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In this paper, a new algorithm to solve the elastic quarter-space, the eighth-space and the finite-length-space contact problems is proposed. This corresponds to an extension of the Hertz theory. The theoretical foundations of such a problem are limited, due to the presence of displacements at the free edges- or stresses at the virtual edges — resulting to complex boundary conditions. The new approach presented here is 3D and based on Guilbault's ingenious fast correction method. In this approach, the edge effects are taken into account by introducing two corrective factors ψ 1 , ψ 2 respectively on the (O x) and (O z) axes to replace the mirror pressure iterative process of Hetenyi. The exact numerical values of these two correction factors are derived analytically. The results show that the free edge can substantially increase locally the contact pressure and therefore the stresses and displacement fields if close to the contact area. So the pressure field and the contact zone present an asymmetry which is more pronounced as the free edge is getting closer. This study is carried out on spaces with one, two and four free edges which will be respectively called: quarter-space, eighth-space and finite-length-space. A validation is performed using a Finite Element Method (FEM) analysis. A parametric study is also performed to exhibit the differences with the Hertz solution, including in the situation where one expects the truncation of the contact area when the free edge is virtually located within the Hertz contact area. • A new algorithm to solve the elastic finite space contact problem is proposed. • Two corrective factors called ψ 1 and ψ 2 are derived from hyper-geometric series. • Surprisingly the contact print moves away from the free edge when it comes closer. • The maximum contact pressure increases when the free edge comes closer. • The model has been validated with the Finite Element Method. [ABSTRACT FROM AUTHOR]

Simulation of the devastating excitations such as the ground motion and transient extreme winds is an important task in the structural response analysis when it comes to the nonlinearity, system stochasticity, parametric excitations and so on. Although the classic spectral representation method (SRM) is widely used in the nonstationary process simulation, it suffers from lower efficiency due to the unavailability of use of fast Fourier transform (FFT). In this study, the classic SRM is extended to the nonstationary process with the time-varying coherence. Then, the FFT-aided and almost accurate simulation algorithm for the nonstationary process with the time-varying coherence is developed with the help of the proper orthogonal decomposition (POD) which is used to factorize the decomposed evolutionary spectra. Especially, the more efficient simulation for the nonstationary process with time-invariant coherence is also proposed, where the spectral matrix decomposition, use of POD and execution of FFT can be reduced significantly. Two examples including downburst and typhoon winds are employed to evaluate the accuracy and efficiency of the proposed method. Results show that the method has the good performance in terms of the efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Adaptive Fourier decomposition (AFD) has been found to be among the most effective greedy algorithms. AFD shows an outstanding performance in signal analysis and system identification. As compensation of effectiveness, the computation complexity is great, that is especially due to maximal selections of the parameters. In this paper, we explore the discretization of the 1-D AFD integration via with discrete Fourier transform (DFT), incorporating fast Fourier transform (FFT). We show that the new algorithm, called FFT-AFD, reduces the computational complexity from O ( M N 2 ) to O ( M N log N ) , the latter being the same as FFT. Through experiments, we verify the effectiveness, accuracy, and robustness of the proposed algorithm. The proposed FFT-based algorithm for AFD lays a foundation for its practical applications. [ABSTRACT FROM AUTHOR]

This research aims to make a comparison between the analytical and numerical methods of simulation of the Gaussian beam propagation in free space. This comparison brings evaluation of the accuracy and applicability limitations of the angular spectrum diffraction algorithm. In this approach, planar harmonic waves are assumed as basic components of a propagating wave, so the algorithm combines the angular spectrum technique and the 2D fast Fourier transformation procedures. It means a quite different approach than the well-established Huygens–Fresnel–Rayleigh–Sommerfeld one, based on spherical waves. The Gaussian beam is a rare case of the exact analytical 3D solution of a specific wave diffraction problem, in paraxial scalar approximation. Gaussian beam form has been chosen here as an evaluation reference. It allows to avoid comparisons between two numerical procedures, both of which may suffer from imperfections. In this comparison, the respective 2D cross-sections of calculated 3D complex valued wave fields distributions are presented. Also values of specific Gaussian beam parameters like full phase and Gouy phase shift and wave-front curvature radius are presented. The comparison between that form and the results of the angular spectrum algorithm brings information about the performance quality of that algorithm. [ABSTRACT FROM AUTHOR]

This work quantitatively explores the dependence of the truncation errors on computational mesh settings for image-inclusion approaches and proposes a corresponding amendment. The new method is based on FFT algorithms and involves four individual portions. A mesh differential refinement scheme, consisting of independent and flexible selections-combinations of the surface, source, and target domains, is conceived to assist the proposed method. Comparisons of the results produced by the new and conventional mesh schemes demonstrate the significant improvements in computational performances. The new method can facilitate the numerical evaluation of local elastic characteristics caused by distributed inclusions or defects in contacting components. [ABSTRACT FROM AUTHOR]

The well-known k -nearest neighbors problem ( k NN ) involves building a data structure that reports the k closest training points to each of a given set of query points, with all points being in a given metric space S . The problem discussed here is an important operation in rotation-invariant image processing. It consists of a nontrivial variant of k NN : given a set of training points X and a set of query points Y find, for each query point y ∈ Y , the k nearest training points to y , where the notion of distance is given by a pseudometric of S defined over cyclic permutations of y and the elements of X . The multiplicity of the query point permutations makes serial brute force search too costly for instances of practical size. We present a transformation that enables any instance of the variant to be solved as a k NN problem. Although this enables the application of any k NN algorithm, the transformation is too time costly to be practical for instances of practical dimensions. For this reason, we present a condensation algorithm for the efficient elimination of unfavorable training points (that cannot be among the k closest neighbors of y ) and an effective parallel programming approach based on the discrete Fourier transform. The significant speedup gained over brute force search on practical datasets is reported. We also provide the mathematical basis of a conjecture that, if true, would enable the speedup to be significantly improved. The application of the approach to classification by support vector machines and k -means clustering is also discussed. [ABSTRACT FROM AUTHOR]

Numerical simulation of microstructure coarsening is a subject of great interest in computational materials science. The coarsening dynamics in a binary mixture can be modeled by the celebrated Cahn–Hilliard equations. To perform efficient and accurate long-time integrations, we develop a fast and stable high order numerical method for solving Cahn–Hilliard equations. The spatial discretization is carried out by the compact central difference scheme with FFT-based fast implementation while the time integration is done through the accurate exponential time differencing multistep approach. We demonstrate the effectiveness of the proposed method by numerical experiments and study computationally the coarsening kinetics corresponding to different choices of the diffusion mobility. [ABSTRACT FROM AUTHOR]

Pricing Asian options is a long-standing hard problem; there is no analytical formula for the probability density of its payoff even when the process of the underlying asset follows the simple lognormal diffusion process. It is known that the density function of a discretely-sampled Asian option’s payoff can be efficiently approximated by the Fast Fourier Transform (FFT). As a result, we can accurately price the option under more general Lévy processes. This paper shows that the pricing error of this approach, called the FFT approach, can be decomposed into the truncation error, the integration error, and the interpolation error. We prove that previous algorithms that follow the FFT approach converge quadratically. To improve the error convergence rate, our proposed algorithms reduce the integration error by the higher-order Newton–Cotes formulas and new integration rules derived from the Lagrange interpolating polynomial. The interpolation error is reduced by the higher-order Newton divided-difference interpolation formula. Consequently, our algorithms can be sped up by the FFT to achieve the same time complexity as previous algorithms, but with a faster error convergence rate. Numerical results are given to verify the efficiency and the fast convergence of our algorithms. [ABSTRACT FROM AUTHOR]

The initial guess transferring mechanism is widely used in iterative DIC algorithms and leads to path-dependence. Using the known deformation at a processed point to estimate the initial guess at its neighboring points could save considerable computation time, and a cogitatively-selected processing path contributes to the improved robustness. In this work, our experimental study demonstrates that a path-independent DIC method is capable to achieve high accuracy, efficiency and robustness in full-field measurement of deformation, by combining an inverse compositional Gauss–Newton (IC-GN) algorithm for sub-pixel registration with a fast Fourier transform-based cross correlation (FFT-CC) algorithm to estimate the initial guess. In the proposed DIC method, the determination of initial guess accelerated by well developed software library can be a negligible burden of computation. The path-independence also endows the DIC method with the ability to handle the images containing large discontinuity of deformation without manual intervention. Furthermore, the possible performance of the proposed path-independent DIC method on parallel computing device is estimated, which shows the feasibility of the development of real-time DIC with high-accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a simple removable post-processing method was employed to improve the pixel-angle resolutions for different surface plasmon resonance (SPR) biochemical sensors. Compared with conventional centroid algorithm, dip span and height proportion of our enhanced algorithm were optimized simultaneously. To improve sensing stability when resonance angle shifting, the calculation region varies with the resonance angle. Besides, FFT algorithm and adjacent-averaging smoothing algorithm were also introduced into our proposed algorithm. It was found that FFT algorithm could reduce standard deviation of resonance angle for dynamic baseline algorithm. Adjacent-averaging smoothing algorithm with an average number of 10 points could also reduce standard deviation of resonance angle. The refractive index (RI) resolution could reach 1.55 ​× ​10−6 RIU, 5.52 ​× ​10−7 RIU and 8.47 ​× ​10−7 RIU for conventional Au-based SPR sensor, MSF and PAA-based plasmonic waveguide resonance (PWR) sensors, respectively. In biochemical sensing experiments, the limit of detection (LOD) of Zn2+ ion for MSF-based PWR chemical sensor could obtain 14.86 ​nM. The LOD of BSA protein could obtain 5.68 pM for PAA-based PWR biosensor. Further, Ag-based SPR biosensor modified with rabbit IgG was used to detect goat anti-rabbit IgG and a LOD of 9.93 pM was achieved. • A simple removable and enhanced centroid algorithm was proposed to improve resolution of plasmonic sensor. • The refractive index (RI) resolution could reach the level of ​10−7 RIU for plasmonic waveguide sensor, respectively. • A LOD of 9.93 pM for IgG protein was obtained for Ag-based SPR biosensor. [ABSTRACT FROM AUTHOR]

A numerical method to compute the Effective Thermal Conductivity (ETC) of granular media surrounded by a stagnant fluid is presented. Based on the geometry and size of grains, a Representative Volume Elements (RVE) of the granular media is created using the Discrete Element Method (DEM) while the ETC of this RVE is estimated with Fast Fourier Transform (FFT) computations. To bridge the gap between the DEM and the FFT, a discretization algorithm (voxelization of convex polyhedra) was developed. Since their physical properties are poorly defined, "fuzzy" voxels associated with solid–gas interfaces or solid–solid contacts, domains inherent in a granular medium, are clearly identified during this step. The assignment of extreme properties to these voxels, assuming negligible radiation, allows to establish lower and upper ETC bounds. This methodology is applied to granular media of Uranium dioxide particles immersed in stagnant Helium; packed beds for which experimental data are available in the literature. First, the effect of RVE and discretization sizes on the simulated ETC are investigated and optimal values of RVE size and discretization ratio are defined. Next, the significant deviation of simulated DEM-FFT ETC bounds, observed at high solid to gas conductivity contrasts, exhibits the key role of interfaces on the computed ETCs. An improved modelling of solid–gas interfaces based on the Knudsen effect and a modelling correction for solid–solid interfaces is therefore proposed. The new modelling is shown to adequately bound and estimate the ETC of considered granular media at high (∼ 100) solid to gas thermal conductivity contrasts. [ABSTRACT FROM AUTHOR]

Abstract: Gradient vector flow (GVF) and generalized GVF (GGVF) have been widely applied in many image processing applications. The high cost of GVF/GGVF computation, however, has restricted their potential applications on images with large size. Motivated by progress in fast image restoration algorithms, we reformulate the GVF/GGVF computation problem using the convex optimization model with equality constraint, and solve it using the inexact augmented Lagrangian method (IALM). With fast Fourier transform (FFT), we provide two novel simple and efficient algorithms for GVF/GGVF computation, respectively. To further improve the computational efficiency, the multiresolution approach is adopted to perform the GVF/GGVF computation in a coarse-to-fine manner. Experimental results show that the proposed methods can improve the computational speed of the original GVF/GGVF by one or two order of magnitude, and are more efficient than the state-of-the-art methods for GVF/GGVF computation. [Copyright &y& Elsevier]

Abstract: Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor-grid methods and the finite-element method with shell transformation in terms of computational complexity, storage requirements and accuracy tested on several benchmark problems. These methods can be subdivided into integral methods (fast Fourier transform methods, tensor-grid method) which solve the stray field directly and in differential equation methods (finite-element method) which compute the stray field as the solution of a partial differential equation. It turns out that for cuboid structures the integral methods, which work on cuboid grids (fast Fourier transform methods and tensor-grid methods), outperform the finite-element method in terms of the ratio of computational effort to accuracy. Among these three methods the tensor-grid method is the fastest for a given spatial discretization. However, the use of the tensor-grid method in the context of full micromagnetic codes is not well investigated yet. The finite-element method performs best for computations on curved structures. [Copyright &y& Elsevier]

Abstract: A circle packing is a set of tangent and disjoint discs. Maps between circle packings with the same tangency are discrete analogues of conformal mappings, which have application for example in mechanical, fluid, and thermal engineering. We describe an advancing front algorithm to compute the circle packing of a strip around a closed planar curve. Conformal mappings preserve local angles and shapes; our algorithm uses these properties to obtain via the fast Fourier transform the centers and radii for the circle packing of successive trigonometric Lagrange curves in a strip. To check the algorithm, different results are compared with well-known conformal mappings. Real time deformations of circle packings are possible by changing the shape of the initial closed curve. [Copyright &y& Elsevier]

Abstract: This paper presents a fully automated numerical tool for computing the accurate effective properties of two-phase linearly elastic composites reinforced by randomly distributed spherical particles. Virtual microstructures were randomly generated by an algorithm based on molecular dynamics. Composites effective properties were computed using a technique based on Fast Fourier Transforms (FFT). The predictions of the numerical tool were compared to those of analytical homogenization models for a broad range of phases mechanical properties contrasts and spheres volume fractions. It is found that none of the tested analytical models provides accurate estimates for the whole range of contrasts and volume fractions tested. Furthermore, no analytical homogenization models stands out of the others as being more accurate for the investigated range of volume fractions and contrasts. The new fully automated tool provides a unique means for computing, once and for all, the accurate properties of composites over a broad range of microstructures. In due course, the database generated with this tool might replace analytical homogenization models. [Copyright &y& Elsevier]

Abstract: Quantics tensor train (QTT), a new data-sparse format for one- and multi-dimensional vectors, is based on a bit representation of mode indices followed by a separation of variables. A radix-2 recursion, that lays behind the famous FFT algorithm, can be efficiently applied to vectors in the QTT format. If input and all intermediate vectors of the FFT algorithm have moderate QTT ranks, the resulted QTT–FFT algorithm outperforms the FFT for large vectors and has asymptotically the same complexity as the superfast quantum Fourier transform. It is instructive to describe a class of such vectors explicitly. We identify all vectors that have QTT ranks one on input, intermediate steps and output of the FFT algorithm. We also give an example of QTT-rank-one vector that has the Fourier image with full QTT ranks. We show by numerical experiments that for certain rank-one vectors with full-rank Fourier images, the practical -ranks remain moderate for large mode sizes. [Copyright &y& Elsevier]

Abstract: A method is presented that performs the exact electromagnetic analysis of 2D periodic dielectric structures of arbitrary profile or index distribution and possibly large period. The generalized source method is used to formulate the problem of light diffraction in the form of a volume integral equation reduced to a linear equation system, which is solvable by known fast algorithms. The calculation time and required memory are linearly proportional to the total number N o of considered diffraction orders instead of N o 3 typical for conventional methods. Numerical examples are provided to demonstrate the potential of the method for the analysis of complex periodic structures. [Copyright &y& Elsevier]

Abstract: Change of support is a common issue in the geosciences when the volumetric support of the available data is smaller than that of the blocks on which numerical modeling is required. In this paper, we present two algorithms for the direct block-support simulation of cross-correlated random fields that are monotonic transforms of stationary Gaussian random fields. The first algorithm is a variation of sequential Gaussian co-simulation, in which each block value is simulated in turn, conditionally to the original data and to the previously simulated block values, while the second algorithm is based on spectral co-simulation in the framework of the discrete Gaussian change-of-support model. These two algorithms are implemented in computer programs and applied to a synthetic case study and to a mining case study. Their properties and performances are compared and discussed. [Copyright &y& Elsevier]

Abstract: We present a method for computing the Hermite interpolation polynomial based on equally spaced nodes on the unit circle with an arbitrary number of derivatives in the case of algebraic and Laurent polynomials. It is an adaptation of the method of the Fast Fourier Transform (FFT) for this type of problems with the following characteristics: easy computation, small number of operations and easy implementation. In the second part of the paper we adapt the algorithm for computing the Hermite interpolation polynomial based on the nodes of the Tchebycheff polynomials and we also study Hermite trigonometric interpolation problems. [ABSTRACT FROM AUTHOR]

Abstract: The Fast Fourier Transform (FFT) is a widely used algorithm that is frequently employed in environments where high performance is critical. In the context of embedded systems, FFTs often have hard runtime constraints and must be evaluated using limited hardware. In this paper, we present a partitioned FFT algorithm (PFFTC) for the Cell Broadband Engine (Cell BE) that improves upon previous FFT implementations for this platform. PFFTC has three main phases to (i) partition the problem into independent sub-problems, (ii) solve the sub-problems in parallel, and (iii) combine the results of the sub-problems to obtain the solution to the original problem. PFFTC includes optimizations for exploiting data transfer parallelism, avoiding unnecessary communication through careful data routing, avoiding data dependency stalls with instruction-level double buffering, and minimizing synchronization overhead through the use of an “synchronous” signal-based barrier. We evaluate the performance of PFFTC and other FFT algorithms for the Cell BE. Our results indicate that PFFTC attains a peak processing rate of 33.6 GFLOPS, and achieves speedups ranging from 31% to 62% over the fastest previous Cell BE FFT algorithm’s reported performance for complex single-precision FFTs with 1,024-16,384 data points. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes and compares four block joint detection algorithms for the orthogonal frequency division multiplexing (OFDM)-code division multiple access (CDMA) communication systems. The performance of the proposed OFDM-CDMA joint detectors with orthogonal and non-orthogonal spreading sequences are investigated in mobile radio channels. The proposed OFDM-CDMA detectors are zero forcing (ZF) and minimum mean square error (MMSE) detectors with decision feedback (DF) structures. The proposed joint detectors do not require discrete Fourier transform (DFT) or fast Fourier transform (FFT) operations and can be used to compensate the channel distortion. Hence for hardware implementation, the proposed detectors are more efficient than the conventional methods. The channel sorting method offers approximately 2dB gain for the DF joint detectors and reduces the impairing effect of error propagation. The bit error rate (BER) performance of orthogonal codes is better than that of non-orthogonal ones in time varying channels. Simulation examples are given to demonstrate the effectiveness of the proposed detectors. [Copyright &y& Elsevier]

Abstract: We describe a cache-friendly version of van der Hoeven’s truncated FFT and inverse truncated FFT, focusing on the case of ‘large’ coefficients, such as those arising in the Schönhage–Strassen algorithm for multiplication in . We describe two implementations and examine their performance. [Copyright &y& Elsevier]

Abstract: We present algorithms for the discrete cosine transform (DCT) and discrete sine transform (DST), of types II and III, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from to for a power-of-two transform size N. Furthermore, we show that an additional N multiplications may be saved by a certain rescaling of the inputs or outputs, generalizing a well-known technique for by Arai et al. These results are derived by considering the DCT to be a special case of a DFT of length , with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split-radix algorithm). The improved algorithms for the DCT-III, DST-II, and DST-III follow immediately from the improved count for the DCT-II. [Copyright &y& Elsevier]

Abstract: We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from to for a power-of-two transform size N, and the exact count is strictly lowered for all . These results are derived by considering the DCT to be a special case of a DFT of length , with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split-radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV. [Copyright &y& Elsevier]

Abstract: In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three-dimensional boundary value problems governed by elliptic systems of partial differential equations. In particular, we consider problems arising in linear elasticity in axisymmetric domains. The proposed algorithm exploits the block circulant structure of the coefficient matrices and makes use of fast Fourier transforms. The algorithm is also applied to problems in thermo-elasticity. Several numerical experiments are carried out. [Copyright &y& Elsevier]

Abstract: We study the Submass Finding Problem: given a string s over a weighted alphabet, i.e., an alphabet with a weight function , we refer to a mass as a submass of s if s has a substring whose weights sum up to M. Now, for a set of input masses , we want to find those which are submasses of s, and return one or all occurrences of substrings with mass . We present efficient algorithms for both the decision and the search problem. Furthermore, our approach allows us to compute efficiently the number of different submasses of s. The main idea of our algorithms is to define appropriate polynomials such that we can determine the solution for the Submass Finding Problem from the coefficients of the product of these polynomials. We obtain very efficient running times by using Fast Fourier Transform to compute this product. Our main algorithm for the decision problem runs in time , where is the total mass of string s. Employing methods for compressing sparse polynomials, this runtime can be viewed as , where denotes the number of different submasses of s. In this case, the runtime is independent of the size of the individual masses of characters. [Copyright &y& Elsevier]

Abstract: Objective: The goal of this work is to determine whether improved performance (compared to patient independent algorithms) can be achieved by an algorithm, developed on the fly, that requires no user input beyond the identification of the first one or two seizures in the record. Methods: The previously developed AutoLearn™ algorithm, which employs the probabilistic neural network (PNN), is tested on 209 seizures obtained from the epilepsy monitoring unit (EMU) or ambulatory recordings. A construction algorithm is used to compare a variety of algorithm architectures and factors. The Taguchi design of experiments (DoE) method is employed find the significant factors without resorting to a full factorial design. Results: Architectures that train a single PNN per channel and use segmentation to identify ranges of similar activity are preferred. The two best architectures are insensitive to the levels of any of the other factors tested. The training time for the algorithm is less than 1s, and approximately 2min are required to find the seizures in an 8h record. Conclusions: The final algorithm, which requires no input from the user other than the marking of the first seizure in a record, performs as well or better than the 3 seizure detectors on EMU and ambulatory records. The algorithm performs nearly as well as human experts on the EMU records. Significance: The described method can be used to identify unusual seizures (or other patterns) that will be missed by the current generation of seizure detectors. We expect that the methods developed here will also aid the development of patient independent seizure detectors that can improve their performance over time by incorporating new examples. [Copyright &y& Elsevier]

Abstract: A stochastic computational method is developed to evaluate global effective properties and local probabilistic behavior of random elastic media. The elasticity solution for random media is addressed with a method that combines a fast iterative numerical method with stochastic decomposition techniques. Stochastic homogenization problems are mathematically formulated with an ensemble average approximation scheme based on a concept of stochastic representative volume element (SRVE). Probabilistic descriptors of local strain are generated based on convolution equations derived from the equilibrium equations of elasticity. With the application of the Galerkin formulation in probability space and the Fourier transform of the convolution equations, an efficient numerical scheme is implemented using an iterative algorithm that takes advantage of fast Fourier transform. Two algorithms are provided for Gaussian and non-Gaussian random media, respectively, with corresponding sufficient conditions for convergence derived. Finally, numerical experiments are conducted for a Gaussian and a non-Gaussian random medium, respectively, with verifications obtained from Monte Carlo simulation. [Copyright &y& Elsevier]

Abstract: We present an algorithm for multiple-precision floating-point multiplication. The conventional algorithms based on the fast Fourier transform (FFT) multiply two n-bit numbers to obtain a 2n-bit result. In multiple-precision floating-point multiplication, we need only the returned result whose precision is equal to the multiple-precision floating-point number. We show that the overall arithmetic operations for FFT-based multiple-precision floating-point multiplication are reduced by decomposition of the full-length multiplication into shorter-length multiplication. [Copyright &y& Elsevier]

Numerical algorithms are presented for two classical free boundary problems for ideal flow past an obstacle: Helmhotz–Kirchhoff and reentrant jet flows. The Levi–Civita representation of the log-hodograph function is used in each case to derive non-linear integral equations for the boundary correspondence between the obstacle and the parameter domain. The integral equations are solved by a method of successive conjugation implemented with the fast Fourier transform. For the reentrant jet flow an additional non-linear system must be solved to update certain flow parameters at each iteration. Several examples are computed for polygonal and curvilinear obstacles. A convergence result is given for the Helmhotz–Kirchhoff flow iteration. [Copyright &y& Elsevier]

This paper evaluates and compares two area-based shape-from-shading algorithms for deriving detailed surface topography and terrain parameters. A Fourier transform-based linear algorithm and an iterative minimization algorithm with integrability constraint are devised and implemented using C++ programming language, and applied to a SPOT panchromatic image. The relative height measurements from the shape-from-shading technique are calibrated into an absolute elevation model using a parametric least-squares adjustment procedure based on a number of ground control points. Surface slope, orientation, and structural lines are also calculated based on the digital elevation model derived from the shape-from-shading technique. The comparative advantages of the two algorithms are discussed, and the combination of two algorithms is also explored. The fundamental requirement for the shape-from-shading algorithms is that the terrain surface under investigation has a relatively homogenous land cover. Source codes in C++ and test data sets are available. [Copyright &y& Elsevier]

Efficient decoding of Dual Tone Multi-Frequency (DTMF) signals can be achieved using the sub-band non-uniform discrete Fourier transform (SB-NDFT). In this paper, the details of its implementation on the ADSP-2192 processor are put forward. The decoder performance in terms of its computational complexity and computational speed of this algorithm, implemented on the ADSP-2192 processor, are compared for different implementations of the SB-NDFT algorithm, with and without optimization for the chosen DSP, ADSP-2912. The algorithm is tested for various types of input signals on the DSP and these are compared with the results from Matlab®. Problems on using other DTMF decoding algorithms that use the conventional discrete Fourier transform (DFT) and the non-uniform discrete Fourier transform (NDFT) are also addressed. [Copyright &y& Elsevier]

In this paper, we propose a high-performance parallel one-dimensional fast Fourier transform (FFT) algorithm on clusters of vector symmetric multiprocessor (SMP) nodes. The four-step FFT algorithm can be altered into a five-step FFT algorithm to expand the innermost loop length. We use the five-step algorithm to implement the parallel one-dimensional FFT algorithm. In our proposed parallel FFT algorithm, since we use cyclic distribution, all-to-all communication takes place only once. Moreover, the input data and output data are both in natural order. Performance results of one-dimensional power-of-two FFTs on clusters of pseudo-vector SMP nodes, Hitachi SR8000, are reported. We succeeded in obtaining performance of over 61 GFLOPS on a 16-node Hitachi SR8000/MPP. [Copyright &y& Elsevier]

We derive an algorithm based on the fast Fourier transform to construct a real symmetric matrix S with eigenvalues λ1≥λ2≥⋯≥λn, with eigenvector e = [1, 1, … ,1]T belonging to the eigenvalue λ1.We find simple conditions on the eigenvalues such that the algorithm constructs an irreducible matrix S = λ1E, where E is a symmetric doubly stochastic matrix. [Copyright &y& Elsevier]

We studied the flow of data in the paths of a fast Fourier transform (FFT) and inverse FFT in the butterfly algorithm in order to establish a relationship between the forward and backward data. We show that an FFT image can be encrypted by modifying the data of a path of FFT and decrypted by restoring the data during the inverse FFT. For encryption, the data in a path of FFT are shuffled by enforcing right bit shifts on the bit representation of the data index. Moreover, the phases of the data are changed by multiples of a fixed fraction of 2 π ; the data index is used as the multiplication constant, and the divisor for the fraction is used as an encryption key. The path number and number of right bit shifts are two other encryption keys. The three integers constitute a set of encryption keys for two-dimensional images. Four different images were encrypted with two sets of encryption keys. The decryptions were performed with partially correct keys in order to test the robustness of our method against brute attacks. The correlation between the original and decrypted images was evaluated using the correlation coefficient. • Optical encryption of a two-dimensional image is accomplished with three simple integers. • Encryption and decryption of a two-dimensional image are done during fast Fourier transform (FFT) and inverse FFT. • Twiddle factor of the butterfly algorithm in FFT is modified and used as an encryption key. • Bit reversal sampling on the bit representation of data index is used as another encryption key. [ABSTRACT FROM AUTHOR]

Abstract: FFT-based convolution is proposed to numerical solve Fresnel–Kirchhoff integral in Fresnel regime carefully and in a very shorter time in comparison to direct solving convolution. To show its capability, the algorithm was implemented to evaluate amplitude of a diffracted plane wave at the focal plane of photon sieves with different focal lengths. The calculated amplitudes are completely the same calculated via convolving operation but has advantageous of taking very very shorter time. The calculation was also repeated using single-FFT algorithm that produce same result for all ranges either below or upper the sampling criteria and different results in comparison to the other two methods. [Copyright &y& Elsevier]