Fourier Algorithm Research Articles

An object‐oriented bulk synchronous parallel library for multicore programming

SUMMARYWe show that the bulk synchronous parallel (BSP) model, originally designed for distributed‐memory systems, is also applicable for shared‐memory multicore systems and, furthermore, that BSP libraries are useful in scientific computing on these systems. A proof‐of‐concept MulticoreBSP library has been implemented in Java, and is used to show that BSP algorithms can attain proper speedups on multicore architectures. This library is based on the BSPlib implementation, adapted to an object‐oriented setting. In comparison, the number of function primitives is reduced, while the overall design simplicity is improved. We detail applying the BSP model and library on the sparse matrix–vector (SpMV) multiplication problem, and show by performing numerical experiments that the resulting BSP SpMV algorithm attains speedups, in one case reaching a speedup of 3.5 for 4 threads. Whereas not described in detail in this paper, algorithms for the fast Fourier transform and the dense LU decomposition are also investigated; in one case, attaining superlinear speedups of 5 for 4 threads. The predictability of BSP algorithms in the case of the SpMV is also investigated. Copyright © 2011 John Wiley & Sons, Ltd.

Design and Development of Intelligent Release Control Unit Based on LPC2478

Intelligent release is core control unit of intelligent appliances, which is used to protect power system and power devices from damage under the faults. In this paper, with LPC2478 as Microcontroller, an intelligent release control unit with Ethernet communication functionality was presented. The intelligent release control unit’s basic functions and extended functions were described in brief. Implementation method of control unit was illustrated in detail. Process flow chart for fault diagnosis was supplied. Full-wave Fourier algorithm was adopted to compute fundamental components and harmonic components to filter decaying DC component and non-integer harmonic. This release can be adjusted according to the requirement of power quality to avoid malfunction under the circumstance that non-fault current and voltage fluctuation occur. Furthermore, through Ethernet communication, more functionality can be implemented to make the release more intelligent.

Calculation about the Fundamental Wave Amplitude of the Current in the Distribution Line on Wavelet Analysis

Wavelet analysis, as a new kind of time-frequency representation technique, has made great progress recently and been applied widely in different engineering practice. To solve the problem of full-wave Fourier algorithm which is disable to filter decaying DC component and has worse frequency characteristic, it is presented an improved algorithm depending on the combination of subtraction filter and full-wave Morlet complex wavelet, to get out the fundamental wave amplitude of the current in the distribution line, by studying each parameter’s influence on the performances of Morlet complex wavelet algorithm. It can filter decaying DC component efficiently and has better frequency characteristic.

Projected changes in thermal seasons and the growing season in Finland

AbstractThe durations of the thermal seasons and the growing season till the end of this century are inferred from projected monthly mean temperatures, separately for the SRES A2 and B1 scenarios. For the baseline period 1971‐2000, we use a high‐resolution observational data set covering Finland, and an average of the temperature responses simulated by 19 global climate models (GCMs) is added to the observed temperatures to obtain projections for the future. Daily climatological temperatures, needed for the determination of the onset and end dates of the seasons and the effective temperature sum, are derived from the monthly means employing a Fourier algorithm that can reproduce monthly mean temperatures perfectly.Under baseline conditions, there are four thermal seasons everywhere in Finland apart from the elevated area in north‐western Lapland. Under the A2 scenario, thermal winter will disappear in the South‐western part of the country by the period 2070‐2099. Elsewhere winter shortens by 2‐4 months. Summer lengthens by slightly over 1 month. Intermediate seasons become longer everywhere except in northernmost Lapland. The thermal growing season lengthens in inland areas by 40‐50 days, on the south‐western coast even more. The effective temperature sum doubles in the north and increases 1.5‐fold in the south. Conditions in Lapland would thus resemble those currently prevailing in southern Finland. Under the B1 scenario the change is smaller, especially in the second half of the century.The robustness of the findings was assessed by considering the differences between the temperature change projections of the various models. The uncertainty in the onset and termination dates was typically of the order of ±2 weeks. Regional downscaling based on regional climate model (RCM) data did not alter the main conclusions. Copyright © 2010 Royal Meteorological Society

Algebraic Signal Processing Theory: Cooley–Tukey-Type Algorithms for Polynomial Transforms Based on Induction

A polynomial transform is the multiplication of an input vector by a matrix whose th element is defined as for polynomials from a list and sample points from a list . Such transforms find applications in the areas of signal processing, data compression, and function interpolation. An important example includes the discrete Fourier transform. In this paper we introduce a novel technique to derive fast algorithms for polynomial transforms. The technique uses the relationship between polynomial transforms and the representation theory of polynomial algebras. Specifically, we derive algorithms by decomposing the regular modules of these algebras as a stepwise induction. As an application, we derive novel general-radix algorithms for the discrete Fourier transform and the discrete cosine transform of type 4.

An Approach of Multiscale Complexity in Texture Analysis of Lymphomas

Complexity is considered with high interest to texture analysis, such as the application of lymphoma inspection. Previously, multiscale entropy was proposed to account for the multiple time scales inherent in complex biological signals, and complexity texture descriptors were considered for content-based medical image retrieval system. However, in the past, these complexity texture descriptors were derived by linear algorithms of Fourier and wavelet transforms. In this study, we introduce a new approach of multiscale complexity (MSC) for texture analysis of lymphomas based on a nonlinear parameter of entropy. An extended algorithm of 2-D entropy was used in the calculations of complexities for the coarse-grained images of different scale factors. Furthermore, five parameters are defined to characterize 58 images of reactive lymphadenopahty and five categories of lymphomas using complexity on three scales and the changes of complexity between two successive scales. MSC analysis performed well to figure out the statistical differences of paired comparisons picked from reactive lymphadenopahty and five categories of lymphomas.

Study on Hardware and Software Realization of Harmonic Detection in Power System

This article introduces a harmonic detection device based on ARM/ DSP. This device uses DSP technology to analysis the harmonic wave in the power system by using complex sequence fast Fourier algorithm, and realizes the power system harmonic on-line detection with the strong control function of ARM module. It overcomes the inconsistency of the time sequence in communicating between DSP and ARM, and solves the synchronous sampling problem of each phase voltage for data acquisition module. In the program it mainly solves the HPI interface of data communication problem between DSP and ARM. Practical applications show that the device can rapidly and accurately detect characterization of power quality, and realize the telecommunication of the power grid data. It can detcet data accurately and reach the level of practical applications.

Remote sensing of atmospheric refractivity from field measurements of vertical receiver array

In this paper we put forward a possibility of refractive index profile retrieval using field measurements at an array of radio receivers through the variational adjoint approach. The derivation of the adjoint model begins with the electromagnetic parabolic equation for a smooth, perfectly conducting surface and horizontal polarization conditions. To deal with the ill-posed difficulties of the inversion, the regularization idea is introduced into the establishment of the cost function. Based on the variational assimilation idea, the retrieval iterative format is constructed. Numerical experiments demonstrate the feasibility of theoretic algorithm for refractivity estimation. However, using the split-step Fourier algorithm to solve the forward model and the adjoint model, the intrinsic error of the solutions will increase with the extension of the propagation range, which reduces the inversion accuracy at long distance propagation. Through adopting a good initial refractivity profile and introducing the background fields in the cost function the inversions could generally be improved.

Numerical study of Hermite-Gaussian beams in nonlocal thermal media

Based on the nonlocal nonlinear Schrdinger equation and Poisson equation of thermal diffusion, using the slip-step Fourier algorithm and multi-grid method, we numerically investigated the propagation properties of Hermite-Guassian beams in the nonlocal thermal media. The results show that low-order Hermite-Gaussian beams can propagate stably, in contrast with the unstable propagation of high-order Hermite-Gaussian beams. The worse the stability is, the higher the order is. The effect of the boundary of the sample with different cross sections on the propagation properties of Hermite-Guassian beam is also discussed in detail. We found that propagation properties in square geometry are in agreement with those in Snyder-Mitchell model. However, in rectangular sample, the evolution of intensity distribution of Hermite-Gaussian beams differs seriously from that in the square sample.

Rogue waves: Classification, measurement and data analysis, and hyperfast numerical modeling

The last twenty years has seen the birth and subsequent evolution of a fundamental new idea in nonlinear wave research: Rogue waves, freak waves or extreme events in the wave field dynamics can often be classified as coherent structure solutions of the requisite nonlinear partial differential wave equations (PDEs). Since a large number of generic nonlinear PDEs occur across many branches of physics, the approach is widely applicable to many fields including the dynamics of ocean surface waves, internal waves, plasma waves, acoustic waves, nonlinear optics, solid state physics, geophysical fluid dynamics and turbulence (vortex dynamics and nonlinear waves), just to name a few. The first goal of this paper is to give a classification scheme for solutions of this type using the inverse scattering transform (IST) with periodic boundary conditions. In this context the methods of algebraic geometry give the solutions of particular PDEs in terms of Riemann theta functions. In the classification scheme the Riemann spectrum fully defines the coherent structure solutions and their mutual nonlinear interactions. I discuss three methods for determining the Riemann spectrum: (1) algebraic-geometric loop integrals, (2) Schottky uniformization and (3) the Nakamura-Boyd approach. I give an overview of several nonlinear wave equations and graph some of their coherent structure solutions using theta functions. The second goal is to discuss how theta functions can be used for developing data analysis (nonlinear Fourier) algorithms; nonlinear filtering techniques allow for the extraction of coherent structures from time series. The third goal is to address hyperfast numerical models of nonlinear wave equations (which are thousands of times faster than traditional spectral methods).

Modeling elasto-plastic indentation on layered materials using the equivalent inclusion method

This paper develops a fast semi-analytical model for solving the three-dimensional elasto-plastic contact problems involving layered materials using the Equivalent Inclusion Method (EIM). The analytical elastic solutions of a half-space subjected to a unit surface pressure and a unit subsurface eigenstrain are employed in this model; the topmost layer is simulated by an equivalent inclusion with fictitious eigenstrain. Accumulative plastic deformation is determined by a procedure involving an iterative plasticity loop and an incremental loading process. Algorithms of the fast Fourier transform (FFT) and the Conjugate Gradient Method (CGM) are utilized to improve the computation efficiency. An analytical elastic solution of layered body contact ( O’Sullivan and King, 1988) and an indentation experiment result involving a layered substrate ( Michler et al., 1999) are used to examine the accuracy of this model. Comparisons between numerical results from the present model and a commercial FEM software (Abaqus) are also presented. Case studies of a rigid ball loaded against a layered elasto-plastic half-space are conducted to explore the effects of the modulus, yield strength, and thickness of the coating on the hardness, stiffness, and plastic deformation of the composite body.

Calibration algorithm for Fourier transform spectrometer with thermal instabilities

Complex domain calibration is an efficient method to correct the amplitude and phase of a spectrum obtained from a Fourier transform spectrometer. This method is, however, not directly applicable in the occurrence of a zero path difference (ZPD) shift between a scene interferogram and calibration blackbody interferograms. This situation is likely to happen for a system with thermal instabilities. It is found that a ZPD shift smaller than 1 sampling point can cause a large disagreement between the spectra evaluated from the two interferometer sweep directions. We have developed an algorithm for a complex calibration in the presence of ZPD shifts. The restricting aspect of the real-time capability is taken into account.

Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets

Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D (15)N- and (13)C-edited NOESY-HSQC spectra of human ubiquitin.

Modeling the acoustic vector field using parabolic equation and normal mode models.

Numerical algorithms for computing the acoustic vector field, i.e., particle velocity and pressure from an acoustic propagation model, are introduced. Implementation using both a parabolic equation and normal mode approach is considered. The parabolic equation model employed uses a split-step Fourier algorithm, although application of the technique is general to other parabolic equation models. Expressions for the normal mode equations are also presented for both coupled and adiabatic mode models. Results for a Pekeris waveguide are presented for a point source, prompting a brief discussion of multipath influence on the estimation of the direction of energy flow. Approximate analytic solutions are used to validate the general results of both models. Results for the range-dependent benchmark wedge are then presented and show generally good agreement between the two types of models. The results from the two-way, coupled normal mode model provide potential benchmark solutions for the wedge and a means of confirming the accuracy of other models. [Work supported by ONR 321OA.]

Combinatorial Sublinear-Time Fourier Algorithms

We study the problem of estimating the best k term Fourier representation for a given frequency sparse signal (i.e., vector) A of length N≫k. More explicitly, we investigate how to deterministically identify k of the largest magnitude frequencies of $\hat{\mathbf{A}}$, and estimate their coefficients, in polynomial(k,log N) time. Randomized sublinear-time algorithms which have a small (controllable) probability of failure for each processed signal exist for solving this problem (Gilbert et al. in ACM STOC, pp. 152–161, 2002; Proceedings of SPIE Wavelets XI, 2005). In this paper we develop the first known deterministic sublinear-time sparse Fourier Transform algorithm which is guaranteed to produce accurate results. As an added bonus, a simple relaxation of our deterministic Fourier result leads to a new Monte Carlo Fourier algorithm with similar runtime/sampling bounds to the current best randomized Fourier method (Gilbert et al. in Proceedings of SPIE Wavelets XI, 2005). Finally, the Fourier algorithm we develop here implies a simpler optimized version of the deterministic compressed sensing method previously developed in (Iwen in Proc. of ACM-SIAM Symposium on Discrete Algorithms (SODA’08), 2008).

Low Computational Complexity, Low Power, and Low Area Design for the Implementation of Recursive DFT and IDFT Algorithms

A novel recursive algorithm for discrete Fourier transform (DFT) and its inverse transform (IDFT) is proposed in this brief. It was found that the proposed algorithm and its implementation outperformed other existing recursive algorithms. The proposed algorithm was found to 1) reduce multiplication computations by 50.5% using the symmetric identity of coefficients and a resource-sharing technique and register-splitting scheme; 2) decrease read-only memory sizes by 50% compared with conventional algorithms; 3) reduce the number of multipliers implemented by 80% compared with the latest algorithm; and 4) increase data throughput by 100% per transformation. This design is suitable for communication systems and digital radio mondiale (DRM) systems, such as dual-tone multifrequency detection and coded orthogonal frequency-division-multiplexing modulation. The algorithm was designed and fabricated using a 0.18 ?m 1P6M complementary metal-oxide-semiconductor process. The core area is 397 × 388 ?m2, including the DFT and IDFT modules. For modern applications (voice over packet and DRM), this processor only consumes 2.96 mW at 25 MHz. Furthermore, it can calculate the 212/165/106/288/256/176/112-point DFTs and IDFTs.

Fourier treatment to the diffractive optical element composed of Fresnel zone and pinholes

Currently, the minimum feature size fabricated is about 15–40 nm. The resolution of Fresnel zone plates is limited by the width of the outermost zone. Although the photon sieves make it possible to focus soft X-rays to spot sizes smaller than the diameter of the smallest pinhole they have low diffraction efficiency. In order to foster strengths and circumvent weaknesses of them, we propose a new model which is composed of Fresnel zone and pinholes and give its fast Fourier algorithm. The simulation results demonstrate that the resolution of photon sieves is not better than that of Fresnel zone plates in low order of local rings. In this case, we can substitute pinholes for Fresnel zone in photon sieves. Resolution is nearly a constant, and also the diffraction efficiency improves.

Complex-exponential Fourier neuronal network and its hidden-neuron growing algorithm

Based on the approximation theory of Fourier-series working in square integrable space, a Fourier neuronal network was constructed by using activation functions of the complex exponential form. Then a weights-direct-determination method was derived to decide the neural-network weights immediately, which remedied the weaknesses of conventional BP neural networks such as small convergence rate, easily converging to local minimum and possibly lengthy or oscillatory learning process. A hidden-neurons-growing algorithm was presented to adjust the neural-network structure adaptively. Theoretical analysis and simulation results substantiate further that the presented Fourier neural network and algorithm could have good properties of high-precision learning, noise-suppressing and discontinuous-function approximating.

Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation

The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe3O4 core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.

An improved windowed Fourier transform for fringe demodulation

A modified algorithm of windowed Fourier transform (WFT) for phase retrieval from electronic speckle-shearing fringe patterns with carriers is proposed. The algorithm is based on the introduction of a fast Fourier transform (FFT) in WFT to reduce computation time for fringe demodulation. Since boundary effects in FFT will influence the accuracy of phase retrieval, the Gerchberg method is employed to extrapolate the fringe pattern at the boundaries to reduce boundary effects. A theoretical analysis of the algorithm is presented. Both simulated and experimental results show that the proposed method has reduced the computation time significantly compared with the convolution method of WFT without sacrificing measurement accuracy.