policy to guide protection decisions for individuals of hybrid origin. Currently, this policy is in limbo because it resulted in several controversial conservation decisions in the past. Biologists from FWS must interpret and apply the best available science to their recommendations and likely use considerable discretion in making recommendations for what species to list, how to define those species, and how to recover them. We used semistructured interviews to collect data on FWS biologists' use of discretion to make recommendations for listed species with hybridization issues. These biologists had a large amount of discretion to determine the best available science and how to interpret it but generally deferred to the scientific consensus on the taxonomic status of an organism. Respondents viewed hybridization primarily as a problem in the context of the ESA, although biologists who had experience with hybridization issues were more likely to describe it in more nuanced terms. Many interviewees expressed a desire to continue the current case-by-case approach for handling hybridization issues, but some wanted more guidance on procedures (i.e., a "flexible" hybrid policy). Field-level information can provide critical insight into which policies are working (or not working) and why. The FWS biologists' we interviewed had a high level of discretion, which greatly influenced ESA implementation, particularly in the context of hybridization. © 2016 Society for Conservation Biology.

The radon transform. Theory and implementation

International Nuclear Information System (INIS)

Toft, P.

1996-01-01

The subject of this Ph.D. thesis is the mathematical Radon transform, which is well suited for curve detection in digital images, and for reconstruction of tomography images. The thesis is divided into two main parts. Part I describes the Radon- and the Hough-transform and especially their discrete approximations with respect to curve parameter detection in digital images. The sampling relationships of the Radon transform is reviewed from a digital signal processing point of view. The discrete Radon transform is investigated for detection of curves, and aspects regarding the performance of the Radon transform assuming various types of noise is covered. Furthermore, a new fast scheme for estimating curve parameters is presented. Part II of the thesis describes the inverse Radon transform in 2D and 3D with focus on reconstruction of tomography images. Some of the direct reconstruction schemes are analyzed, including their discrete implementation. Furthermore, several iterative reconstruction schemes based on linear algebra are reviewed and applied for reconstruction of Positron Emission Tomography (PET) images. A new and very fast implementation of 2D iterative reconstruction methods is devised. In a more practical oriented chapter, the noise in PET images is modelled from a very large number of measurements. Several packagers for Radon- and Hough-transform based curve detection and direct/iterative 2D and 3D reconstruction have been developed and provided for free. (au) 140 refs

A parallel 3-D discrete wavelet transform architecture using pipelined lifting scheme approach for video coding

Science.gov (United States)

Hegde, Ganapathi; Vaya, Pukhraj

2013-10-01

This article presents a parallel architecture for 3-D discrete wavelet transform (3-DDWT). The proposed design is based on the 1-D pipelined lifting scheme. The architecture is fully scalable beyond the present coherent Daubechies filter bank (9, 7). This 3-DDWT architecture has advantages such as no group of pictures restriction and reduced memory referencing. It offers low power consumption, low latency and high throughput. The computing technique is based on the concept that lifting scheme minimises the storage requirement. The application specific integrated circuit implementation of the proposed architecture is done by synthesising it using 65 nm Taiwan Semiconductor Manufacturing Company standard cell library. It offers a speed of 486 MHz with a power consumption of 2.56 mW. This architecture is suitable for real-time video compression even with large frame dimensions.

Minimum K-S estimator using PH-transform technique

Directory of Open Access Journals (Sweden)

Somchit Boonthiem

2016-07-01

Full Text Available In this paper, we propose an improvement of the Minimum Kolmogorov-Smirnov (K-S estimator using proportional hazards transform (PH-transform technique. The data of experiment is 47 fire accidents data of an insurance company in Thailand. This experiment has two operations, the first operation, we minimize K-S statistic value using grid search technique for nine distributions; Rayleigh distribution, gamma distribution, Pareto distribution, log-logistic distribution, logistic distribution, normal distribution, Weibull distribution, lognormal distribution, and exponential distribution and the second operation, we improve K-S statistic using PHtransform. The result appears that PH-transform technique can improve the Minimum K-S estimator. The algorithms give better the Minimum K-S estimator for seven distributions; Rayleigh distribution, logistic distribution, gamma distribution, Pareto distribution, log-logistic distribution, normal distribution, Weibull distribution, log-normal distribution, and exponential distribution while the Minimum K-S estimators of normal distribution and logistic distribution are unchanged

The Roadmaker's algorithm for the discrete pulse transform.

Science.gov (United States)

Laurie, Dirk P

2011-02-01

The discrete pulse transform (DPT) is a decomposition of an observed signal into a sum of pulses, i.e., signals that are constant on a connected set and zero elsewhere. Originally developed for 1-D signal processing, the DPT has recently been generalized to more dimensions. Applications in image processing are currently being investigated. The time required to compute the DPT as originally defined via the successive application of LULU operators (members of a class of minimax filters studied by Rohwer) has been a severe drawback to its applicability. This paper introduces a fast method for obtaining such a decomposition, called the Roadmaker's algorithm because it involves filling pits and razing bumps. It acts selectively only on those features actually present in the signal, flattening them in order of increasing size by subtracing an appropriate positive or negative pulse, which is then appended to the decomposition. The implementation described here covers 1-D signal as well as two and 3-D image processing in a single framework. This is achieved by considering the signal or image as a function defined on a graph, with the geometry specified by the edges of the graph. Whenever a feature is flattened, nodes in the graph are merged, until eventually only one node remains. At that stage, a new set of edges for the same nodes as the graph, forming a tree structure, defines the obtained decomposition. The Roadmaker's algorithm is shown to be equivalent to the DPT in the sense of obtaining the same decomposition. However, its simpler operators are not in general equivalent to the LULU operators in situations where those operators are not applied successively. A by-product of the Roadmaker's algorithm is that it yields a proof of the so-called Highlight Conjecture, stated as an open problem in 2006. We pay particular attention to algorithmic details and complexity, including a demonstration that in the 1-D case, and also in the case of a complete graph, the Roadmaker

Design of fractional order differentiator using type-III and type-IV discrete cosine transform

Directory of Open Access Journals (Sweden)

Manjeet Kumar

2017-02-01

Full Text Available In this paper, an interpolation method based on discrete cosine transform (DCT is employed for digital finite impulse response-fractional order differentiator (FIR-FOD design. Here, a fractional order digital differentiator is modeled as finite impulse response (FIR system to get an optimized frequency response that approximates the ideal response of a fractional order differentiator. Next, DCT-III and DCT-IV are utilized to determine the filter coefficients of FIR filter that compute the Fractional derivative of a given signal. To improve the frequency response of the proposed FIR-FOD, the filter coefficients are further modified using windows. Several design examples are presented to demonstrate the superiority of the proposed method. The simulation results have also been compared with the existing FIR-FOD design methods such as DFT interpolation, radial basis function (RBF interpolation, DCT-II interpolation and DST interpolation methods. The result reveals that the proposed FIR-FOD design technique using DCT-III and DCT-IV outperforms DFT interpolation, RBF interpolation, DCT-II interpolation and DST interpolation methods in terms of magnitude error.

A high-throughput two channel discrete wavelet transform architecture for the JPEG2000 standard

Science.gov (United States)

Badakhshannoory, Hossein; Hashemi, Mahmoud R.; Aminlou, Alireza; Fatemi, Omid

2005-07-01

The Discrete Wavelet Transform (DWT) is increasingly recognized in image and video compression standards, as indicated by its use in JPEG2000. The lifting scheme algorithm is an alternative DWT implementation that has a lower computational complexity and reduced resource requirement. In the JPEG2000 standard two lifting scheme based filter banks are introduced: the 5/3 and 9/7. In this paper a high throughput, two channel DWT architecture for both of the JPEG2000 DWT filters is presented. The proposed pipelined architecture has two separate input channels that process the incoming samples simultaneously with minimum memory requirement for each channel. The architecture had been implemented in VHDL and synthesized on a Xilinx Virtex2 XCV1000. The proposed architecture applies DWT on a 2K by 1K image at 33 fps with a 75 MHZ clock frequency. This performance is achieved with 70% less resources than two independent single channel modules. The high throughput and reduced resource requirement has made this architecture the proper choice for real time applications such as Digital Cinema.

Discrete Fourier Transform-Based Multivariate Image Analysis: Application to Modeling of Aromatase Inhibitory Activity.

Science.gov (United States)

Barigye, Stephen J; Freitas, Matheus P; Ausina, Priscila; Zancan, Patricia; Sola-Penna, Mauro; Castillo-Garit, Juan A

2018-02-12

We recently generalized the formerly alignment-dependent multivariate image analysis applied to quantitative structure-activity relationships (MIA-QSAR) method through the application of the discrete Fourier transform (DFT), allowing for its application to noncongruent and structurally diverse chemical compound data sets. Here we report the first practical application of this method in the screening of molecular entities of therapeutic interest, with human aromatase inhibitory activity as the case study. We developed an ensemble classification model based on the two-dimensional (2D) DFT MIA-QSAR descriptors, with which we screened the NCI Diversity Set V (1593 compounds) and obtained 34 chemical compounds with possible aromatase inhibitory activity. These compounds were docked into the aromatase active site, and the 10 most promising compounds were selected for in vitro experimental validation. Of these compounds, 7419 (nonsteroidal) and 89 201 (steroidal) demonstrated satisfactory antiproliferative and aromatase inhibitory activities. The obtained results suggest that the 2D-DFT MIA-QSAR method may be useful in ligand-based virtual screening of new molecular entities of therapeutic utility.

Discrete density of states

Energy Technology Data Exchange (ETDEWEB)

Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr

2016-03-22

By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

Methods for performing fast discrete curvelet transforms of data

Science.gov (United States)

Candes, Emmanuel; Donoho, David; Demanet, Laurent

2010-11-23

Fast digital implementations of the second generation curvelet transform for use in data processing are disclosed. One such digital transformation is based on unequally-spaced fast Fourier transforms (USFFT) while another is based on the wrapping of specially selected Fourier samples. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. Both implementations are fast in the sense that they run in about O(n.sup.2 log n) flops for n by n Cartesian arrays or about O(N log N) flops for Cartesian arrays of size N=n.sup.3; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity.

Properties of wavelet discretization of Black-Scholes equation

Science.gov (United States)

Finěk, Václav

2017-07-01

Using wavelet methods, the continuous problem is transformed into a well-conditioned discrete problem. And once a non-symmetric problem is given, squaring yields a symmetric positive definite formulation. However squaring usually makes the condition number of discrete problems substantially worse. This note is concerned with a wavelet based numerical solution of the Black-Scholes equation for pricing European options. We show here that in wavelet coordinates a symmetric part of the discretized equation dominates over an unsymmetric part in the standard economic environment with low interest rates. It provides some justification for using a fractional step method with implicit treatment of the symmetric part of the weak form of the Black-Scholes operator and with explicit treatment of its unsymmetric part. Then a well-conditioned discrete problem is obtained.

a pyramid algorithm for the haar discrete wavelet packet transform

African Journals Online (AJOL)

PROF EKWUEME

computer-aided signal processing of non-stationary signals, this paper develops a pyramid algorithm for the discrete wavelet packet ... Edith T. Luhanga, School of Computational and Communication Sciences and Engineering, Nelson Mandela African. Institute of ..... Mathematics, Washington University. 134. EDITH T.

Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System

Directory of Open Access Journals (Sweden)

Jie Ran

2015-01-01

Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.

A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue

International Nuclear Information System (INIS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-01-01

In the present paper, we propose a two-component generalization of the reduced Ostrovsky (Vakhnenko) equation, whose differential form can be viewed as the short-wave limit of a two-component Degasperis–Procesi (DP) equation. They are integrable due to the existence of Lax pairs. Moreover, we have shown that the two-component reduced Ostrovsky equation can be reduced from an extended BKP hierarchy with negative flow through a pseudo 3-reduction and a hodograph (reciprocal) transform. As a by-product, its bilinear form and N -soliton solution in terms of pfaffians are presented. One- and two-soliton solutions are provided and analyzed. In the second part of the paper, we start with a modified BKP hierarchy, which is a Bäcklund transformation of the above extended BKP hierarchy, an integrable semi-discrete analogue of the two-component reduced Ostrovsky equation is constructed by defining an appropriate discrete hodograph transform and dependent variable transformations. In particular, the backward difference form of above semi-discrete two-component reduced Ostrovsky equation gives rise to the integrable semi-discretization of the short wave limit of a two-component DP equation. Their N -soliton solutions in terms of pffafians are also provided. (paper)

Representations of classical groups on the lattice and its application to the field theory on discrete space-time

OpenAIRE

Lorente, M.

2003-01-01

We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of any dimension invariant and apply these transformations to field equations.

DOMINO, Coupling of Discrete Ordinate Program DOT with Monte-Carlo Program MORSE

International Nuclear Information System (INIS)

1974-01-01

1 - Nature of physical problem solved: DOMINO is a general purpose code for coupling discrete ordinates and Monte Carlo radiation transport calculations. 2 - Method of solution: DOMINO transforms the angular flux as a function of energy group, mesh interval and discrete angle into current and subsequently into normalized probability distributions. 3 - Restrictions on the complexity of the problem: The discrete ordinates calculation is limited to an r-z geometry

An optical Fourier transform coprocessor with direct phase determination.

Science.gov (United States)

Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

2017-10-20

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

Fourier transforms principles and applications

CERN Document Server

Hansen, Eric W

2014-01-01

Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods.  Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.

Foundations of a discrete physics

International Nuclear Information System (INIS)

McGoveran, D.; Noyes, P.

1988-01-01

Starting from the principles of finiteness, discreteness, finite computability and absolute nonuniqueness, we develop the ordering operator calculus, a strictly constructive mathematical system having the empirical properties required by quantum mechanical and special relativistic phenomena. We show how to construct discrete distance functions, and both rectangular and spherical coordinate systems(with a discrete version of ''π''). The richest discrete space constructible without a preferred axis and preserving translational and rotational invariance is shown to be a discrete 3-space with the usual symmetries. We introduce a local ordering parameter with local (proper) time-like properties and universal ordering parameters with global (cosmological) time-like properties. Constructed ''attribute velocities'' connect ensembles with attributes that are invariant as the appropriate time-like parameter increases. For each such attribute, we show how to construct attribute velocities which must satisfy the '' relativistic Doppler shift'' and the ''relativistic velocity composition law,'' as well as the Lorentz transformations. By construction, these velocities have finite maximum and minimum values. In the space of all attributes, the minimum of these maximum velocities will predominate in all multiple attribute computations, and hence can be identified as a fundamental limiting velocity, General commutation relations are constructed which under the physical interpretation are shown to reduce to the usual quantum mechanical commutation relations. 50 refs., 18 figs

Discretization and Numerical Solution of a Plane Problem in the Mechanics of Interfacial Cracks

Science.gov (United States)

Khoroshun, L. P.

2017-01-01

The Fourier transform is used to reduce the linear plane problem of the tension of a body with an interfacial crack to a system of dual equations for the transformed stresses and, then, to a system of integro-differential equations for the difference of displacements of the crack faces. After discretization, this latter system transforms into a system of algebraic equations for displacements of the crack faces. The effect of the bielastic constant and the number of discretization points on the half-length of the crack faces and the distribution of stresses at the interface is studied

Analysis on Behaviour of Wavelet Coefficient during Fault Occurrence in Transformer

Science.gov (United States)

Sreewirote, Bancha; Ngaopitakkul, Atthapol

2018-03-01

The protection system for transformer has play significant role in avoiding severe damage to equipment when disturbance occur and ensure overall system reliability. One of the methodology that widely used in protection scheme and algorithm is discrete wavelet transform. However, characteristic of coefficient under fault condition must be analyzed to ensure its effectiveness. So, this paper proposed study and analysis on wavelet coefficient characteristic when fault occur in transformer in both high- and low-frequency component from discrete wavelet transform. The effect of internal and external fault on wavelet coefficient of both fault and normal phase has been taken into consideration. The fault signal has been simulate using transmission connected to transformer experimental setup on laboratory level that modelled after actual system. The result in term of wavelet coefficient shown a clearly differentiate between wavelet characteristic in both high and low frequency component that can be used to further design and improve detection and classification algorithm that based on discrete wavelet transform methodology in the future.

The continous Legendre transform, its inverse transform, and applications

Directory of Open Access Journals (Sweden)

P. L. Butzer

1980-01-01

Full Text Available This paper is concerned with the continuous Legendre transform, derived from the classical discrete Legendre transform by replacing the Legendre polynomial Pk(x by the function Pλ(x with λ real. Another approach to T.M. MacRobert's inversion formula is found; for this purpose an inverse Legendre transform, mapping L1(ℝ+ into L2(−1,1, is defined. Its inversion in turn is naturally achieved by the continuous Legendre transform. One application is devoted to the Shannon sampling theorem in the Legendre frame together with a new type of error estimate. The other deals with a new representation of Legendre functions giving information about their behaviour near the point x=−1.

Wavelet transforms as solutions of partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Zweig, G.

1997-10-01

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Wavelet transforms are useful in representing transients whose time and frequency structure reflect the dynamics of an underlying physical system. Speech sound, pressure in turbulent fluid flow, or engine sound in automobiles are excellent candidates for wavelet analysis. This project focused on (1) methods for choosing the parent wavelet for a continuous wavelet transform in pattern recognition applications and (2) the more efficient computation of continuous wavelet transforms by understanding the relationship between discrete wavelet transforms and discretized continuous wavelet transforms. The most interesting result of this research is the finding that the generalized wave equation, on which the continuous wavelet transform is based, can be used to understand phenomena that relate to the process of hearing.

Damage detection of simply supported reinforced concrete beam by S transform

Science.gov (United States)

Liu, Ning; Xi, Jiaxin; Zhang, Xuebing; Liu, Zhenzhou

2017-08-01

Signal processing is the key component of vibration-based structural damage detection. The S transform is variable window of short time Fourier transform (STFT) or an extension of wavelet transform (WT). The goal of using S transform is to extract subtle changes in the vibration signals in order to detect and quantify the damage in the structure. This paper presents the concentrated load is applied to the simply supported reinforced concrete beam and adopting the stepwise loading method, the vibration signals of each loading and unloading state is obtained by using the hammer impact. Then the vibration data of the reinforced concrete beam pre-damage and post-damage is analysed by S transform. Experimental result shows the potential ability of S transform in identifying peak energy changes and multiple reflections with different loading force state.

Large quantum Fourier transforms are never exactly realized by braiding conformal blocks

International Nuclear Information System (INIS)

Freedman, Michael H.; Wang, Zhenghan

2007-01-01

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {U(2), controlled-NOT}, the discrete Fourier transforms F N =(ω ij ) NxN , i,j=0,1,...,N-1, ω=e 2πi at ∼sol∼ at N , can be realized exactly by quantum circuits of size O(n 2 ), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F N and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks

Complete orthonormal sets on the past light cone - II: Functions belonging to spin 1/2 and non-zero rest mass

International Nuclear Information System (INIS)

Derrick, G.H.

1987-12-01

This is the second of a series of papers preparing the mathematical framework for a past light cone formulation for the quantum mechanics of particles of arbitrary mass and spin. The aim of past light cone quantum theory is to define quantum states solely in terms of data accessible to an observer, i.e. information from within his current past light cone. In order to set up such a theory one needs to define on the past light cone complete orthonormal sets of functions which belong to the appropriate representation of the Poincare group. Such functions are interpreted as energy-momentum eigenfunctions. The present paper treats the case of spin 1/2 and non-zero rest mass. (author). 7 refs

Using the generalized Radon transform for detection of curves in noisy images

DEFF Research Database (Denmark)

Toft, Peter Aundal

1996-01-01

In this paper the discrete generalized Radon transform will be investigated as a tool for detection of curves in noisy digital images. The discrete generalized Radon transform maps an image into a parameter domain, where curves following a specific parameterized curve form will correspond to a peak...

Detection of ULF geomagnetic signals associated with seismic events in Central Mexico using Discrete Wavelet Transform

Directory of Open Access Journals (Sweden)

O. Chavez

2010-12-01

Full Text Available The geomagnetic observatory of Juriquilla Mexico, located at longitude –100.45° and latitude 20.70°, and 1946 m a.s.l., has been operational since June 2004 compiling geomagnetic field measurements with a three component fluxgate magnetometer. In this paper, the results of the analysis of these measurements in relation to important seismic activity in the period of 2007 to 2009 are presented. For this purpose, we used superposed epochs of Discrete Wavelet Transform of filtered signals for the three components of the geomagnetic field during relative seismic calm, and it was compared with seismic events of magnitudes greater than M_s > 5.5, which have occurred in Mexico. The analysed epochs consisted of 18 h of observations for a dataset corresponding to 18 different earthquakes (EQs. The time series were processed for a period of 9 h prior to and 9 h after each seismic event. This data processing was compared with the same number of observations during a seismic calm. The proposed methodology proved to be an efficient tool to detect signals associated with seismic activity, especially when the seismic events occur in a distance (D from the observatory to the EQ, such that the ratio D/ρ < 1.8 where ρ is the earthquake radius preparation zone. The methodology presented herein shows important anomalies in the Ultra Low Frequency Range (ULF; 0.005–1 Hz, primarily for 0.25 to 0.5 Hz. Furthermore, the time variance (σ² increases prior to, during and after the seismic event in relation to the coefficient D1 obtained, principally in the Bx (N-S and By (E-W geomagnetic components. Therefore, this paper proposes and develops a new methodology to extract the abnormal signals of the geomagnetic anomalies related to different stages of the EQs.

Combining soft decision algorithms and scale-sequential hypotheses pruning for object recognition

Energy Technology Data Exchange (ETDEWEB)

Kumar, V.P.; Manolakos, E.S. [Northeastern Univ., Boston, MA (United States)

1996-12-31

This paper describes a system that exploits the synergy of Hierarchical Mixture Density (HMD) estimation with multiresolution decomposition based hypothesis pruning to perform efficiently joint segmentation and labeling of partially occluded objects in images. First we present the overall structure of the HMD estimation algorithm in the form of a recurrent neural network which generates the posterior probabilities of the various hypotheses associated with the image. Then in order to reduce the large memory and computation requirement we propose a hypothesis pruning scheme making use of the orthonormal discrete wavelet transform for dimensionality reduction. We provide an intuitive justification for the validity of this scheme and present experimental results and performance analysis on real and synthetic images to verify our claims.

Infrared and visible image fusion using discrete cosine transform and swarm intelligence for surveillance applications

Science.gov (United States)

Paramanandham, Nirmala; Rajendiran, Kishore

2018-01-01

A novel image fusion technique is presented for integrating infrared and visible images. Integration of images from the same or various sensing modalities can deliver the required information that cannot be delivered by viewing the sensor outputs individually and consecutively. In this paper, a swarm intelligence based image fusion technique using discrete cosine transform (DCT) domain is proposed for surveillance application which integrates the infrared image with the visible image for generating a single informative fused image. Particle swarm optimization (PSO) is used in the fusion process for obtaining the optimized weighting factor. These optimized weighting factors are used for fusing the DCT coefficients of visible and infrared images. Inverse DCT is applied for obtaining the initial fused image. An enhanced fused image is obtained through adaptive histogram equalization for a better visual understanding and target detection. The proposed framework is evaluated using quantitative metrics such as standard deviation, spatial frequency, entropy and mean gradient. The experimental results demonstrate the outperformance of the proposed algorithm over many other state- of- the- art techniques reported in literature.

The transformation techniques in path integration

International Nuclear Information System (INIS)

Inomata, A.

1989-01-01

In this paper general remarks are made concerning the time transformation techniques in path integration and their implementations. Time transformations may be divided into two classes: global (integrable) time transformations and local (nonintegrable) time transformations. Although a brief account of global time transformations is given, attention is focused on local transformations. First, time transformations in the classical Kepler problem are reviewed. Then, problems encountered in implementing a local time transformation in quantum mechanics are analyzed. A several propositions pertinent to the implementation of local time transformations, particularly basic to the local time rescaling trick in a discretized path integral, are presented

Discrete gauge symmetries in discrete MSSM-like orientifolds

International Nuclear Information System (INIS)

Ibáñez, L.E.; Schellekens, A.N.; Uranga, A.M.

2012-01-01

Motivated by the necessity of discrete Z N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z 2 (R-parity) and Z 3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.

Wavelet packet transform-based robust video watermarking technique

Indian Academy of Sciences (India)

If any conflict happens to the copyright identification and authentication, ... the present work is concentrated on the robust digital video watermarking. .... the wavelet decomposition, resulting in a new family of orthonormal bases for function ...

The S-Transform on Hardy Spaces and Its Duals

Directory of Open Access Journals (Sweden)

Sunil Kumar Singh

2015-03-01

Full Text Available In this paper, continuity and boundedness results for the continuous S-transform in BMO and Hardy spaces are obtained. Furthermore, the continuous S-transform is also studied on the weighted BMO$_k$ and weighted Hardy spaces associated with a tempered weight function which was proposed by L. H\\"ormander in the study of the theory of partial differential equations.

Comparative analysis of chosen transforms in the context of de-noising harmonic signals

Directory of Open Access Journals (Sweden)

Artur Zacniewski

2015-09-01

Full Text Available In the article, comparison of popular transforms used i.a. in denoising harmonical signals was presented. The division of signals submitted to mathematical analysis was shown and chosen transforms such as Short Time Fourier Transform, Wigner-Ville Distribution, Wavelet Transform and Discrete Cosine Transform were presented. Harmonic signal with white noise added was submitted for research. During research, the parameters of noise were changed to analyze the effects of using particular transform on noised signal. The importance of right choice for transform and its parameters (different for particular kind of transform was shown. Small changes in parameters or different functions used in transform can lead to considerably different results.[b]Keywords[/b]: denoising of harmonical signals, wavelet transform, discrete cosine transform, DCT

Secure Hashing of Dynamic Hand Signatures Using Wavelet-Fourier Compression with BioPhasor Mixing and Discretization

Directory of Open Access Journals (Sweden)

Wai Kuan Yip

2007-01-01

Full Text Available We introduce a novel method for secure computation of biometric hash on dynamic hand signatures using BioPhasor mixing and discretization. The use of BioPhasor as the mixing process provides a one-way transformation that precludes exact recovery of the biometric vector from compromised hashes and stolen tokens. In addition, our user-specific discretization acts both as an error correction step as well as a real-to-binary space converter. We also propose a new method of extracting compressed representation of dynamic hand signatures using discrete wavelet transform (DWT and discrete fourier transform (DFT. Without the conventional use of dynamic time warping, the proposed method avoids storage of user's hand signature template. This is an important consideration for protecting the privacy of the biometric owner. Our results show that the proposed method could produce stable and distinguishable bit strings with equal error rates (EERs of and for random and skilled forgeries for stolen token (worst case scenario, and for both forgeries in the genuine token (optimal scenario.

Discrete Routh reduction

International Nuclear Information System (INIS)

Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew

2006-01-01

This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure

Darboux–Bäcklund transformations, dressing & impurities in multi-component NLS

Energy Technology Data Exchange (ETDEWEB)

Adamopoulou, Panagiota, E-mail: p.adamopoulou@hw.ac.uk [Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Doikou, Anastasia, E-mail: a.doikou@hw.ac.uk [Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Papamikos, Georgios, E-mail: g.papamikos@reading.ac.uk [Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX (United Kingdom)

2017-05-15

We consider the discrete and continuous vector non-linear Schrödinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in turn yields the time part of a typical Darboux–Bäcklund transformation. Within this spirit we then explicitly work out the generic Bäcklund transformation and the dressing associated to both discrete and continuous spectrum, i.e. the Darboux transformation is expressed in the matrix and integral representation respectively.

Darboux–Bäcklund transformations, dressing & impurities in multi-component NLS

International Nuclear Information System (INIS)

Adamopoulou, Panagiota; Doikou, Anastasia; Papamikos, Georgios

2017-01-01

We consider the discrete and continuous vector non-linear Schrödinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in turn yields the time part of a typical Darboux–Bäcklund transformation. Within this spirit we then explicitly work out the generic Bäcklund transformation and the dressing associated to both discrete and continuous spectrum, i.e. the Darboux transformation is expressed in the matrix and integral representation respectively.

OBS Data Denoising Based on Compressed Sensing Using Fast Discrete Curvelet Transform

Science.gov (United States)

Nan, F.; Xu, Y.

2017-12-01

OBS (Ocean Bottom Seismometer) data denoising is an important step of OBS data processing and inversion. It is necessary to get clearer seismic phases for further velocity structure analysis. Traditional methods for OBS data denoising include band-pass filter, Wiener filter and deconvolution etc. (Liu, 2015). Most of these filtering methods are based on Fourier Transform (FT). Recently, the multi-scale transform methods such as wavelet transform (WT) and Curvelet transform (CvT) are widely used for data denoising in various applications. The FT, WT and CvT could represent signal sparsely and separate noise in transform domain. They could be used in different cases. Compared with Curvelet transform, the FT has Gibbs phenomenon and it cannot handle points discontinuities well. WT is well localized and multi scale, but it has poor orientation selectivity and could not handle curves discontinuities well. CvT is a multiscale directional transform that could represent curves with only a small number of coefficients. It provide an optimal sparse representation of objects with singularities along smooth curves, which is suitable for seismic data processing. As we know, different seismic phases in OBS data are showed as discontinuous curves in time domain. Hence, we promote to analysis the OBS data via CvT and separate the noise in CvT domain. In this paper, our sparsity-promoting inversion approach is restrained by L1 condition and we solve this L1 problem by using modified iteration thresholding. Results show that the proposed method could suppress the noise well and give sparse results in Curvelet domain. Figure 1 compares the Curvelet denoising method with Wavelet method on the same iterations and threshold through synthetic example. a)Original data. b) Add-noise data. c) Denoised data using CvT. d) Denoised data using WT. The CvT can well eliminate the noise and has better result than WT. Further we applied the CvT denoise method for the OBS data processing. Figure 2a

Image Enhancement In HSI Space Using Wavelet Transform

Science.gov (United States)

Bansal, Sonia; Malhotra, Deepti

2010-11-01

Image processing modifies images to improve them (enhancement, restoration), extract information (analysis, recognition), and change their structure (composition, image editing). Image Enhancement is simple and most appealing area among all the digital image processing techniques. The main purpose of image enhancement is to bring out detail that is hidden in an image or to increase contrast in a low contrast image [1]. The color restoration functions of some real color image enhancement algorithms are greatly at random and not proved , and the real color images enhanced which are based on illumination-reflectance model have the loss of details and the `halos', we proposed a new algorithm to overcome these disadvantages. Firstly, we transform the real color image from RGB space to HSI space which is approximately orthonormal system. Secondly, the illumination and the reflectance of value are separated by homomorphic filtering based on illumination-reflectance model. We have discovered that the high dynamic range of image including high bright lights is mainly caused by the reflectance. Thirdly, the details of reflectance are preserved by wavelet transform. Fourthly, the dynamic range of reflectance is compressed by Butterworth filtering. Lastly, the energy of the saturation of real color image in HSI space is attenuated according to the spectral sensitivity of most human vision.

Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

Science.gov (United States)

Yu, Fajun

2015-03-01

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

An efficient and secure partial image encryption for wireless multimedia sensor networks using discrete wavelet transform, chaotic maps and substitution box

Science.gov (United States)

Khan, Muazzam A.; Ahmad, Jawad; Javaid, Qaisar; Saqib, Nazar A.

2017-03-01

Wireless Sensor Networks (WSN) is widely deployed in monitoring of some physical activity and/or environmental conditions. Data gathered from WSN is transmitted via network to a central location for further processing. Numerous applications of WSN can be found in smart homes, intelligent buildings, health care, energy efficient smart grids and industrial control systems. In recent years, computer scientists has focused towards findings more applications of WSN in multimedia technologies, i.e. audio, video and digital images. Due to bulky nature of multimedia data, WSN process a large volume of multimedia data which significantly increases computational complexity and hence reduces battery time. With respect to battery life constraints, image compression in addition with secure transmission over a wide ranged sensor network is an emerging and challenging task in Wireless Multimedia Sensor Networks. Due to the open nature of the Internet, transmission of data must be secure through a process known as encryption. As a result, there is an intensive demand for such schemes that is energy efficient as well as highly secure since decades. In this paper, discrete wavelet-based partial image encryption scheme using hashing algorithm, chaotic maps and Hussain's S-Box is reported. The plaintext image is compressed via discrete wavelet transform and then the image is shuffled column-wise and row wise-wise via Piece-wise Linear Chaotic Map (PWLCM) and Nonlinear Chaotic Algorithm, respectively. To get higher security, initial conditions for PWLCM are made dependent on hash function. The permuted image is bitwise XORed with random matrix generated from Intertwining Logistic map. To enhance the security further, final ciphertext is obtained after substituting all elements with Hussain's substitution box. Experimental and statistical results confirm the strength of the anticipated scheme.

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

Higuchi’s Method applied to detection of changes in timbre of digital sound synthesis of string instruments with the functional transformation method

Science.gov (United States)

Kanjanapen, Manorth; Kunsombat, Cherdsak; Chiangga, Surasak

2017-09-01

The functional transformation method (FTM) is a powerful tool for detailed investigation of digital sound synthesis by the physical modeling method, the resulting sound or measured vibrational characteristics at discretized points on real instruments directly solves the underlying physical effect of partial differential equation (PDE). In this paper, we present the Higuchi’s method to examine the difference between the timbre of tone and estimate fractal dimension of musical signals which contains information about their geometrical structure that synthesizes by FTM. With the Higuchi’s method we obtain the whole process is not complicated, fast processing, with the ease of analysis without expertise in the physics or virtuoso musicians and the easiest way for the common people can judge that sounds similarly presented.

Family of columns isospectral to gravity-loaded columns with tip force: A discrete approach

Science.gov (United States)

Ramachandran, Nirmal; Ganguli, Ranjan

2018-06-01

A discrete model is introduced to analyze transverse vibration of straight, clamped-free (CF) columns of variable cross-sectional geometry under the influence of gravity and a constant axial force at the tip. The discrete model is used to determine critical combinations of loading parameters - a gravity parameter and a tip force parameter - that cause onset of dynamic instability in the CF column. A methodology, based on matrix-factorization, is described to transform the discrete model into a family of models corresponding to weightless and unloaded clamped-free (WUCF) columns, each with a transverse vibration spectrum isospectral to the original model. Characteristics of models in this isospectral family are dependent on three transformation parameters. A procedure is discussed to convert the isospectral discrete model description into geometric description of realistic columns i.e. from the discrete model, we construct isospectral WUCF columns with rectangular cross-sections varying in width and depth. As part of numerical studies to demonstrate efficacy of techniques presented, frequency parameters of a uniform column and three types of tapered CF columns under different combinations of loading parameters are obtained from the discrete model. Critical combinations of these parameters for a typical tapered column are derived. These results match with published results. Example CF columns, under arbitrarily-chosen combinations of loading parameters are considered and for each combination, isospectral WUCF columns are constructed. Role of transformation parameters in determining characteristics of isospectral columns is discussed and optimum values are deduced. Natural frequencies of these WUCF columns computed using Finite Element Method (FEM) match well with those of the given gravity-loaded CF column with tip force, hence confirming isospectrality.

Recursive Pyramid Algorithm-Based Discrete Wavelet Transform for Reactive Power Measurement in Smart Meters

Directory of Open Access Journals (Sweden)

Mahin K. Atiq

2013-09-01

Full Text Available Measurement of the active, reactive, and apparent power is one of the most fundamental tasks of smart meters in energy systems. Recently, a number of studies have employed the discrete wavelet transform (DWT for power measurement in smart meters. The most common way to implement DWT is the pyramid algorithm; however, this is not feasible for practical DWT computation because it requires either a log N cascaded filter or O (N word size memory storage for an input signal of the N-point. Both solutions are too expensive for practical applications of smart meters. It is proposed that the recursive pyramid algorithm is more suitable for smart meter implementation because it requires only word size storage of L × Log (N-L, where L is the length of filter. We also investigated the effect of varying different system parameters, such as the sampling rate, dc offset, phase offset, linearity error in current and voltage sensors, analog to digital converter resolution, and number of harmonics in a non-sinusoidal system, on the reactive energy measurement using DWT. The error analysis is depicted in the form of the absolute difference between the measured and the true value of the reactive energy.

A Framework of Secured Embedding Scheme Using Vector Discrete Wavelet Transformation and Lagrange Interpolation

Directory of Open Access Journals (Sweden)

Maheswari Subramanian

2018-01-01

Full Text Available Information hiding techniques have a significant role in recent application areas. Steganography is the embedding of information within an innocent cover work in a way which cannot be detected by any person without accessing the steganographic key. The proposed work uses a steganographic scheme for useful information with the help of human skin tone regions as cover image. The proposed algorithm has undergone Lagrange interpolation encryption for enhancement of the security of the hidden information. First, the skin tone regions are identified by using YCbCr color space which can be used as a cover image. Image pixels which belong to the skin regions are used to carry more secret bits, and the secret information is hidden in both horizontal and vertical sequences of the skin areas of the cover image. The secret information will hide behind the human skin regions rather than other objects in the same image because the skin pixels have high intensity value. The performance of embedding is done and is quite invisible by the vector discrete wavelet transformation (VDWT technique. A new Lagrange interpolation-based encryption method is introduced to achieve high security of the hidden information with higher payload and better visual quality.

Generalized differential transform method to differential-difference equation

International Nuclear Information System (INIS)

Zou Li; Wang Zhen; Zong Zhi

2009-01-01

In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Pade technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation.

Convergence of discrete Aubry–Mather model in the continuous limit

Science.gov (United States)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

Science.gov (United States)

Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier

2018-01-01

The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.

Discrete mKdV and discrete sine-Gordon flows on discrete space curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2014-01-01

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

Science.gov (United States)

Rao, T. R. Ramesh

2018-04-01

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

Implementation of the 2-D Wavelet Transform into FPGA for Image

Science.gov (United States)

León, M.; Barba, L.; Vargas, L.; Torres, C. O.

2011-01-01

This paper presents a hardware system implementation of the of discrete wavelet transform algoritm in two dimensions for FPGA, using the Daubechies filter family of order 2 (db2). The decomposition algorithm of this transform is designed and simulated with the Hardware Description Language VHDL and is implemented in a programmable logic device (FPGA) XC3S1200E reference, Spartan IIIE family, by Xilinx, take advantage the parallels properties of these gives us and speeds processing that can reach them. The architecture is evaluated using images input of different sizes. This implementation is done with the aim of developing a future images encryption hardware system using wavelet transform for security information.

Implementation of the 2-D Wavelet Transform into FPGA for Image

Energy Technology Data Exchange (ETDEWEB)

Leon, M; Barba, L; Vargas, L; Torres, C O, E-mail: madeleineleon@unicesar.edu.co [Laboratorio de Optica e Informatica, Universidad Popular del Cesar, Sede balneario Hurtado, Valledupar, Cesar (Colombia)

2011-01-01

This paper presents a hardware system implementation of the of discrete wavelet transform algorithm in two dimensions for FPGA, using the Daubechies filter family of order 2 (db2). The decomposition algorithm of this transform is designed and simulated with the Hardware Description Language VHDL and is implemented in a programmable logic device (FPGA) XC3S1200E reference, Spartan IIIE family, by Xilinx, take advantage the parallels properties of these gives us and speeds processing that can reach them. The architecture is evaluated using images input of different sizes. This implementation is done with the aim of developing a future images encryption hardware system using wavelet transform for security information.

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-06-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

Search for the periodicity of the prime Indian and American stock exchange indices using date-compensated discrete Fourier transform

International Nuclear Information System (INIS)

Samadder, Swetadri; Ghosh, Koushik; Basu, Tapasendra

2015-01-01

The behaviour of Indian stock markets has a persistent close association with the behaviour of American stock exchange. The present work is an effort in this direction and the purpose of the present work is to investigate the periodicity of the two prime Indian stock market indices viz. SENSEX and NIFTY and the prime American stock market indices viz. DOW-JONES and S&P500. To serve the present purpose we have here used SENSEX logarithmic daily close data during the period from 1st January, 1990 to 31st December, 2013, NIFTY logarithmic daily close data during the period from 3rd July, 1990 to 31st December, 2013, DOW-JONES logarithmic daily close data during the period from 10th January, 1928 to 31st December, 2013 and S&P500 logarithmic daily close data during the period 3rd January, 1950 to 31st December, 2013. For the present analysis we have first used double exponential smoothing on all the four time series in order to remove the trend and next we have generated monthly averages of the smoothed time series in order to remove the irregular fluctuations. At the final stage Ferraz-Mello method of date-compensated discrete Fourier transform (DCDFT) has been applied on the present four double-smoothed monthly averaged time series. Study reveals periods for SENSEX of 11, 53 and 142 months; for NIFTY periods of 22, 38, 52 and 139 months; for DOW-JONES periods of 23, 25, 27, 30, 59, 107, 138, 194 and 494 months and for S&P500 periods of 28, 66, 74, 149 and 384 months. With this specific periodic behaviour we have also observed some pseudo-periods in the present four financial time series which certainly adds to the uncertainty in the process of prediction for the same

Analytic discrete cosine harmonic wavelet transform based OFDM ...

Indian Academy of Sciences (India)

ADCHWT_OFDM) has been proposed in this paper. Analytic DCHWT has been realized by applying DCHWT to the original signal and to its Hilbert transform. ADCHWT has been found to be computationally efficient and very effective in improving ...

Discrete symmetries and the complex structure of Calabi-Yau manifolds

International Nuclear Information System (INIS)

Ross, G.G.

1988-01-01

We show how the discrete symmetries, which may be present after Calabi-Yau compactification for specific choices of the complex structure, extend to the h 2,1 moduli - the scalar fields whose vacuum expectation values determine the complex structure. This allows us to determine much about the coupling of the moduli and hence the energetically favoured complex structure. The discrete symmetry transformation properties of the moduli are worked out in detail for a three-generation Calabi-Yau model and it is shown how minimization of the effective potential involving these fields selects the complex structure which leaves unbroken a set of discrete symmetries. The phenomenological implications of the symmetries are briefly discussed. (orig.)

Image secure transmission for optical orthogonal frequency-division multiplexing visible light communication systems using chaotic discrete cosine transform

Science.gov (United States)

Wang, Zhongpeng; Zhang, Shaozhong; Chen, Fangni; Wu, Ming-Wei; Qiu, Weiwei

2017-11-01

A physical encryption scheme for orthogonal frequency-division multiplexing (OFDM) visible light communication (VLC) systems using chaotic discrete cosine transform (DCT) is proposed. In the scheme, the row of the DCT matrix is permutated by a scrambling sequence generated by a three-dimensional (3-D) Arnold chaos map. Furthermore, two scrambling sequences, which are also generated from a 3-D Arnold map, are employed to encrypt the real and imaginary parts of the transmitted OFDM signal before the chaotic DCT operation. The proposed scheme enhances the physical layer security and improves the bit error rate (BER) performance for OFDM-based VLC. The simulation results prove the efficiency of the proposed encryption method. The experimental results show that the proposed security scheme not only protects image data from eavesdroppers but also keeps the good BER and peak-to-average power ratio performances for image-based OFDM-VLC systems.

A discrete convolution kernel for No-DC MRI

International Nuclear Information System (INIS)

Zeng, Gengsheng L; Li, Ya

2015-01-01

An analytical inversion formula for the exponential Radon transform with an imaginary attenuation coefficient was developed in 2007 (2007 Inverse Problems 23 1963–71). The inversion formula in that paper suggested that it is possible to obtain an exact MRI (magnetic resonance imaging) image without acquiring low-frequency data. However, this un-measured low-frequency region (ULFR) in the k-space (which is the two-dimensional Fourier transform space in MRI terminology) must be very small. This current paper derives a FBP (filtered backprojection) algorithm based on You’s formula by suggesting a practical discrete convolution kernel. A point spread function is derived for this FBP algorithm. It is demonstrated that the derived FBP algorithm can have a larger ULFR than that in the 2007 paper. The significance of this paper is that we present a closed-form reconstruction algorithm for a special case of under-sampled MRI data. Usually, under-sampled MRI data requires iterative (instead of analytical) algorithms with L 1 -norm or total variation norm to reconstruct the image. (paper)

Auto-Bäcklund transformations for a differential-delay equation

Science.gov (United States)

Gordoa, Pilar R.; Pickering, Andrew

2013-03-01

Discrete Painlevé equations have, over recent years, generated much interest. One property of such equations that is considered to be particularly important is the existence of auto-Bäcklund transformations, that is, mappings between solutions of the equation in question, usually involving changes in the values of parameters appearing as coefficients. We have recently presented extensions of discrete Painlevé equations to equations involving derivatives as well as shifts in the independent variable. Here we show how auto-Bäcklund transformations can also be constructed for such differential-delay equations. We emphasise that this is the first time that an auto-Bäcklund transformation has been given for a differential-delay equation.

Data-Driven Process Discovery: A Discrete Time Algebra for Relational Signal Analysis

National Research Council Canada - National Science Library

Conrad, David

1996-01-01

.... Proposed is a time series transformation that encodes and compresses real-valued data into a well defined, discrete-space of 13 primitive elements where comparative evaluation between variables...

Parallel Fast Legendre Transform

NARCIS (Netherlands)

Alves de Inda, M.; Bisseling, R.H.; Maslen, D.K.

1998-01-01

We discuss a parallel implementation of a fast algorithm for the discrete polynomial Legendre transform We give an introduction to the DriscollHealy algorithm using polynomial arithmetic and present experimental results on the eciency and accuracy of our implementation The algorithms were

Setting the Foundation for Transforming the U.S. Energy System

Energy Technology Data Exchange (ETDEWEB)

Davis, Jon M.; Virden, Jud W.; Walton, Terry L.; Brog, Terrence K.; Stiles, Dennis L.; Alderson, Karis P.; Melland, Jodi C.; Hobbs, Lori L.; Martinez, Sam J.; Quadrel, Marilyn J.; Quinn, Rod K.

2008-12-29

Setting the Foundation for Transforming the U.S. Energy System: Three Federal Action Plans for Near- and Long-term Success is a short document written for the incoming U.S. Federal Administration's Transistion Team. The document represents what we believe to be foundational elements of a broad campaign to make rapid progress towards these goals for the longterm transformation necessary to meet our national economic, security, and environmental goals. The three immediate action plans include: * Creating Tomorrow’s Electricity Infrastructure * Decarbonizing the Energy Economy *Enabling Science-Based Policy

The De-Noising of Sonic Echo Test Data through Wavelet Transform Reconstruction

Directory of Open Access Journals (Sweden)

J.N. Watson

1999-01-01

Full Text Available This paper presents the results of feasibility study into the application of the wavelet transform signal processing method to sonic based non-destructive testing techniques. Finite element generated data from cast in situ foundation piles were collated and processed using both continuous and discrete wavelet transform techniques. Results were compared with conventional Fourier based methods. The discrete Daubechies wavelets and the continuous Mexican hat wavelet were used and their relative merits investigated. It was found that both the continuous Mexican hat and discrete Daubechies D8 wavelets were significantly better at locating the pile toe compared than the Fourier filtered case. The wavelet transform method was then applied to field test data and found to be successful in facilitating the detection of the pile toe.

Fast and Scalable Computation of the Forward and Inverse Discrete Periodic Radon Transform.

Science.gov (United States)

Carranza, Cesar; Llamocca, Daniel; Pattichis, Marios

2016-01-01

The discrete periodic radon transform (DPRT) has extensively been used in applications that involve image reconstructions from projections. Beyond classic applications, the DPRT can also be used to compute fast convolutions that avoids the use of floating-point arithmetic associated with the use of the fast Fourier transform. Unfortunately, the use of the DPRT has been limited by the need to compute a large number of additions and the need for a large number of memory accesses. This paper introduces a fast and scalable approach for computing the forward and inverse DPRT that is based on the use of: a parallel array of fixed-point adder trees; circular shift registers to remove the need for accessing external memory components when selecting the input data for the adder trees; an image block-based approach to DPRT computation that can fit the proposed architecture to available resources; and fast transpositions that are computed in one or a few clock cycles that do not depend on the size of the input image. As a result, for an N × N image (N prime), the proposed approach can compute up to N(2) additions per clock cycle. Compared with the previous approaches, the scalable approach provides the fastest known implementations for different amounts of computational resources. For example, for a 251×251 image, for approximately 25% fewer flip-flops than required for a systolic implementation, we have that the scalable DPRT is computed 36 times faster. For the fastest case, we introduce optimized just 2N + ⌈log(2) N⌉ + 1 and 2N + 3 ⌈log(2) N⌉ + B + 2 cycles, architectures that can compute the DPRT and its inverse in respectively, where B is the number of bits used to represent each input pixel. On the other hand, the scalable DPRT approach requires more 1-b additions than for the systolic implementation and provides a tradeoff between speed and additional 1-b additions. All of the proposed DPRT architectures were implemented in VHSIC Hardware Description Language

Discrete elements method of neutral particle transport

International Nuclear Information System (INIS)

Mathews, K.A.

1983-01-01

A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method

Quasicanonical structure of optimal control in constrained discrete systems

Science.gov (United States)

Sieniutycz, S.

2003-06-01

This paper considers discrete processes governed by difference rather than differential equations for the state transformation. The basic question asked is if and when Hamiltonian canonical structures are possible in optimal discrete systems. Considering constrained discrete control, general optimization algorithms are derived that constitute suitable theoretical and computational tools when evaluating extremum properties of constrained physical models. The mathematical basis of the general theory is the Bellman method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage criterion which allows a variation of the terminal state that is otherwise fixed in the Bellman's method. Two relatively unknown, powerful optimization algorithms are obtained: an unconventional discrete formalism of optimization based on a Hamiltonian for multistage systems with unconstrained intervals of holdup time, and the time interval constrained extension of the formalism. These results are general; namely, one arrives at: the discrete canonical Hamilton equations, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory along with all basic results of variational calculus. Vast spectrum of applications of the theory is briefly discussed.

A reversible transform for seismic data processing

International Nuclear Information System (INIS)

Burnett, William A; Ferguson, Robert J

2011-01-01

We use the nonstationary equivalent of the Fourier shift theorem to derive a general one-dimensional integral transform for the application and removal of certain seismic data processing steps. This transform comes from the observation that many seismic data processing steps can be viewed as nonstationary shifts. The continuous form of the transform is exactly reversible, and the discrete form provides a general framework for unitary and pseudounitary imaging operators. Any processing step which can be viewed as a nonstationary shift in any domain is a special case of this transform. Nonstationary shifts generally produce coordinate distortions between input and output domains, and those that preserve amplitudes do not conserve the energy of the input signal. The nonstationary frequency distortions, time distortions and nonphysical energy changes inherent to such operations are predicted and quantified by this transform. Processing steps of this type are conventionally implemented using interpolation operators to map discrete data values between input and output coordinate frames. Although not explicitly derived to perform interpolation, the transform here assumes the Fourier basis to predict values of the input signal between sampling locations. We demonstrate how interpolants commonly used in seismic data processing and imaging approximate the proposed method. We find that our transform is equivalent to the conventional sinc interpolant with no truncation. Once the transform is developed, we demonstrate its numerical implementation by matrix–vector multiplication. As an example, we use our transform to apply and remove normal moveout

Optical chirp z-transform processor with a simplified architecture.

Science.gov (United States)

Ngo, Nam Quoc

2014-12-29

Using a simplified chirp z-transform (CZT) algorithm based on the discrete-time convolution method, this paper presents the synthesis of a simplified architecture of a reconfigurable optical chirp z-transform (OCZT) processor based on the silica-based planar lightwave circuit (PLC) technology. In the simplified architecture of the reconfigurable OCZT, the required number of optical components is small and there are no waveguide crossings which make fabrication easy. The design of a novel type of optical discrete Fourier transform (ODFT) processor as a special case of the synthesized OCZT is then presented to demonstrate its effectiveness. The designed ODFT can be potentially used as an optical demultiplexer at the receiver of an optical fiber orthogonal frequency division multiplexing (OFDM) transmission system.

Special relativity with a discrete spectrum of singular velocities

International Nuclear Information System (INIS)

Gonzales Gascon, F.

1977-01-01

The introduction of real transformation formulae containing a whole discrete spectrum of singularities is suggested. Some phenomenological hypotheses are introduced and the group property is substituted by weaker conditions. The first singular speed (c 1 =c) is invariant with respect to the measures of it from subluminal frames, but the remaining speeds are not invariant. The proposed transformations do not form a closed set (for the superluminal speeds) and, therefore, the problem of having (within this framework) a principle of relativity valid for any velocity remains open

Study on time-varying velocity measurement with self-mixing laser diode based on Discrete Chirp-Fourier Transform

International Nuclear Information System (INIS)

Zhang Zhaoyun; Gao Yang; Zhao Xinghai; Zhao Xiang

2011-01-01

Laser's optical output power and frequency are modulated when the optical beam is back-scattered into the active cavity of the laser. By signal processing, the Doppler frequency can be acquired, and the target's velocity can be calculated. Based on these properties, an interferometry velocity sensor can be designed. When target move in time-varying velocity mode, it is difficult to extract the target's velocity. Time-varying velocity measurement by self-mixing laser diode is explored. A mathematics model was proposed for the time-varying velocity (invariable acceleration) measurement by self-mixing laser diode. Based on this model, a Discrete Chirp-Fourier Transform (DCFT) method was applied, DCFT is analogous to DFT. We show that when the signal length N is prime, the magnitudes of all the side lobes are 1, whereas the magnitudes of the main lobe is √N, And the coordinates of the main lobe shows the target's velocity and acceleration information. The simulation results prove the validity of the algorithm even in the situation of low SNR when N is prime.

Mittag-Leffler function for discrete fractional modelling

Directory of Open Access Journals (Sweden)

Guo-Cheng Wu

2016-01-01

Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.

Structural-functional lung imaging using a combined CT-EIT and a Discrete Cosine Transformation reconstruction method.

Science.gov (United States)

Schullcke, Benjamin; Gong, Bo; Krueger-Ziolek, Sabine; Soleimani, Manuchehr; Mueller-Lisse, Ullrich; Moeller, Knut

2016-05-16

Lung EIT is a functional imaging method that utilizes electrical currents to reconstruct images of conductivity changes inside the thorax. This technique is radiation free and applicable at the bedside, but lacks of spatial resolution compared to morphological imaging methods such as X-ray computed tomography (CT). In this article we describe an approach for EIT image reconstruction using morphologic information obtained from other structural imaging modalities. This leads to recon- structed images of lung ventilation that can easily be superimposed with structural CT or MRI images, which facilitates image interpretation. The approach is based on a Discrete Cosine Transformation (DCT) of an image of the considered transversal thorax slice. The use of DCT enables reduction of the dimensionality of the reconstruction and ensures that only conductivity changes of the lungs are reconstructed and displayed. The DCT based approach is well suited to fuse morphological image information with functional lung imaging at low computational costs. Results on simulated data indicate that this approach preserves the morphological structures of the lungs and avoids blurring of the solution. Images from patient measurements reveal the capabilities of the method and demonstrate benefits in possible applications.

Classical integrable defects as quasi Bäcklund transformations

Energy Technology Data Exchange (ETDEWEB)

Doikou, Anastasia, E-mail: a.doikou@hw.ac.uk

2016-10-15

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the “equations of motion” on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Bäcklund transformations. And although these equations are similar they are not exactly the same to the Bäcklund transformations. We also consider specific examples of integrable models to demonstrate our construction, i.e. the Toda chain and the sine-Gordon model. The equations of the time (space) evolution of the defect (discontinuity) degrees of freedom for these models are explicitly derived.

Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data

Directory of Open Access Journals (Sweden)

Darian M. Onchiș

2011-09-01

Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.

Single-crossover recombination in discrete time.

Science.gov (United States)

von Wangenheim, Ute; Baake, Ellen; Baake, Michael

2010-05-01

Modelling the process of recombination leads to a large coupled nonlinear dynamical system. Here, we consider a particular case of recombination in discrete time, allowing only for single crossovers. While the analogous dynamics in continuous time admits a closed solution (Baake and Baake in Can J Math 55:3-41, 2003), this no longer works for discrete time. A more general model (i.e. without the restriction to single crossovers) has been studied before (Bennett in Ann Hum Genet 18:311-317, 1954; Dawson in Theor Popul Biol 58:1-20, 2000; Linear Algebra Appl 348:115-137, 2002) and was solved algorithmically by means of Haldane linearisation. Using the special formalism introduced by Baake and Baake (Can J Math 55:3-41, 2003), we obtain further insight into the single-crossover dynamics and the particular difficulties that arise in discrete time. We then transform the equations to a solvable system in a two-step procedure: linearisation followed by diagonalisation. Still, the coefficients of the second step must be determined in a recursive manner, but once this is done for a given system, they allow for an explicit solution valid for all times.

CHANNEL ESTIMATION FOR ZT DFT-s-OFDM

DEFF Research Database (Denmark)

2018-01-01

A signal modulated according to zero-tail discrete Fourier transform spread orthogonal frequency division multiplexing (ZT DFT-s-OFDM) is received over a channel. The signal is down-sampled into a first sequence comprising N samples, N corresponding to the number of used subcarriers. The first Nh...

A Novel Intelligent Method for the State of Charge Estimation of Lithium-Ion Batteries Using a Discrete Wavelet Transform-Based Wavelet Neural Network

Directory of Open Access Journals (Sweden)

Deyu Cui

2018-04-01

Full Text Available State of charge (SOC estimation is becoming increasingly important, along with electric vehicle (EV rapid development, while SOC is one of the most significant parameters for the battery management system, indicating remaining energy and ensuring the safety and reliability of EV. In this paper, a hybrid wavelet neural network (WNN model combining the discrete wavelet transform (DWT method and adaptive WNN is proposed to estimate the SOC of lithium-ion batteries. The WNN model is trained by Levenberg-Marquardt (L-M algorithm, whose inputs are processed by discrete wavelet decomposition and reconstitution. Compared with back-propagation neural network (BPNN, L-M based BPNN (LMBPNN, L-M based WNN (LMWNN, DWT with L-M based BPNN (DWTLMBPNN and extend Kalman filter (EKF, the proposed intelligent SOC estimation method is validated and proved to be effective. Under the New European Driving Cycle (NEDC, the mean absolute error and maximum error can be reduced to 0.59% and 3.13%, respectively. The characteristics of high accuracy and strong robustness of the proposed method are verified by comparison study and robustness evaluation results (e.g., measurement noise test and untrained driving cycle test.

Discrete Green’s functions for propagators between complex objects in discrete space-time nonlinear electromagnetics

NARCIS (Netherlands)

Arnold, J.M.; Hon, de B.P.; Graglia, R.D.

2007-01-01

We propose a potential-based form of the FDTD scheme, with potentials driven by sources that are themselves simple dynamical systems. This formulation admits a radiative boundary condition for the discrete-mesh Maxwell's equations in a multiply connected exterior domain, which facilitates

Formal degrees of unipotent discrete series representations and the exotic Fourier transform

NARCIS (Netherlands)

Ciubotaru, D.; Opdam, E.

2015-01-01

We introduce a notion of elliptic fake degrees for unipotent elliptic representations of a semisimple p-adic group. We conjecture, and verify in some cases, that the relation between the formal degrees of unipotent discrete series representations of a semisimple p-adic group and the elliptic fake

Hybrid SN Laplace Transform Method For Slab Lattice Calculations

International Nuclear Information System (INIS)

Segatto, Cynthia F.; Vilhena, Marco T.; Zani, Jose H.; Barros, Ricardo C.

2008-01-01

In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this paper we describe a hybrid discrete ordinates (S N ) method for slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. We use special fuel-moderator interface conditions based on an approximate angular flux interpolation analytical method and the Laplace transform (LTS N ) numerical method to calculate the neutron flux distribution and the thermal disadvantage factor. We present numerical results for a range of typical model problems. (authors)

Noniterative MAP reconstruction using sparse matrix representations.

Science.gov (United States)

Cao, Guangzhi; Bouman, Charles A; Webb, Kevin J

2009-09-01

We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.

The origin of discrete particles

CERN Document Server

Bastin, T

2009-01-01

This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (10 7 ). Sample Chapter(s). Foreword (56 KB). Chapter 1: Introduction

The problem with time in mixed continuous/discrete time modelling

NARCIS (Netherlands)

Rovers, K.C.; Kuper, Jan; Smit, Gerardus Johannes Maria

The design of cyber-physical systems requires the use of mixed continuous time and discrete time models. Current modelling tools have problems with time transformations (such as a time delay) or multi-rate systems. We will present a novel approach that implements signals as functions of time,

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy

Science.gov (United States)

Gninzanlong, Carlos Lawrence; Ndjomatchoua, Frank Thomas; Tchawoua, Clément

2018-04-01

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.

Conservative adaptivity and two-way self-nesting using discrete wavelets

Science.gov (United States)

Dubos, Thomas

2010-05-01

In simulating atmosphere and oceans, multiscale modelling is desirable to track high-intensity weather patterns, to investigate the interactions between the various spatio-temporal scales of the climate system, and to perform assessments of climate change at scales small enough to derive impacts on society and ecosystems. The mainstream approach to multiscale modelling is to nest a fine, limited-area model into a coarse, global model. These models are then coupled, either one-way or two-way, in order to combine the global coverage of the global model and the fine details of the fine model. In the long simulations typical of climate studies, initial conditions are unimportant, except for the few quantities like mass that are exactly conserved. In this context it is crucial that numerical models conserve at least mass exactly at the discrete level. However even with elaborate strategies like adaptive mesh refinement (AMR) conservation is not straightforwardly achieved. Although the continuous wavelet transform has become a standard tool of geophysical data analysis, it is less known that discrete wavelets and the associated transforms provide the basis for spatially adaptive numerical methods. Such methods are now well-developed in the fluid dynamics community. Since they allow spatial adaptivity, they can also be seen as two-way self-nesting methods. However since they are not specifically designed for geophysical purposes they are usually not exactly conservative. I present a fairly general framework in which a wavelet-based layer is added to an existing conservative scheme (finite-volume or finite-difference) to make it spatially adaptive without breaking the exact conservation of linear invariants. Discrete wavelet transforms involve an upscaling operation by which fields are transferred from a fine grid to a coarser grid with half the resolution. The method requires that mass fluxes be upscaled in a way that is consistent with the upscaling of mass. This

Large-scale chromosome folding versus genomic DNA sequences: A discrete double Fourier transform technique.

Science.gov (United States)

Chechetkin, V R; Lobzin, V V

2017-08-07

Using state-of-the-art techniques combining imaging methods and high-throughput genomic mapping tools leaded to the significant progress in detailing chromosome architecture of various organisms. However, a gap still remains between the rapidly growing structural data on the chromosome folding and the large-scale genome organization. Could a part of information on the chromosome folding be obtained directly from underlying genomic DNA sequences abundantly stored in the databanks? To answer this question, we developed an original discrete double Fourier transform (DDFT). DDFT serves for the detection of large-scale genome regularities associated with domains/units at the different levels of hierarchical chromosome folding. The method is versatile and can be applied to both genomic DNA sequences and corresponding physico-chemical parameters such as base-pairing free energy. The latter characteristic is closely related to the replication and transcription and can also be used for the assessment of temperature or supercoiling effects on the chromosome folding. We tested the method on the genome of E. coli K-12 and found good correspondence with the annotated domains/units established experimentally. As a brief illustration of further abilities of DDFT, the study of large-scale genome organization for bacteriophage PHIX174 and bacterium Caulobacter crescentus was also added. The combined experimental, modeling, and bioinformatic DDFT analysis should yield more complete knowledge on the chromosome architecture and genome organization. Copyright © 2017 Elsevier Ltd. All rights reserved.

An integrable (2+1)-dimensional Toda equation with two discrete variables

International Nuclear Information System (INIS)

Cao Cewen; Cao Jianli

2007-01-01

An integrable (2+1)-dimensional Toda equation with two discrete variables is presented from the compatible condition of a Lax triad composed of the ZS-AKNS (Zakharov, Shabat; Ablowitz, Kaup, Newell, Segur) eigenvalue problem and two discrete spectral problems. Through the nonlinearization technique, the Lax triad is transformed into a Hamiltonian system and two symplectic maps, respectively, which are integrable in the Liouville sense, sharing the same set of integrals, functionally independent and involutive with each other. In the Jacobi variety of the associated algebraic curve, both the continuous and the discrete flows are straightened out by the Abel-Jacobi coordinates, and are integrated by quadratures. An explicit algebraic-geometric solution in the original variable is obtained by the Riemann-Jacobi inversion

On discrete 2D integrable equations of higher order

International Nuclear Information System (INIS)

Adler, V E; Postnikov, V V

2014-01-01

We study two-dimensional discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the Bäcklund–Darboux transformations for the lattice equations of Bogoyavlensky type. (paper)

Integrable relativistic Toda type lattice hierarchies, associated coupling systems and the Darboux transformation

International Nuclear Information System (INIS)

Yang Hongxiang; Xu Xixiang; Sun Yepeng; Ding Haiyong

2006-01-01

Starting from a discrete isospectral problem, integrable positive and negative relativistic Toda type lattice hierarchies are derived. The two lattice hierarchies are proven to have discrete zero-curvature representations associated with a discrete spectral problem, and the positive and negative lattice hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. The integrable positive and negative coupling systems of the resulting hierarchies are constructed through enlarging Lax pairs. In addition, with the help of gauge transformations of spectral problems, a Darboux transformation is established for the relativistic Toda type lattice. As an application, an exact solution is explicitly presented

Discretization analysis of bifurcation based nonlinear amplifiers

Science.gov (United States)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2017-09-01

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

S-duality as Fourier transform for arbitrary ϵ1, ϵ2

International Nuclear Information System (INIS)

N Nemkov

2014-01-01

The Alday–Gaiotto–Tachikawa relations reduce S-duality to the modular transformations of conformal blocks. It was recently conjectured that, for the four-point conformal block, the modular transform up to the non-perturbative contributions can be written in the form of the ordinary Fourier transform when β ≡ −ϵ 1 /ϵ 2 = 1. Here I extend this conjecture to general values of ϵ 1 , ϵ 2 . Namely, I argue that, for a properly normalized four-point conformal block the S-duality is perturbatively given by the Fourier transform for arbitrary values of the deformation parameters ϵ 1 , ϵ 2 . The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant g 2 ≡ −ϵ 1 ϵ 2 and hypermultiplet masses. (paper)

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

Discrete systems related to the sixth Painleve equation

International Nuclear Information System (INIS)

Ramani, A; Ohta, Y; Grammaticos, B

2006-01-01

We present discrete Painleve equations which can be obtained as contiguity relations of the solutions of the continuous Painleve VI. The derivation is based on the geometry of the affine Weyl group D (1) 4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau-Ablowitz-Fokas equation, which is a Miura transformed, 'modified', P VI

Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach

Directory of Open Access Journals (Sweden)

Ludwig Kohaupt

2015-12-01

Full Text Available The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating images in computer tomography. In order to achieve this, appropriate algorithms are necessary. In this context, the fast Fourier transform (FFT plays a key role which is an algorithm for calculating the discrete Fourier transform (DFT; this, in turn, is tightly connected with the discrete Fourier series. The last one itself is the discrete analog of the common (continuous-time Fourier series and is usually learned by mathematics students from a theoretical point of view. The aim of this expository/pedagogical paper is to give an introduction to the discrete Fourier series for both mathematics and engineering students. It is intended to expand the purely mathematical view; the engineering aspect is taken into account by applying the FFT to an example from signal processing that is small enough to be used in class-room teaching and elementary enough to be understood also by mathematics students. The MATLAB program is employed to do the computations.

40-Gb/s transmission over 100m graded-index plastic optical fiber based on discrete multitone modulation

NARCIS (Netherlands)

Yang, H.; Lee, S.C.J.; Tangdiongga, E.; Breyer, F.; Randel, S.; Koonen, A.M.J.

2009-01-01

Spectral-efficient 40-Gb/s discrete multitone transmission over 100m of graded-index plastic optical fiber is experimentally demonstrated by intensity-modulation of a 10-GHz DFB-laser (1302nm) and direct-detection with a 25-µm large diameter photodetector.

Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models.

Science.gov (United States)

Franke, John E; Yakubu, Abdul-Aziz

2008-12-01

The dynamics of simple discrete-time epidemic models without disease-induced mortality are typically characterized by global transcritical bifurcation. We prove that in corresponding models with disease-induced mortality a tiny number of infectious individuals can drive an otherwise persistent population to extinction. Our model with disease-induced mortality supports multiple attractors. In addition, we use a Ricker recruitment function in an SIS model and obtained a three component discrete Hopf (Neimark-Sacker) cycle attractor coexisting with a fixed point attractor. The basin boundaries of the coexisting attractors are fractal in nature, and the example exhibits sensitive dependence of the long-term disease dynamics on initial conditions. Furthermore, we show that in contrast to corresponding models without disease-induced mortality, the disease-free state dynamics do not drive the disease dynamics.

Trend analyses of transformer problems in the U.S. nuclear power plants

International Nuclear Information System (INIS)

Shimada, Yoshio

2009-01-01

Up to 2007, the authors have conducted the trend analyses of trouble events related to main generators, emergency diesel generators, breakers and motors, which are more likely to cause problems than other electric equipments in nuclear power plants. The frequency of trouble events in transformers in domestic nuclear power plants at present is approximately one third of the publicly reported cases in the U.S. However, as the situation of maintenance in Japan in the future will become similar to those in the U.S. if the operating period is extended or the maintenance method is to be shifted from preventive maintenance to condition based maintenance, there is a concern that the frequency of transformer events in Japan will increase in Japan, also. Thus, trend analyses were conducted on transformers events which had not been subject to such analyses, from among electrical equipments which are likely to cause problems. The trend analyses were performed on 23 transformer events which had occurred in the U.S. nuclear power plants in five years from 2003 through 2007 among events reported in the Licensee Event Reports (LERs: event reports submitted to NRC by U.S. nuclear power plants) which have been registered in the nuclear information database of the Institute of Nuclear Safety System, Incorporated's (INSS), as well as 8 events registered in the Nuclear Information Archives (NUCIA), which had occurred in domestic nuclear power plants in five from 2003 through 2007. Lessons learned from the trend analyses of the transformer trouble events in the U.S. revealed that for transformers in general, the maintenance management of tap changers is important, while for the main transformers which are most likely to cause problems, it is vital to prevent the deterioration of insulation and insulating oil. (author)

Electromyography (EMG) signal recognition using combined discrete wavelet transform based adaptive neuro-fuzzy inference systems (ANFIS)

Science.gov (United States)

Arozi, Moh; Putri, Farika T.; Ariyanto, Mochammad; Khusnul Ari, M.; Munadi, Setiawan, Joga D.

2017-01-01

People with disabilities are increasing from year to year either due to congenital factors, sickness, accident factors and war. One form of disability is the case of interruptions of hand function. The condition requires and encourages the search for solutions in the form of creating an artificial hand with the ability as a human hand. The development of science in the field of neuroscience currently allows the use of electromyography (EMG) to control the motion of artificial prosthetic hand into the necessary use of EMG as an input signal to control artificial prosthetic hand. This study is the beginning of a significant research planned in the development of artificial prosthetic hand with EMG signal input. This initial research focused on the study of EMG signal recognition. Preliminary results show that the EMG signal recognition using combined discrete wavelet transform and Adaptive Neuro-Fuzzy Inference System (ANFIS) produces accuracy 98.3 % for training and 98.51% for testing. Thus the results can be used as an input signal for Simulink block diagram of a prosthetic hand that will be developed on next study. The research will proceed with the construction of artificial prosthetic hand along with Simulink program controlling and integrating everything into one system.

Rolling Bearing Fault Diagnosis Using Modified Neighborhood Preserving Embedding and Maximal Overlap Discrete Wavelet Packet Transform with Sensitive Features Selection

Directory of Open Access Journals (Sweden)

Fei Dong

2018-01-01

Full Text Available In order to enhance the performance of bearing fault diagnosis and classification, features extraction and features dimensionality reduction have become more important. The original statistical feature set was calculated from single branch reconstruction vibration signals obtained by using maximal overlap discrete wavelet packet transform (MODWPT. In order to reduce redundancy information of original statistical feature set, features selection by adjusted rand index and sum of within-class mean deviations (FSASD was proposed to select fault sensitive features. Furthermore, a modified features dimensionality reduction method, supervised neighborhood preserving embedding with label information (SNPEL, was proposed to realize low-dimensional representations for high-dimensional feature space. Finally, vibration signals collected from two experimental test rigs were employed to evaluate the performance of the proposed procedure. The results show that the effectiveness, adaptability, and superiority of the proposed procedure can serve as an intelligent bearing fault diagnosis system.

Identification of parameters of discrete-continuous models

International Nuclear Information System (INIS)

Cekus, Dawid; Warys, Pawel

2015-01-01

In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible

Identification of parameters of discrete-continuous models

Energy Technology Data Exchange (ETDEWEB)

Cekus, Dawid, E-mail: cekus@imipkm.pcz.pl; Warys, Pawel, E-mail: warys@imipkm.pcz.pl [Institute of Mechanics and Machine Design Foundations, Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa (Poland)

2015-03-10

In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible.

Clebsch-Gordan coefficients of discrete groups in subgroup bases

Science.gov (United States)

Chen, Gaoli

2018-04-01

We express each Clebsch-Gordan (CG) coefficient of a discrete group as a product of a CG coefficient of its subgroup and a factor, which we call an embedding factor. With an appropriate definition, such factors are fixed up to phase ambiguities. Particularly, they are invariant under basis transformations of irreducible representations of both the group and its subgroup. We then impose on the embedding factors constraints, which relate them to their counterparts under complex conjugate and therefore restrict the phases of embedding factors. In some cases, the phase ambiguities are reduced to sign ambiguities. We describe the procedure of obtaining embedding factors and then calculate CG coefficients of the group 𝒫𝒮ℒ2(7) in terms of embedding factors of its subgroups S4 and 𝒯7.

The fractional Fourier transform and applications

Science.gov (United States)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

Science.gov (United States)

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

Network Science Research Laboratory (NSRL) Discrete Event Toolkit

Science.gov (United States)

2016-01-01

ARL-TR-7579 ● JAN 2016 US Army Research Laboratory Network Science Research Laboratory (NSRL) Discrete Event Toolkit by...Laboratory (NSRL) Discrete Event Toolkit by Theron Trout and Andrew J Toth Computational and Information Sciences Directorate, ARL...Research Laboratory (NSRL) Discrete Event Toolkit 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Theron Trout

Fourier transformations for difference analogs of the harmonic oscillator

International Nuclear Information System (INIS)

Askey, R.; Atakishiyev, N.M.

1995-01-01

The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs

The inverse of winnowing: a FORTRAN subroutine and discussion of unwinnowing discrete data

Science.gov (United States)

Bracken, Robert E.

2004-01-01

This report describes an unwinnowing algorithm that utilizes a discrete Fourier transform, and a resulting Fortran subroutine that winnows or unwinnows a 1-dimensional stream of discrete data; the source code is included. The unwinnowing algorithm effectively increases (by integral factors) the number of available data points while maintaining the original frequency spectrum of a data stream. This has utility when an increased data density is required together with an availability of higher order derivatives that honor the original data.

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-01-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads

Discrete transparent boundary conditions for Schroedinger-type equations

International Nuclear Information System (INIS)

Schmidt, F.; Yevick, D.

1997-01-01

We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schroedinger-type equations. Our method supplies boundary conditions for the θ-family of implicit one-step discretizations of Schroedinger's equation in time. The use of Mikusinski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner. 14 refs., 9 figs

Unfolding and effective bandstructure calculations as discrete real- and reciprocal-space operations

Energy Technology Data Exchange (ETDEWEB)

Boykin, Timothy B., E-mail: boykin@ece.uah.edu [Department of Electrical and Computer Engineering, The University of Alabama in Huntsville, Huntsville, AL 35899 (United States); Ajoy, Arvind [School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853 (United States); Ilatikhameneh, Hesameddin; Povolotskyi, Michael; Klimeck, Gerhard [Network for Computational Nanotechnology, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 (United States)

2016-06-15

In recent years, alloy electronic structure calculations based on supercell Brillouin zone unfolding have become popular. There are a number of formulations of the method which on the surface might appear different. Here we show that a discrete real-space description, based on discrete Fourier transforms, is fully general. Furthermore, such an approach can more easily show the effects of alloy scattering. We present such a method for treating the random alloy problem. This treatment features straightforward mathematics and a transparent physical interpretation of the calculated effective (i.e., approximate) energy bands.

Space monitoring of the earth on the presence of solid domestic wastes using a discrete orthogonal transforms

Directory of Open Access Journals (Sweden)

Kazaryan Maretta

2017-01-01

Full Text Available The paper investigates multivariate Wavelet Haar’s series. To study on the correctness is made by means of Tikhonov’s method. A theorem on stability and uniform convergence of a regularized summable function of the wavelet-Haar’s series functions in Lipschitz class with approximate coefficients is proved. An experiment confirms the validity of Tikhonov’s method using space monitoring of waste disposal facilities is conducted as an example. Namely, the decoding of space images-images using N-dimensional Haar’s wavelet transform is used.

Discrete population balance models of random agglomeration and cleavage in polymer pyrolysis

Directory of Open Access Journals (Sweden)

John E. J. Staggs

2017-05-01

Full Text Available The processes of random agglomeration and cleavage (both of which are important for the development of new models of polymer combustion, but are also applicable in a wide range of fields including atmospheric physics, radiation modelling and astrophysics are analysed using population balance methods. The evolution of a discrete distribution of particles is considered within this framework, resulting in a set of ordinary differential equations for the individual particle concentrations. Exact solutions for these equations are derived, together with moment generating functions. Application of the discrete Laplace transform (analogous to the Z-transform is found to be effective in these problems, providing both exact solutions for particle concentrations and moment generating functions. The combined agglomeration-cleavage problem is also considered. Unfortunately, it has been impossible to find an exact solution for the full problem, but a stable steady state has been identified and computed.

The discrete symmetry of the N=2 supersymmetric modified NLS hierarchy

International Nuclear Information System (INIS)

Sorin, A.

1996-01-01

A few new N=2 superintegrable mappings in the (1|2) superspace are proposed and their origin is analyzed. Using one of them, acting like the discrete symmetry transformation of the N=2 supersymmetric modified NLS hierarchy, the recursion operator and Hamiltonian structures of the hierarchy are constructed

Bell's theorem, the measurement problem, Newton's self-gravitation and its connections to violations of the discrete symmetries C, P, T

International Nuclear Information System (INIS)

Hiesmayr, Beatrix C

2015-01-01

About 50 years ago John St. Bell published his famous Bell theorem that initiated a new field in physics. This contribution discusses how discrete symmetries relate to the big open questions of quantum mechanics, in particular:(i) how correlations stronger than those predicted by theories sharing randomness (Bell's theorem) relate to the violation of the CP symmetry and the P symmetry; and its relation to the security of quantum cryptography,(ii) how the measurement problem (“why do we observe no tables in superposition?”) can be polled in weakly decaying systems,(iii) how strongly and weakly interacting quantum systems are affected by Newton's self gravitation.These presented preliminary results show that the meson-antimeson systems and the hyperon- antihyperon systems are a unique laboratory to tackle deep fundamental questions and to contribute to the understand what impact the violation of discrete symmetries has. (paper)

Modeling and simulation of discrete event systems

CERN Document Server

Choi, Byoung Kyu

2013-01-01

Computer modeling and simulation (M&S) allows engineers to study and analyze complex systems. Discrete-event system (DES)-M&S is used in modern management, industrial engineering, computer science, and the military. As computer speeds and memory capacity increase, so DES-M&S tools become more powerful and more widely used in solving real-life problems. Based on over 20 years of evolution within a classroom environment, as well as on decades-long experience in developing simulation-based solutions for high-tech industries, Modeling and Simulation of Discrete-Event Systems is the only book on

A spherical x-ray transform and hypercube sections

DEFF Research Database (Denmark)

Kazantsev, Ivan G; Schmidt, Soren

2014-01-01

We investigate the problem of sampling a unit great circle on the unit sphere S-3 as a support of orientation distribution functions on which acts the discrete spherical x-ray transform. The circle's partition subsets are gnomonically mapped onto lines that constitute a convex polygon inside...... the bounding cubes of hypercube. Thus the problem of the great circle tracing is reduced to the problem of the four-dimensional cube sectioning by the plane containing the circle and the intersection figure (the polygon) vertices finding. In this paper, a fast, non-combinatorial approach for the polygon...

Discrete variable representation for singular Hamiltonians

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2004-01-01

We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...

Research of generalized wavelet transformations of Haar correctness in remote sensing of the Earth

Science.gov (United States)

Kazaryan, Maretta; Shakhramanyan, Mihail; Nedkov, Roumen; Richter, Andrey; Borisova, Denitsa; Stankova, Nataliya; Ivanova, Iva; Zaharinova, Mariana

2017-10-01

In this paper, Haar's generalized wavelet functions are applied to the problem of ecological monitoring by the method of remote sensing of the Earth. We study generalized Haar wavelet series and suggest the use of Tikhonov's regularization method for investigating them for correctness. In the solution of this problem, an important role is played by classes of functions that were introduced and described in detail by I.M. Sobol for studying multidimensional quadrature formulas and it contains functions with rapidly convergent series of wavelet Haar. A theorem on the stability and uniform convergence of the regularized summation function of the generalized wavelet-Haar series of a function from this class with approximate coefficients is proved. The article also examines the problem of using orthogonal transformations in Earth remote sensing technologies for environmental monitoring. Remote sensing of the Earth allows to receive from spacecrafts information of medium, high spatial resolution and to conduct hyperspectral measurements. Spacecrafts have tens or hundreds of spectral channels. To process the images, the device of discrete orthogonal transforms, and namely, wavelet transforms, was used. The aim of the work is to apply the regularization method in one of the problems associated with remote sensing of the Earth and subsequently to process the satellite images through discrete orthogonal transformations, in particular, generalized Haar wavelet transforms. General methods of research. In this paper, Tikhonov's regularization method, the elements of mathematical analysis, the theory of discrete orthogonal transformations, and methods for decoding of satellite images are used. Scientific novelty. The task of processing of archival satellite snapshots (images), in particular, signal filtering, was investigated from the point of view of an incorrectly posed problem. The regularization parameters for discrete orthogonal transformations were determined.

Hybrid fast Hankel transform implementation for optics simulation

Science.gov (United States)

Davis, Paul K.

2013-09-01

The most compute intensive part of a full optics simulation, especially including diffraction effects, is the Fourier transform between pupil and image spaces. This is typically performed as a two dimensional fast discrete transform. For a nearly radially symmetric system there are advantages to using polar coordinates, in which case the radial transform becomes a Hankel transform, using Bessel functions instead of circular functions. However, there are special difficulties in calculating and handling Bessel functions. Several solutions have been proposed. We present a hybrid Hankel transform which divides the domain, calculating a portion using Bessel function approximations but converting most of the domain into a one dimensional Fourier transform which can be handled by standard methods.

Preclinical Diagnosis of Magnetic Resonance (MR Brain Images via Discrete Wavelet Packet Transform with Tsallis Entropy and Generalized Eigenvalue Proximal Support Vector Machine (GEPSVM

Directory of Open Access Journals (Sweden)

Yudong Zhang

2015-03-01

Full Text Available Background: Developing an accurate computer-aided diagnosis (CAD system of MR brain images is essential for medical interpretation and analysis. In this study, we propose a novel automatic CAD system to distinguish abnormal brains from normal brains in MRI scanning. Methods: The proposed method simplifies the task to a binary classification problem. We used discrete wavelet packet transform (DWPT to extract wavelet packet coefficients from MR brain images. Next, Shannon entropy (SE and Tsallis entropy (TE were harnessed to obtain entropy features from DWPT coefficients. Finally, generalized eigenvalue proximate support vector machine (GEPSVM, and GEPSVM with radial basis function (RBF kernel, were employed as classifier. We tested the four proposed diagnosis methods (DWPT + SE + GEPSVM, DWPT + TE + GEPSVM, DWPT + SE + GEPSVM + RBF, and DWPT + TE + GEPSVM + RBF on three benchmark datasets of Dataset-66, Dataset-160, and Dataset-255. Results: The 10 repetition of K-fold stratified cross validation results showed the proposed DWPT + TE + GEPSVM + RBF method excelled not only other three proposed classifiers but also existing state-of-the-art methods in terms of classification accuracy. In addition, the DWPT + TE + GEPSVM + RBF method achieved accuracy of 100%, 100%, and 99.53% on Dataset-66, Dataset-160, and Dataset-255, respectively. For Dataset-255, the offline learning cost 8.4430s and online prediction cost merely 0.1059s. Conclusions: We have proved the effectiveness of the proposed method, which achieved nearly 100% accuracy over three benchmark datasets.

Detection and classification of power quality disturbances using S-transform and modular neural network

Energy Technology Data Exchange (ETDEWEB)

Bhende, C.N.; Mishra, S.; Panigrahi, B.K. [Department of Electrical Engineering, Indian Institute of Technology, New Delhi 110016 (India)

2008-01-15

This paper presents an S-transform based modular neural network (NN) classifier for recognition of power quality disturbances. The excellent time - frequency resolution characteristics of the S-transform makes it an attractive candidate for the analysis of power quality (PQ) disturbances under noisy condition and has the ability to detect the disturbance correctly. On the other hand, the performance of wavelet transform (WT) degrades while detecting and localizing the disturbances in the presence of noise. Features extracted by using the S-transform are applied to a modular NN for automatic classification of the PQ disturbances that solves a relatively complex problem by decomposing it into simpler subtasks. Modularity of neural network provides better classification, model complexity reduction and better learning capability, etc. Eleven types of PQ disturbances are considered for the classification. The simulation results show that the combination of the S-transform and a modular NN can effectively detect and classify different power quality disturbances. (author)

SeismicWaveTool: Continuous and discrete wavelet analysis and filtering for multichannel seismic data

Science.gov (United States)

Galiana-Merino, J. J.; Rosa-Herranz, J. L.; Rosa-Cintas, S.; Martinez-Espla, J. J.

2013-01-01

A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of multichannel seismic data. The considered time-frequency transforms include the continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform. The developed approaches provide a fast and precise time-frequency examination of the seismograms at different frequency bands. Moreover, filtering methods for noise, transients or even baseline removal, are implemented. The primary motivation is to support seismologists with a user-friendly and fast program for the wavelet analysis, providing practical and understandable results. Program summaryProgram title: SeismicWaveTool Catalogue identifier: AENG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 611072 No. of bytes in distributed program, including test data, etc.: 14688355 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) version 7.8.0.347 (R2009a) or higher. Wavelet Toolbox is required. Computer: Developed on a MacBook Pro. Tested on Mac and PC. No computer-specific optimization was performed. Operating system: Any supporting MATLAB (MathWorks Inc.) v7.8.0.347 (R2009a) or higher. Tested on Mac OS X 10.6.8, Windows XP and Vista. Classification: 13. Nature of problem: Numerous research works have developed a great number of free or commercial wavelet based software, which provide specific solutions for the analysis of seismic data. On the other hand, standard toolboxes, packages or libraries, such as the MathWorks' Wavelet Toolbox for MATLAB, offer command line functions and interfaces for the wavelet analysis of one-component signals. Thus, software usually is focused on very specific problems

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

Science.gov (United States)

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A.

2016-01-01

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of “maximum flow-minimum cut” graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered. PMID:27089174

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.

Science.gov (United States)

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A

2016-08-25

There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

Efficiency and Flexibility of Fingerprint Scheme Using Partial Encryption and Discrete Wavelet Transform to Verify User in Cloud Computing.

Science.gov (United States)

Yassin, Ali A

2014-01-01

Now, the security of digital images is considered more and more essential and fingerprint plays the main role in the world of image. Furthermore, fingerprint recognition is a scheme of biometric verification that applies pattern recognition techniques depending on image of fingerprint individually. In the cloud environment, an adversary has the ability to intercept information and must be secured from eavesdroppers. Unluckily, encryption and decryption functions are slow and they are often hard. Fingerprint techniques required extra hardware and software; it is masqueraded by artificial gummy fingers (spoof attacks). Additionally, when a large number of users are being verified at the same time, the mechanism will become slow. In this paper, we employed each of the partial encryptions of user's fingerprint and discrete wavelet transform to obtain a new scheme of fingerprint verification. Moreover, our proposed scheme can overcome those problems; it does not require cost, reduces the computational supplies for huge volumes of fingerprint images, and resists well-known attacks. In addition, experimental results illustrate that our proposed scheme has a good performance of user's fingerprint verification.

Automatic gender determination from 3D digital maxillary tooth plaster models based on the random forest algorithm and discrete cosine transform.

Science.gov (United States)

Akkoç, Betül; Arslan, Ahmet; Kök, Hatice

2017-05-01

One of the first stages in the identification of an individual is gender determination. Through gender determination, the search spectrum can be reduced. In disasters such as accidents or fires, which can render identification somewhat difficult, durable teeth are an important source for identification. This study proposes a smart system that can automatically determine gender using 3D digital maxillary tooth plaster models. The study group was composed of 40 Turkish individuals (20 female, 20 male) between the ages of 21 and 24. Using the iterative closest point (ICP) algorithm, tooth models were aligned, and after the segmentation process, models were transformed into depth images. The local discrete cosine transform (DCT) was used in the process of feature extraction, and the random forest (RF) algorithm was used for the process of classification. Classification was performed using 30 different seeds for random generator values and 10-fold cross-validation. A value of 85.166% was obtained for average classification accuracy (CA) and a value of 91.75% for the area under the ROC curve (AUC). A multi-disciplinary study is performed here that includes computer sciences, medicine and dentistry. A smart system is proposed for the determination of gender from 3D digital models of maxillary tooth plaster models. This study has the capacity to extend the field of gender determination from teeth. Copyright © 2017 Elsevier B.V. All rights reserved.

Discrete wavelet transform analysis of surface electromyography for the fatigue assessment of neck and shoulder muscles.

Science.gov (United States)

Chowdhury, Suman Kanti; Nimbarte, Ashish D; Jaridi, Majid; Creese, Robert C

2013-10-01

Assessment of neuromuscular fatigue is essential for early detection and prevention of risks associated with work-related musculoskeletal disorders. In recent years, discrete wavelet transform (DWT) of surface electromyography (SEMG) has been used to evaluate muscle fatigue, especially during dynamic contractions when the SEMG signal is non-stationary. However, its application to the assessment of work-related neck and shoulder muscle fatigue is not well established. Therefore, the purpose of this study was to establish DWT analysis as a suitable method to conduct quantitative assessment of neck and shoulder muscle fatigue under dynamic repetitive conditions. Ten human participants performed 40min of fatiguing repetitive arm and neck exertions while SEMG data from the upper trapezius and sternocleidomastoid muscles were recorded. The ten of the most commonly used wavelet functions were used to conduct the DWT analysis. Spectral changes estimated using power of wavelet coefficients in the 12-23Hz frequency band showed the highest sensitivity to fatigue induced by the dynamic repetitive exertions. Although most of the wavelet functions tested in this study reasonably demonstrated the expected power trend with fatigue development and recovery, the overall performance of the "Rbio3.1" wavelet in terms of power estimation and statistical significance was better than the remaining nine wavelets. Copyright © 2013 Elsevier Ltd. All rights reserved.

A novel adaptive discrete cosine transform-domain filter for gap-inpainting of high resolution PET scanners

International Nuclear Information System (INIS)

Shih, Cheng-Ting; Lin, Hsin-Hon; Chuang, Keh-Shih; Wu, Jay; Chang, Shu-Jun

2014-01-01

Purpose: Several positron emission tomography (PET) scanners with special detector block arrangements have been developed in recent years to improve the resolution of PET images. However, the discontinuous detector blocks cause gaps in the sinogram. This study proposes an adaptive discrete cosine transform-based (aDCT) filter for gap-inpainting. Methods: The gap-corrupted sinogram was morphologically closed and subsequently converted to the DCT domain. A certain number of the largest coefficients in the DCT spectrum were identified to determine the low-frequency preservation region. The weighting factors for the remaining coefficients were determined by an exponential weighting function. The aDCT filter was constructed and applied to two digital phantoms and a simulated phantom introduced with various levels of noise. Results: For the Shepp-Logan head phantom, the aDCT filter filled the gaps effectively. For the Jaszczak phantom, no secondary artifacts were induced after aDCT filtering. The percent mean square error and mean structure similarity of the aDCT filter were superior to those of the DCT2 filter at all noise levels. For the simulated striatal dopamine innervation study, the aDCT filter recovered the shape of the striatum and restored the striatum to reference activity ratios to the ideal value. Conclusions: The proposed aDCT filter can recover the missing gap data in the sinogram and improve the image quality and quantitative accuracy of PET images

A novel adaptive discrete cosine transform-domain filter for gap-inpainting of high resolution PET scanners

Energy Technology Data Exchange (ETDEWEB)

Shih, Cheng-Ting; Lin, Hsin-Hon; Chuang, Keh-Shih [Department of Biomedical Engineering and Environmental Sciences, National Tsing Hua University, Hsinchu 30013, Taiwan (China); Wu, Jay, E-mail: jwu@mail.cmu.edu.tw [Department of Biomedical Imaging and Radiological Science, China Medical University, Taichung 40402, Taiwan (China); Chang, Shu-Jun [Health Physics Division, Institute of Nuclear Energy Research, Atomic Energy Council, Taoyuan 32546, Taiwan (China)

2014-08-15

Purpose: Several positron emission tomography (PET) scanners with special detector block arrangements have been developed in recent years to improve the resolution of PET images. However, the discontinuous detector blocks cause gaps in the sinogram. This study proposes an adaptive discrete cosine transform-based (aDCT) filter for gap-inpainting. Methods: The gap-corrupted sinogram was morphologically closed and subsequently converted to the DCT domain. A certain number of the largest coefficients in the DCT spectrum were identified to determine the low-frequency preservation region. The weighting factors for the remaining coefficients were determined by an exponential weighting function. The aDCT filter was constructed and applied to two digital phantoms and a simulated phantom introduced with various levels of noise. Results: For the Shepp-Logan head phantom, the aDCT filter filled the gaps effectively. For the Jaszczak phantom, no secondary artifacts were induced after aDCT filtering. The percent mean square error and mean structure similarity of the aDCT filter were superior to those of the DCT2 filter at all noise levels. For the simulated striatal dopamine innervation study, the aDCT filter recovered the shape of the striatum and restored the striatum to reference activity ratios to the ideal value. Conclusions: The proposed aDCT filter can recover the missing gap data in the sinogram and improve the image quality and quantitative accuracy of PET images.

Mimetic discretization methods

CERN Document Server

Castillo, Jose E

2013-01-01

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and

Applications of a fast, continuous wavelet transform

Energy Technology Data Exchange (ETDEWEB)

Dress, W.B.

1997-02-01

A fast, continuous, wavelet transform, based on Shannon`s sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon`s sampling theorem lets us view the Fourier transform of the data set as a continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time- domain sampling of the signal under analysis. Computational cost and nonorthogonality aside, the inherent flexibility and shift invariance of the frequency-space wavelets has advantages. The method has been applied to forensic audio reconstruction speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants` heart beats. Audio reconstruction is aided by selection of desired regions in the 2-D representation of the magnitude of the transformed signal. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass-spring system (e.g., a vehicle) by an occupants beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, features such as the glottal closing rate and word and phrase segmentation may be extracted from voice data.

Nonlinear dynamic range transformation in visual communication channels.

Science.gov (United States)

Alter-Gartenberg, R

1996-01-01

The article evaluates nonlinear dynamic range transformation in the context of the end-to-end continuous-input/discrete processing/continuous-display imaging process. Dynamic range transformation is required when we have the following: (i) the wide dynamic range encountered in nature is compressed into the relatively narrow dynamic range of the display, particularly for spatially varying irradiance (e.g., shadow); (ii) coarse quantization is expanded to the wider dynamic range of the display; and (iii) nonlinear tone scale transformation compensates for the correction in the camera amplifier.

Influence of discretization method on the digital control system performance

Directory of Open Access Journals (Sweden)

Futás József

2003-12-01

Full Text Available The design of control system can be divided into two steps. First the process or plant have to be convert into mathematical model form, so that its behavior can be analyzed. Then an appropriate controller have to be design in order to get the desired response of the controlled system. In the continuous time domain the system is represented by differential equations. Replacing a continuous system into discrete time form is always an approximation of the continuous system. The different discretization methods give different digital controller performance. The methods presented on the paper are Step Invariant or Zero Order Hold (ZOH Method, Matched Pole-Zero Method, Backward difference Method and Bilinear transformation. The above mentioned discretization methods are used in developing PI position controller of a dc motor. The motor model was converted by the ZOH method. The performances of the different methods are compared and the results are presented.

The discrete cones method for two-dimensional neutron transport calculations

International Nuclear Information System (INIS)

Watanabe, Y.; Maynard, C.W.

1986-01-01

A novel method, the discrete cones method (DC/sub N/), is proposed as an alternative to the discrete ordinates method (S/sub N/) for solutions of the two-dimensional neutron transport equation. The new method utilizes a new concept, discrete cones, which are made by partitioning a unit spherical surface that the direction vector of particles covers. In this method particles in a cone are simultaneously traced instead of those in discrete directions so that an anomaly of the S/sub N/ method, the ray effects, can be eliminated. The DC/sub N/ method has been formulated for X-Y geometry and a program has been creaed by modifying the standard S/sub N/ program TWOTRAN-II. Our sample calculations demonstrate a strong mitigation of the ray effects without a computing cost penalty

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

Science.gov (United States)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

The Bargmann transform and canonical transformations

International Nuclear Information System (INIS)

Villegas-Blas, Carlos

2002-01-01

This paper concerns a relationship between the kernel of the Bargmann transform and the corresponding canonical transformation. We study this fact for a Bargmann transform introduced by Thomas and Wassell [J. Math. Phys. 36, 5480-5505 (1995)]--when the configuration space is the two-sphere S 2 and for a Bargmann transform that we introduce for the three-sphere S 3 . It is shown that the kernel of the Bargmann transform is a power series in a function which is a generating function of the corresponding canonical transformation (a classical analog of the Bargmann transform). We show in each case that our canonical transformation is a composition of two other canonical transformations involving the complex null quadric in C 3 or C 4 . We also describe quantizations of those two other canonical transformations by dealing with spaces of holomorphic functions on the aforementioned null quadrics. Some of these quantizations have been studied by Bargmann and Todorov [J. Math. Phys. 18, 1141-1148 (1977)] and the other quantizations are related to the work of Guillemin [Integ. Eq. Operator Theory 7, 145-205 (1984)]. Since suitable infinite linear combinations of powers of the generating functions are coherent states for L 2 (S 2 ) or L 2 (S 3 ), we show finally that the studied Bargmann transforms are actually coherent states transforms

Can we use the known fast spherical fourier transforms in numerical meterology?

OpenAIRE

Sprengel, F.

2001-01-01

In numerical meteorology, there are many solvers using spectral methods. Most of the computing time is spent computing the discrete Legendre function transforms. The aim of this paper is to clarify whether the recently published fast Legendre function transforms can be used here.

An essay on discrete foundations for physics

International Nuclear Information System (INIS)

Noyes, H.P.; McGoveran, D.O.

1988-07-01

We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non-uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs

An essay on discrete foundations for physics

International Nuclear Information System (INIS)

Noyes, H.P.; McGoveran, D.O.

1988-01-01

We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non- uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs

An essay on discrete foundations for physics

Energy Technology Data Exchange (ETDEWEB)

Noyes, H.P.; McGoveran, D.O.

1988-07-01

We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non-uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.

An essay on discrete foundations for physics

Energy Technology Data Exchange (ETDEWEB)

Noyes, H.P.; McGoveran, D.O.

1988-10-05

We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non- uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.

On constructing optimistic simulation algorithms for the discrete event system specification

International Nuclear Information System (INIS)

Nutaro, James J.

2008-01-01

This article describes a Time Warp simulation algorithm for discrete event models that are described in terms of the Discrete Event System Specification (DEVS). The article shows how the total state transition and total output function of a DEVS atomic model can be transformed into an event processing procedure for a logical process. A specific Time Warp algorithm is constructed around this logical process, and it is shown that the algorithm correctly simulates a DEVS coupled model that consists entirely of interacting atomic models. The simulation algorithm is presented abstractly; it is intended to provide a basis for implementing efficient and scalable parallel algorithms that correctly simulate DEVS models

Discrete level schemes and their gamma radiation branching ratios (CENPL-DLS). Pt. 1

International Nuclear Information System (INIS)

Su Zongdi; Zhang Limin; Zhou Chunmei; Sun Zhengjun

1994-01-01

The DLS data file, which is a sub-library (version 1) of Chinese Evaluated Nuclear Parameter Library (CENPL), consists of data and information of discrete levels and gamma radiations. The data and information of this data file are translated from the Evaluated Nuclear Structure Data File (ENSDF). The transforming code from ENSDF to DLS was written. In the DLS data file, there are the data on discrete levels with determinate energy and their gamma radiations. At present, this file contains the data of 79456 levels and 100411 gammas for 1908 nuclides

A novel application of the S-transform in removing powerline interference from biomedical signals

International Nuclear Information System (INIS)

Huang, Chien-Chun; Young, Ming-Shing; Liang, Sheng-Fu; Shaw, Fu-Zen

2009-01-01

Powerline interference always disturbs recordings of biomedical signals. Numerous methods have been developed to reduce powerline interference. However, most of these techniques not only reduce the interference but also attenuate the 60 Hz power of the biomedical signals themselves. In the present study, we applied the S-transform, which provides an absolute phase of each frequency in a multi-resolution time–frequency analysis, to reduce 60 Hz interference. According to results from an electrocardiogram (ECG) to which a simulated 60 Hz noise was added, the S-transform de-noising process restored a power spectrum identical to that of the original ECG coincident with a significant reduction in the 60 Hz interference. Moreover, the S-transform de-noised the signal in an intensity-independent manner when reducing the 60 Hz interference. In both a real ECG signal from the MIT database and natural brain activity contaminated with 60 Hz interference, the S-transform also displayed superior merit to a notch filter in the aspect of reducing noise and preserving the signal. Based on these data, a novel application of the S-transform for removing powerline interference is established

Generalized Synchronization of Time-Delayed Discrete Systems

International Nuclear Information System (INIS)

Jing Jianyi; Min Lequan

2009-01-01

This paper establishes two theorems for two time-delayed (chaotic) discrete systems to achieve time-delayed generalized synchronization (TDGS). These two theorems uncover the general forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems. (interdisciplinary physics and related areas of science and technology)

Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

International Nuclear Information System (INIS)

Zhao Gang-Ling; Chen Li-Qun; Fu Jing-Li; Hong Fang-Yu

2013-01-01

In this paper, Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated. Firstly, the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices. Secondly, for cases of the two lattices, based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates, we present the quasi-extremal equation, the discrete analogues of Noether identity, Noether theorems, and the Noether conservation laws of the systems. Thirdly, in cases of the two lattices, we study the Mei symmetry in which we give the discrete analogues of the criterion, the theorem, and the conservative laws of Mei symmetry for the systems. Finally, an example is discussed for the application of the results

Design of an Optimal Preview Controller for Linear Discrete-Time Descriptor Noncausal Multirate Systems

Directory of Open Access Journals (Sweden)

Mengjuan Cao

2014-01-01

Full Text Available The linear discrete-time descriptor noncausal multirate system is considered for the presentation of a new design approach for optimal preview control. First, according to the characteristics of causal controllability and causal observability, the descriptor noncausal system is constructed into a descriptor causal closed-loop system. Second, by using the characteristics of the causal system and elementary transformation, the descriptor causal closed-loop system is transformed into a normal system. Then, taking advantage of the discrete lifting technique, the normal multirate system is converted to a single-rate system. By making use of the standard preview control method, we construct the descriptor augmented error system. The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system. In addition, a new single-rate system is obtained, the optimal control law of which is given. Returning to the original system, the optimal preview controller for linear discrete-time descriptor noncausal multirate systems is derived. The stabilizability and detectability of the lifted single-rate system are discussed in detail. The optimal preview control design techniques are illustrated by simulation results for a simple example.

U.S. Army Transformation Towards a Brigade-Centric Model: Lessons Learned for the Spanish Army

Science.gov (United States)

2009-06-12

students at the U.S. Army War College. These essays consider the nature and direction of Transformation, and define its concept. It is far beyond the...Century Transformation of the U.S. Armed Forces”, he [SecDef Rumsfeld] gave a lyrical account of the “transformational battle” of Mazar-e-Sharif, the

Albania’s Transformation since 1997: Successes and Failures

Directory of Open Access Journals (Sweden)

Jusufi Islam

2017-03-01

Full Text Available In 1997 Albania experienced a collapse of order and widespread violence, which resulted in a situation where the government was overthrown and some 2,000 people were killed. The 1997 disorder came as a result of the collapse of fraudulent financial pyramid schemes that had all the features of a war-like economic structure. During the 1997 events, large-scale confiscation and stealing of state assets occurred. Albania’s transitional period from communism to democracy, which began in 1990, led to the establishment of new structures for profiting from the country’s resources. Some of these political and economic structures, in the aftermath of the 1997 events, disappeared and others, including their structural effects, persist and have had an impact on the country’s political stability and economic progress. Today, both the successes and failures of the country are assessed based on the progress that the country has made since the 1997 events. The paper analyses the 1997 events and the transformation of Albania’s political and economic structures between 1997 and 2016, considering both achievements and failures. It looks at how the country has dealt with the post-1997 peace-building and development agenda from the perspective of it being a success. It looks at the factors that led to state failure in 1997 and at the factors that continue and have generated a path dependency to the current political context of the country. Although a lot has been written concerning the 1997 events, very little analysis has been conducted concerning what it means from the perspective of research on state failure. In this context, the proposed paper seeks to offer Albania as a case study example of a transformation process, from the uprising to the current situation, which is characterized as a mixture of successes and failures. The belief is that the proposed paper will point to some lessons learned for the strategies directed at the transformation processes.

Spatiotemporal Signal Analysis via the Phase Velocity Transform

International Nuclear Information System (INIS)

Mattor, Nathan

2000-01-01

The phase velocity transform (PVT) is an integral transform that divides a function of space and time into components that propagate at uniform phase velocities without distortion. This paper examines the PVT as a method to analyze spatiotemporal fluctuation data. The transform is extended to systems with discretely sampled data on a periodic domain, and applied to data from eight azimuthally distributed probes on the Sustained Spheromak Physics Experiment (SSPX). This reveals features not shown by Fourier analysis, particularly regarding nonsinusoidal mode structure. (c) 2000 The American Physical Society

Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

OpenAIRE

Cresson, Jacky; Pierret, Frédéric

2015-01-01

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.

Distortional solutions for loaded semi-discretized thin-walled beams

DEFF Research Database (Denmark)

Andreassen, Michael Joachim; Jönsson, Jeppe

2012-01-01

distortional displacement fields which decouple the reduced order differential equations. In this process the cross section is discretized into finite cross-section elements, and the natural distortional modes as well as the related axial variations are found as solutions to the established coupled fourth...... order homogeneous differential equations of GBT.In this paper the non-homogeneous distortional differential equations of GBT are formulated using this novel semi-discretization process. Transforming these non-homogeneous distortional differential equations into the natural eigenmode space by using...... the distortional modal matrix found for the homogeneous system, we get the uncoupled set of differential equations including the distributed loads. This uncoupling is very important in GBT, since the shear stiffness contribution from St. Venant torsional shear stress as well as “Bredt's shear flow” cannot...

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

Digital Discretion

DEFF Research Database (Denmark)

Busch, Peter Andre; Zinner Henriksen, Helle

2018-01-01

discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...

S-folds and 4d N=3 superconformal field theories

Energy Technology Data Exchange (ETDEWEB)

Aharony, Ofer [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 7610001 (Israel); Tachikawa, Yuji [Department of Physics, Faculty of Science,University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); Kavli Institute for the Physics and Mathematics of the Universe,University of Tokyo, Kashiwa, Chiba 277-8583 (Japan)

2016-06-08

S-folds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by non-trivial S-duality transformations. They were recently used by García-Etxebarria and Regalado to provide the first construction of four dimensional N=3 superconformal theories. In this note, we classify the different variants of these N=3-preserving S-folds, distinguished by an analog of discrete torsion, using both a direct analysis of the different torsion classes and the compactification of the S-folds to three dimensional M-theory backgrounds. Upon adding D3-branes, these variants lead to different classes of N=3 superconformal field theories. We also analyze the holographic duals of these theories, and in particular clarify the role of discrete gauge and global symmetries in holography.

Real-time frequency-to-time mapping based on spectrally-discrete chromatic dispersion.

Science.gov (United States)

Dai, Yitang; Li, Jilong; Zhang, Ziping; Yin, Feifei; Li, Wangzhe; Xu, Kun

2017-07-10

Traditional photonics-assisted real-time Fourier transform (RTFT) usually suffers from limited chromatic dispersion, huge volume, or large time delay and attendant loss. In this paper we propose frequency-to-time mapping (FTM) by spectrally-discrete dispersion to increase frequency sensitivity greatly. The novel media has periodic ON/OFF intensity frequency response while quadratic phase distribution along disconnected channels, which de-chirps matched optical input to repeated Fourier-transform-limited output. Real-time FTM is then obtained within each period. Since only discrete phase retardation rather than continuously-changed true time delay is required, huge equivalent dispersion is then available by compact device. Such FTM is theoretically analyzed, and implementation by cascaded optical ring resonators is proposed. After a numerical example, our theory is demonstrated by a proof-of-concept experiment, where a single loop containing 0.5-meters-long fiber is used. FTM under 400-MHz unambiguous bandwidth and 25-MHz resolution is reported. Highly-sensitive and linear mapping is achieved with 6.25 ps/MHz, equivalent to ~4.6 × 10 4 -km standard single mode fiber. Extended instantaneous bandwidth is expected by ring cascading. Our proposal may provide a promising method for real-time, low-latency Fourier transform.

Discrete pseudo-integrals

Czech Academy of Sciences Publication Activity Database

Mesiar, Radko; Li, J.; Pap, E.

2013-01-01

Roč. 54, č. 3 (2013), s. 357-364 ISSN 0888-613X R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : concave integral * pseudo-addition * pseudo-multiplication Subject RIV: BA - General Mathematics Impact factor: 1.977, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-discrete pseudo-integrals.pdf

Higher-order schemes for the Laplace transformation method for parabolic problems

KAUST Repository

Douglas, C.

2011-01-01

In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely high order convergent. Second, higher-order compact schemes of order four and six are used for the the spatial discretization. Finally, the discretized linear algebraic systems are solved using multigrid to show the actual convergence rate for numerical examples, which are compared to other numerical solution methods. © 2011 Springer-Verlag.

Modelling and real-time simulation of continuous-discrete systems in mechatronics

Energy Technology Data Exchange (ETDEWEB)

Lindow, H. [Rostocker, Magdeburg (Germany)

1996-12-31

This work presents a methodology for simulation and modelling of systems with continuous - discrete dynamics. It derives hybrid discrete event models from Lagrange`s equations of motion. This method combines continuous mechanical, electrical and thermodynamical submodels on one hand with discrete event models an the other hand into a hybrid discrete event model. This straight forward software development avoids numeric overhead.

Robust electrocardiogram (ECG) beat classification using discrete wavelet transform

International Nuclear Information System (INIS)

Minhas, Fayyaz-ul-Amir Afsar; Arif, Muhammad

2008-01-01

This paper presents a robust technique for the classification of six types of heartbeats through an electrocardiogram (ECG). Features extracted from the QRS complex of the ECG using a wavelet transform along with the instantaneous RR-interval are used for beat classification. The wavelet transform utilized for feature extraction in this paper can also be employed for QRS delineation, leading to reduction in overall system complexity as no separate feature extraction stage would be required in the practical implementation of the system. Only 11 features are used for beat classification with the classification accuracy of ∼99.5% through a KNN classifier. Another main advantage of this method is its robustness to noise, which is illustrated in this paper through experimental results. Furthermore, principal component analysis (PCA) has been used for feature reduction, which reduces the number of features from 11 to 6 while retaining the high beat classification accuracy. Due to reduction in computational complexity (using six features, the time required is ∼4 ms per beat), a simple classifier and noise robustness (at 10 dB signal-to-noise ratio, accuracy is 95%), this method offers substantial advantages over previous techniques for implementation in a practical ECG analyzer

Darboux transformation for the NLS equation

International Nuclear Information System (INIS)

Aktosun, Tuncay; Mee, Cornelis van der

2010-01-01

We analyze a certain class of integral equations associated with Marchenko equations and Gel'fand-Levitan equations. Such integral equations arise through a Fourier transformation on various ordinary differential equations involving a spectral parameter. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution in terms of the unperturbed quantities and the finite-rank perturbation. We show that this result provides a fundamental approach to derive Darboux transformations for various systems of ordinary differential operators. We illustrate our theory by providing the explicit Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a simple discrete eigenvalue is added to the spectrum, and thus we also provide a one-parameter family of Darboux transformations for the nonlinear Schroedinger equation.

Technique for image interpolation using polynomial transforms

NARCIS (Netherlands)

Escalante Ramírez, B.; Martens, J.B.; Haskell, G.G.; Hang, H.M.

1993-01-01

We present a new technique for image interpolation based on polynomial transforms. This is an image representation model that analyzes an image by locally expanding it into a weighted sum of orthogonal polynomials. In the discrete case, the image segment within every window of analysis is

Ultradiscrete sine-Gordon Equation over Symmetrized Max-Plus Algebra, and Noncommutative Discrete and Ultradiscrete sine-Gordon Equations

Directory of Open Access Journals (Sweden)

Kenichi Kondo

2013-11-01

Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.

Deteksi Pemalsuan Citra dengan Teknik Copy-Move Menggunakan Metode Ordinal Measure dari Koefisien Discrete Cosine Transform

Directory of Open Access Journals (Sweden)

Zulfan

2016-07-01

Full Text Available This article discusses a new method for the detection of forgery images generated by copy-move technique. Copy-move technique is one of image forgery techniques which taking a particular object from its original image and add it on that image for the purpose of increasing the number of or changing the same object in the original image. This study aims to detect the forged image generated by the copy-move techniques and copy-move forged image that has been modified by the rotation operation and histogram equalization. Detection feature used is Ordinal Measure of Discrete Cosine Transform coefficient (OM-DCT. Detection starts with division of the image into a block size of BXB (B = 16x16, 32x32 and 64x64 and two-dimensional DCT was performed to each of blocks. The feature distance from the original to the fake image, was calculated by the Euclidian distance and each feature has a distance of less than or equal to the threshold value (T according to the observations will be marked as a forged part. The results show that there are blocks detected on the copy-move image, whether on the unmodified copy-move forge image or those which modified by the rotation operation and histogram equalization. The number of blocks that are found in the copy-move object varies according to the size of the detection block used.

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Discrete symmetries and their stringy origin

International Nuclear Information System (INIS)

Mayorga Pena, Damian Kaloni

2014-05-01

Discrete symmetries have proven to be very useful in controlling the phenomenology of theories beyond the standard model. In this work we explore how these symmetries emerge from string compactifications. Our approach is twofold: On the one hand, we consider the heterotic string on orbifold backgrounds. In this case the discrete symmetries can be derived from the orbifold conformal field theory, and it can be shown that they are in close relation with the orbifold geometry. We devote special attention to R-symmetries, which arise from discrete remnants of the Lorentz group in compact space. Further we discuss the physical implications of these symmetries both in the heterotic mini-landscape and in newly constructed models based on the Z 2 x Z 4 orbifold. In both cases we observe that the discrete symmetries favor particular locations in the orbifold where the particles of standard model should live. On the other hand we consider a class of F-theory models exhibiting an SU(5) gauge group, times additional U(1) symmetries. In this case, the smooth compactification background does not permit us to track the discrete symmetries as transparently as in orbifold models. Hence, we follow a different approach and search for discrete subgroups emerging after the U(1)s are broken. We observe that in this approach it is possible to obtain the standard Z 2 matter parity of the MSSM.

S2SA preconditioning for the Sn equations with strictly non negative spatial discretization

International Nuclear Information System (INIS)

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-01-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S n transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use a linear diffusion equation has important implications for preconditioning the S n equations with a strictly non negative spatial discretization in multiple dimensions. (authors)

SU(2 and SU(1,1 Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms

Directory of Open Access Journals (Sweden)

Maurice R. Kibler

2010-07-01

Full Text Available We propose a group-theoretical approach to the generalized oscillator algebra Aκ recently investigated in J. Phys. A: Math. Theor. 2010, 43, 115303. The case κ ≥ 0 corresponds to the noncompact group SU(1,1 (as for the harmonic oscillator and the Pöschl-Teller systems while the case κ < 0 is described by the compact group SU(2 (as for the Morse system. We construct the phase operators and the corresponding temporally stable phase eigenstates for Aκ in this group-theoretical context. The SU(2 case is exploited for deriving families of mutually unbiased bases used in quantum information. Along this vein, we examine some characteristics of a quadratic discrete Fourier transform in connection with generalized quadratic Gauss sums and generalized Hadamard matrices.

Jack Mezirow's Conceptualisation of Adult Transformative Learning: A Review

Science.gov (United States)

Calleja, Colin

2014-01-01

This paper traces the evolution of Jack Mezirow's transformative learning theory and its conceptualisation. It discusses the three major influences, namely Thomas Khun's philosophical conception of paradigm, Freire's conception of conscientisation and consciousness growth, and Habermas' domains of learning and the discussion of…

Design Transformations for Rule-based Procedural Modeling

KAUST Repository

Lienhard, Stefan; Lau, Cheryl; Mü ller, Pascal; Wonka, Peter; Pauly, Mark

2017-01-01

We introduce design transformations for rule-based procedural models, e.g., for buildings and plants. Given two or more procedural designs, each specified by a grammar, a design transformation combines elements of the existing designs to generate new designs. We introduce two technical components to enable design transformations. First, we extend the concept of discrete rule switching to rule merging, leading to a very large shape space for combining procedural models. Second, we propose an algorithm to jointly derive two or more grammars, called grammar co-derivation. We demonstrate two applications of our work: we show that our framework leads to a larger variety of models than previous work, and we show fine-grained transformation sequences between two procedural models.

Design Transformations for Rule-based Procedural Modeling

KAUST Repository

Lienhard, Stefan

2017-05-24

We introduce design transformations for rule-based procedural models, e.g., for buildings and plants. Given two or more procedural designs, each specified by a grammar, a design transformation combines elements of the existing designs to generate new designs. We introduce two technical components to enable design transformations. First, we extend the concept of discrete rule switching to rule merging, leading to a very large shape space for combining procedural models. Second, we propose an algorithm to jointly derive two or more grammars, called grammar co-derivation. We demonstrate two applications of our work: we show that our framework leads to a larger variety of models than previous work, and we show fine-grained transformation sequences between two procedural models.

Cell shape characterization and classification with discrete Fourier transforms and self-organizing maps.

Science.gov (United States)

Kriegel, Fabian L; Köhler, Ralf; Bayat-Sarmadi, Jannike; Bayerl, Simon; Hauser, Anja E; Niesner, Raluca; Luch, Andreas; Cseresnyes, Zoltan

2018-03-01

Cells in their natural environment often exhibit complex kinetic behavior and radical adjustments of their shapes. This enables them to accommodate to short- and long-term changes in their surroundings under physiological and pathological conditions. Intravital multi-photon microscopy is a powerful tool to record this complex behavior. Traditionally, cell behavior is characterized by tracking the cells' movements, which yields numerous parameters describing the spatiotemporal characteristics of cells. Cells can be classified according to their tracking behavior using all or a subset of these kinetic parameters. This categorization can be supported by the a priori knowledge of experts. While such an approach provides an excellent starting point for analyzing complex intravital imaging data, faster methods are required for automated and unbiased characterization. In addition to their kinetic behavior, the 3D shape of these cells also provide essential clues about the cells' status and functionality. New approaches that include the study of cell shapes as well may also allow the discovery of correlations amongst the track- and shape-describing parameters. In the current study, we examine the applicability of a set of Fourier components produced by Discrete Fourier Transform (DFT) as a tool for more efficient and less biased classification of complex cell shapes. By carrying out a number of 3D-to-2D projections of surface-rendered cells, the applied method reduces the more complex 3D shape characterization to a series of 2D DFTs. The resulting shape factors are used to train a Self-Organizing Map (SOM), which provides an unbiased estimate for the best clustering of the data, thereby characterizing groups of cells according to their shape. We propose and demonstrate that such shape characterization is a powerful addition to, or a replacement for kinetic analysis. This would make it especially useful in situations where live kinetic imaging is less practical or not

Managing the Transformation: A Change Management Strategy for U.S. Marine Corps Expeditionary Energy Initiatives

Science.gov (United States)

2017-12-01

sensegiving in transformational change processes from the bottom up. Higher Education , 65(6), 761–780. doi:10.1007/s10734-012-9575-7 Kezar, A...NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS Approved for public release. Distribution is unlimited. MANAGING THE TRANSFORMATION : A...DATE December 2017 3. REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE MANAGING THE TRANSFORMATION : A CHANGE MANAGEMENT STRATEGY

DROpS: an object of learning in computer simulation of discrete events

Directory of Open Access Journals (Sweden)

Hugo Alves Silva Ribeiro

2015-09-01

Full Text Available This work presents the “Realistic Dynamics Of Simulated Operations” (DROpS, the name given to the dynamics using the “dropper” device as an object of teaching and learning. The objective is to present alternatives for professors teaching content related to simulation of discrete events to graduate students in production engineering. The aim is to enable students to develop skills related to data collection, modeling, statistical analysis, and interpretation of results. This dynamic has been developed and applied to the students by placing them in a situation analogous to a real industry, where various concepts related to computer simulation were discussed, allowing the students to put these concepts into practice in an interactive manner, thus facilitating learning

Baecklund transformations as exact integrable time discretizations for the trigonometric Gaudin model

International Nuclear Information System (INIS)

Ragnisco, Orlando; Zullo, Federico

2010-01-01

We construct a two-parameter family of Baecklund transformations for the trigonometric classical Gaudin magnet. The approach follows closely the one introduced by Sklyanin and Kuznetsov (1998 J. Phys. A: Math. Gen. 31 2241-51) in a number of seminal papers and takes advantage of the intimate relation between the trigonometric and the rational case. As in the paper by Hone, Kuznetsov and one of the authors (OR) (2001 J. Phys. A: Math. Gen. 34 2477-90) the Baecklund transformations are presented as explicit symplectic maps, starting from their Lax representation. The (expected) connection with the xxz Heisenberg chain is established and the rational (xxx) case is recovered in a suitable limit. It is shown how to obtain a 'physical' transformation mapping real variables into real variables. The interpolating Hamiltonian flow is derived and some numerical iterations of the map are presented.

An Analog Circuit Approximation of the Discrete Wavelet Transform for Ultra Low Power Signal Processing in Wearable Sensor Nodes.

Science.gov (United States)

Casson, Alexander J

2015-12-17

Ultra low power signal processing is an essential part of all sensor nodes, and particularly so in emerging wearable sensors for biomedical applications. Analog signal processing has an important role in these low power, low voltage, low frequency applications, and there is a key drive to decrease the power consumption of existing analog domain signal processing and to map more signal processing approaches into the analog domain. This paper presents an analog domain signal processing circuit which approximates the output of the Discrete Wavelet Transform (DWT) for use in ultra low power wearable sensors. Analog filters are used for the DWT filters and it is demonstrated how these generate analog domain DWT-like information that embeds information from Butterworth and Daubechies maximally flat mother wavelet responses. The Analog DWT is realised in hardware via g(m)C circuits, designed to operate from a 1.3 V coin cell battery, and provide DWT-like signal processing using under 115 nW of power when implemented in a 0.18 μm CMOS process. Practical examples demonstrate the effective use of the new Analog DWT on ECG (electrocardiogram) and EEG (electroencephalogram) signals recorded from humans.

An Analog Circuit Approximation of the Discrete Wavelet Transform for Ultra Low Power Signal Processing in Wearable Sensor Nodes

Directory of Open Access Journals (Sweden)

Alexander J. Casson

2015-12-01

Full Text Available Ultra low power signal processing is an essential part of all sensor nodes, and particularly so in emerging wearable sensors for biomedical applications. Analog signal processing has an important role in these low power, low voltage, low frequency applications, and there is a key drive to decrease the power consumption of existing analog domain signal processing and to map more signal processing approaches into the analog domain. This paper presents an analog domain signal processing circuit which approximates the output of the Discrete Wavelet Transform (DWT for use in ultra low power wearable sensors. Analog filters are used for the DWT filters and it is demonstrated how these generate analog domain DWT-like information that embeds information from Butterworth and Daubechies maximally flat mother wavelet responses. The Analog DWT is realised in hardware via g m C circuits, designed to operate from a 1.3 V coin cell battery, and provide DWT-like signal processing using under 115 nW of power when implemented in a 0.18 μm CMOS process. Practical examples demonstrate the effective use of the new Analog DWT on ECG (electrocardiogram and EEG (electroencephalogram signals recorded from humans.

Practical Aspects of Log-ratio Coordinate Representations in Regression with Compositional Response

Directory of Open Access Journals (Sweden)

Fišerová Eva

2016-10-01

Full Text Available Regression analysis with compositional response, observations carrying relative information, is an appropriate tool for statistical modelling in many scientific areas (e.g. medicine, geochemistry, geology, economics. Even though this technique has been recently intensively studied, there are still some practical aspects that deserve to be further analysed. Here we discuss the issue related to the coordinate representation of compositional data. It is shown that linear relation between particular orthonormal coordinates and centred log-ratio coordinates can be utilized to simplify the computation concerning regression parameters estimation and hypothesis testing. To enhance interpretation of regression parameters, the orthogonal coordinates and their relation with orthonormal and centred log-ratio coordinates are presented. Further we discuss the quality of prediction in different coordinate system. It is shown that the mean squared error (MSE for orthonormal coordinates is less or equal to the MSE for log-transformed data. Finally, an illustrative real-world example from geology is presented.

Pathological Brain Detection Using Weiner Filtering, 2D-Discrete Wavelet Transform, Probabilistic PCA, and Random Subspace Ensemble Classifier

Directory of Open Access Journals (Sweden)

Debesh Jha

2017-01-01

Full Text Available Accurate diagnosis of pathological brain images is important for patient care, particularly in the early phase of the disease. Although numerous studies have used machine-learning techniques for the computer-aided diagnosis (CAD of pathological brain, previous methods encountered challenges in terms of the diagnostic efficiency owing to deficiencies in the choice of proper filtering techniques, neuroimaging biomarkers, and limited learning models. Magnetic resonance imaging (MRI is capable of providing enhanced information regarding the soft tissues, and therefore MR images are included in the proposed approach. In this study, we propose a new model that includes Wiener filtering for noise reduction, 2D-discrete wavelet transform (2D-DWT for feature extraction, probabilistic principal component analysis (PPCA for dimensionality reduction, and a random subspace ensemble (RSE classifier along with the K-nearest neighbors (KNN algorithm as a base classifier to classify brain images as pathological or normal ones. The proposed methods provide a significant improvement in classification results when compared to other studies. Based on 5×5 cross-validation (CV, the proposed method outperforms 21 state-of-the-art algorithms in terms of classification accuracy, sensitivity, and specificity for all four datasets used in the study.

Theoretical foundation for jung's “Mandala Symbolism” based on discrete chaotic dynamics of interacting neurons

Directory of Open Access Journals (Sweden)

V. Gontar

2000-01-01

Full Text Available Based on discrete chaotic dynamics algorithms different patterns in a form of mandalas have been generated. This fact gives us the possibility to make a link between mechanism of biochemical reaction dynamics undergoing in brain resulted to the brain creativity process in form of mandalas. Obtained patterns can be related to the space distributed chemicals according to the law of extended principle of maximum entropy, consideration of the information exchange during biochemical transformations, mass conservation law and discrete chaotic dynamics principles.

Police investigations: discretion denied yet undeniably exercised

Science.gov (United States)

Belur, J.; Tilley, N.; Osrin, D.; Daruwalla, N.; Kumar, M.; Tiwari, V.

2014-01-01

Police investigations involve determining whether a crime has been committed, and if so what type of crime, who has committed it and whether there is the evidence to charge the perpetrators. Drawing on fieldwork in Delhi and Mumbai, this paper explores how police investigations unfolded in the specific context of women’s deaths by burning in India. In particular, it focuses on the use of discretion despite its denial by those exercising it. In India, there are distinctive statutes relating to women’s suspicious deaths, reflecting the widespread expectation that the bride’s family will pay a dowry to the groom’s family and the tensions to which this may on occasion give rise in the early years of a marriage. Often, there are conflicting claims influencing how the woman’s death is classified. These in turn affect police investigation. The nature and direction of police discretion in investigating women’s deaths by burning reflect in part the unique nature of the legislation and the particular sensitivities in relation to these types of death. They also highlight processes that are liable to be at work in any crime investigation. It was found that police officers exercised unacknowledged discretion at seven specific points in the investigative process, with potentially significant consequences for the achievement of just outcomes: first response, recording the victim’s ‘dying declaration’, inquest, registering of the ‘First Information Report’, collecting evidence, arrest and framing of the charges. PMID:26376482

Structural transformation of MoO3 nanobelts into MoS2 nanotubes

International Nuclear Information System (INIS)

Deepak, Francis Leonard; Mayoral, Alvaro; Yacaman, Miguel Jose

2009-01-01

The structural transformation of MoO 3 nanobelts into MoS 2 nanotubes using a simple sulfur source has been reported. This transformation has been extensively investigated using electron microscopic and spectroscopic techniques including scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), electron diffraction (ED), and energy-dispersive X-ray analysis (SEM-EDAX and TEM-EDX). The method described in this report will serve as a generic route for the transformation of other oxide nanostructures into the chalcogenide nanostructures. (orig.)

Visualization of a Turbulent Jet Using Wavelets

Institute of Scientific and Technical Information of China (English)

Hui LI

2001-01-01

An application of multiresolution image analysis to turbulence was investigated in this paper, in order to visualize the coherent structure and the most essential scales governing turbulence. The digital imaging photograph of jet slice was decomposed by two-dimensional discrete wavelet transform based on Daubechies, Coifman and Baylkin bases. The best choice of orthogonal wavelet basis for analyzing the image of the turbulent structures was first discussed. It is found that these orthonormal wavelet families with index N＜10 were inappropriate for multiresolution image analysis of turbulent flow. The multiresolution images of turbulent structures were very similar when using the wavelet basis with the higher index number, even though wavelet bases are different functions. From the image components in orthogonal wavelet spaces with different scales, the further evident of the multi-scale structures in jet can be observed, and the edges of the vortices at different resolutions or scales and the coherent structure can be easily extracted.

Becoming-evolutionary? : Animal Transformations in Kingsley’s Alton Locke

NARCIS (Netherlands)

Moore, B.P.

2017-01-01

Focusing on Chapter 36 of Charles Kingsley’s novel Alton Locke (1850), where the hero recounts a dream during which he undergoes a series of transformations into various animals, beginning at ‘the lowest point of created life’ as a madrepore or coral, and culminating with the early history of

An automatic system for Turkish word recognition using Discrete Wavelet Neural Network based on adaptive entropy

International Nuclear Information System (INIS)

Avci, E.

2007-01-01

In this paper, an automatic system is presented for word recognition using real Turkish word signals. This paper especially deals with combination of the feature extraction and classification from real Turkish word signals. A Discrete Wavelet Neural Network (DWNN) model is used, which consists of two layers: discrete wavelet layer and multi-layer perceptron. The discrete wavelet layer is used for adaptive feature extraction in the time-frequency domain and is composed of Discrete Wavelet Transform (DWT) and wavelet entropy. The multi-layer perceptron used for classification is a feed-forward neural network. The performance of the used system is evaluated by using noisy Turkish word signals. Test results showing the effectiveness of the proposed automatic system are presented in this paper. The rate of correct recognition is about 92.5% for the sample speech signals. (author)

The short time Fourier transform and local signals

Science.gov (United States)

Okumura, Shuhei

In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

Bäcklund transformations and Hamiltonian flows

International Nuclear Information System (INIS)

Zullo, Federico

2013-01-01

In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)

Entropic Phase Maps in Discrete Quantum Gravity

Directory of Open Access Journals (Sweden)

Benjamin F. Dribus

2017-06-01

Full Text Available Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar models appearing in the literature, such as causal sets. Path summation defined in terms of these histories enables derivation of discrete Schrödinger-type equations describing quantum spacetime dynamics for any suitable choice of algebraic quantities associated with each evolutionary pathway. These quantities, called phases, collectively define a phase map from the space of evolutionary pathways to a target object, such as the unit circle S 1 ⊂ C , or an analogue such as S 3 or S 7 . This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of S 1 -valued maps defined in terms of “structural increments” of histories, called terminal states. Invariants such as state automorphism groups determine multiplicities of states, and induce families of natural entropy functions. A phase map defined in terms of such a function is called an entropic phase map. The associated dynamical law may be viewed as an abstract combination of Schrödinger’s equation and the second law of thermodynamics.

Universal discrete Fourier optics RF photonic integrated circuit architecture.

Science.gov (United States)

Hall, Trevor J; Hasan, Mehedi

2016-04-04

This paper describes a coherent electro-optic circuit architecture that generates a frequency comb consisting of N spatially separated orders using a generalised Mach-Zenhder interferometer (MZI) with its N × 1 combiner replaced by an optical N × N Discrete Fourier Transform (DFT). Advantage may be taken of the tight optical path-length control, component and circuit symmetries and emerging trimming algorithms offered by photonic integration in any platform that offers linear electro-optic phase modulation such as LiNbO3, silicon, III-V or hybrid technology. The circuit architecture subsumes all MZI-based RF photonic circuit architectures in the prior art given an appropriate choice of output port(s) and dimension N although the principal application envisaged is phase correlated subcarrier generation for all optical orthogonal frequency division multiplexing. A transfer matrix approach is used to model the operation of the architecture. The predictions of the model are validated by simulations performed using an industry standard software tool. Implementation is found to be practical.

On Discrete Killing Vector Fields and Patterns on Surfaces

KAUST Repository

Ben-Chen, Mirela

2010-09-21

Symmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape\\'s aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented using infinitesimal rigid transformations, which are given as tangent vector fields on the surface - known as Killing Vector Fields. As exact symmetries are quite rare, especially when considering noisy sampled surfaces, we propose a method for relaxing the exact symmetry constraint to allow for approximate symmetries and approximate Killing Vector Fields, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal compilation © 2010 The Eurographics Association and Blackwell Publishing Ltd.

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2017-01-01

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

A Top-Down Account of Linear Canonical Transforms

Directory of Open Access Journals (Sweden)

Kurt Bernardo Wolf

2012-06-01

Full Text Available We contend that what are called Linear Canonical Transforms (LCTs should be seen as a part of the theory of unitary irreducible representations of the '2+1' Lorentz group. The integral kernel representation found by Collins, Moshinsky and Quesne, and the radial and hyperbolic LCTs introduced thereafter, belong to the discrete and continuous representation series of the Lorentz group in its parabolic subgroup reduction. The reduction by the elliptic and hyperbolic subgroups can also be considered to yield LCTs that act on functions, discrete or continuous in other Hilbert spaces. We gather the summation and integration kernels reported by Basu and Wolf when studiying all discrete, continuous, and mixed representations of the linear group of 2×2 real matrices. We add some comments on why all should be considered canonical.

CKM and PMNS mixing matrices from discrete subgroups of SU(2)

International Nuclear Information System (INIS)

Potter, Franklin

2015-01-01

Remaining within the realm of the Standard Model(SM) local gauge group, this first principles derivation of both the PMNS and CKM matrices utilizes quaternion generators of the three discrete (i.e., finite) binary rotational subgroups of SU(2) called [3,3,2], [4,3,2], and [5,3,2] for three lepton families in R 3 and four related discrete binary rotational subgroups [3,3,3], [4,3,3], [3,4,3], and [5,3,3] represented by four quark families in R 4 . The traditional 3x3 CKM matrix is extracted as a submatrix of the 4x4 CKM4 matrix. If these two additional quarks b' and t' of a 4th quark family exist, there is the possibility that the SM lagrangian may apply all the way down to the Planck scale. There are then numerous other important consequences. The Weinberg angle is derived using these same quaternion generators, and the triangle anomaly cancellation is satisfied even though there is an obvious mismatch of three lepton families to four quark families. In a discrete space, one can also use these generators to derive a unique connection from the electroweak local gauge group SU(2) L x U(1) Y acting in R 4 to the discrete group Weyl E 8 in R 8 . By considering Lorentz transformations in discrete (3,1)-D spacetime, one obtains another Weyl E 8 discrete symmetry group in R 8 , so that the combined symmetry is Weyl E 8 x Weyl E 8 = 'discrete' SO(9,1) in 10-D spacetime. This unique connection is in direct contrast to the 10 500 possible connections for superstring theory! (paper)

Social Work Discretion between Professionalism and Managerialism in Denmark

DEFF Research Database (Denmark)

Skals, Anette

working with clients who are unfit for work or work market as a result of ill health. In Denmark the local municipal Job Centre is the primary service delivery involved in welfare-to-work. Here values, interest and policies, transformed into rules and regulation, meet the concrete practices of welfare-to-work...... for working in order to helping clients in becoming self-supporting after ill health. As well as examining how social work discretion is made possible in the work organization, the research behind the paper focuses on the issue of new forms of professionalism in social work. In the light of policy changes......Professionalism and managerialism are important and conflicting concepts in the study of professionals working in public service organizations. By focusing on street-level social workers and social work discretion, it is possible to see how welfare-to-work policies are practiced as well as how...

Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations

Directory of Open Access Journals (Sweden)

Zhinan Xia

2014-01-01

Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.

DISCRETE MATHEMATICS/NUMBER THEORY

OpenAIRE

Mrs. Manju Devi*

2017-01-01

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

Science.gov (United States)

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved

Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues

International Nuclear Information System (INIS)

Maruno, Ken-ichi; Biondini, Gino

2004-01-01

We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)

Discrete symmetries in the Weyl expansion for quantum billiards

International Nuclear Information System (INIS)

Pavloff, N.

1994-01-01

2 and 3 dimensional quantum billiards with discrete symmetries are considered. The boundary condition is either Dirichlet or Neumann. The first terms of the Weyl expansion are derived for the level density projected onto the irreducible representations of the symmetry group. The formulae require only the knowledge of the character table of the group and the geometrical properties (such as surface, perimeter etc.) of sub-parts of the billiard invariant under a group transformation. (author). 17 refs., 1 fig., 1 tab