Filtran: A fortran program for one-dimensional fourier transforms

FILTRAN is an operational FORTRAN IV program that calculates one-dimensional Fast Fourier Transforms using the algorithm of Good as modified by Cooley-Tukey and Gentleman-Sande. Options permit selection of time or distance to frequency and then inverse transforms. Input data may be cards, tape, or disk-files and output includes plots on line printer, logical units, or Calcomp Plotter.The program is useful for frequency analysis of many forms of segmented digital data. Filtering and such operations as optimally discriminating, interpolating additional values, and stretching of their data sets. It is versatile, easy to use, and without many of the data restrictions of other Fourier routines.     

Cooperative adaptive sampling of random fields with partially known covariance

This paper considers autonomous robotic sensor networks taking measurements of a physical process for predictive purposes. The physical process is modeled as a spatiotemporal random field. The network objective is to take samples at locations that maximize the information content of the data. The combination of information‐based optimization and distributed control presents difficult technical challenges as standard measures of information are not distributed in nature. Moreover, the lack of prior knowledge on the statistical structure of the field can make the problem arbitrarily difficult. Assuming the mean of the field is an unknown linear combination of known functions and its covariance structure is determined by a function known up to an unknown parameter, we provide a novel distributed method for performing sequential optimal design by a network comprised static and mobile devices. We characterize the correctness of the proposed algorithm and examine in detail the time, communication, and space complexities required for its implementation. Copyright © 2011 John Wiley & Sons, Ltd.     

Minimax linear filtering of random sequences with uncertain covariance function

Consideration was given to the development of a numerical method for determination of the minimax filter in the linear stochastic difference system studied over a finite horizon in the presence of an uncertain covariance function in the model of useful signal. Selection of the considered uncertainty sets relied on the form of the corresponding confidence regions. The developed iterative procedure was applied to filtering of the position of a maneuvering target with inexactly given acceleration covariance function.     

Optimal linear filtering and extrapolation of realizations of a vector random function observed with errors

A solution to an optimal linear filtering and extrapolation problem is proposed. The investigation object is a realization of multidimensional random function, which is measured with random errors. The solution method does not put any essential constraints on the investigated random fimction, measurment error characteristics, and on the character of relations between them. The solution is based on Pugachov’s canonical decomposition of the investigated random function, and its form is convenient for use with a computer. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 125–132, July–August, 2000.     

A software for evaluating local accuracy in the fourier transform

With the evolution of computers toward ever increasing computing speed, the numerical algorithms implemented on such computers are more and more complex, and require a very great number of computations. The numerical errors inherent in floating-point arithmetic of the computer generate errors in the results which may be fairly great. In this paper we propose a software based on the Perturbation Method for estimating the local accuracy in the Fast Fourier Transform, both in the case of exact data (computing errors alone) and in the case of experimental data (data errors and computing errors).     

A general purpose subroutine for fast fourier transform on a distributed memory parallel machine

One issue which is central in developing a general purpose FFT subroutine on a distributed memory parallel machine is the data distribution. It is possible that different users would like to use the FFT routine with different data distributions. Thus there is a need to design FFT schemes on distributed memory parallel machines which can support a variety of data distributions. In this paper we present an FFT implementation on a distributed memory parallel machine which works for a number of data distributions commonly encountered in scientific applications. We have also addressed the problem of rearranging the data after computing the FFT. We have evaluated the performance of our implementation on a distributed memory parallel machine, the Intel iPSC/860.     

Application of the fast fourier transform method for compression of spectral data obtained from a photodiode array spectrophotometer

Data compression using the Fourier transform method was applied to data generated from an ultraviolet-visible photodiode array spectrophotometer. The spectroscopic data were converted into the Fourier domain by using the fast Fourier transform technique. Four different methods were utilized to reduce the number of Fourier coefficients required for accurate reproductions of the original spectra. The performance of these methods in data compression was evaluated by using synthetic spectra as well as experimental absorption spectra. It was found that the storage space of the spectral data can be reduced by more than 90% by using three of the suggested methods.     

A method for computation of the discrete Fourier transform over a finite field

The discrete Fourier transform over a finite field finds applications in algebraic coding theory. The proposed computation method for the discrete Fourier transform is based on factorizing the transform matrix into a product of a binary block circulant matrix and a diagonal block circulant matrix.     

On the potential applications of a 3D random finite element model for the simulation of shot peening

Shot peening is a cold-working process that is used mainly to improve the fatigue life of metallic components. Experimental investigation of the mechanisms involved in shot peening is very expensive and complicated. Therefore, the Finite Element (FE) method has been recognized as an effective mean for characterizing the shot peening process and several types of FE models have been developed to evaluate the effects of shot peening parameters. However, in most of the existing FE models, the shot peening sequence and impact location were defined a priori. It is therefore the purpose of this study to consider the random property of the shot peening process. A novel 3D FE model with multiple randomly distributed shots was developed combining a Matlab program with the ANSYS preprocessor. The explicit solver LS-DYNA has been used to simulate the dynamic impingement process. Several potential applications of this novel model such as: the quantitative relationship of the peening intensity, coverage and roughness with respect to the number of shots have been presented. Moreover, simulations with multiple oblique impacts have been carried out in order to compare with results from normal impingements. Our work shows that such a computing strategy can help understanding and predicting the shot peening results better than conventional FE simulations.     

Recursive computation of the discrete fourier transform,with applications to a pulse-Doppler radar system

A recursive method of computing the discrete Fourier transform (DFT) is described. Applications of this method in a range-gated pulse-Doppler radar system is discussed. The filter bank of the pulse-Doppler radar receiver is shown to be realizable by a set of digital filters that can be obtained directly from the DFT. Filter responses are obtained and an example is given to show the computational speed necessary in an actual application.     

TBSIM: A computer program for conditional simulation of three-dimensional Gaussian random fields via the turning bands method

The simulation of spatially correlated Gaussian random fields is widespread in geologic, hydrologic and environmental applications for characterizing the uncertainty about the unsampled values of regionalized attributes. In this respect, the turning bands method has received attention among practitioners, for it allows multidimensional simulations to be generated at the CPU cost of one-dimensional simulations.This work provides and documents a set of computer programs for (i) constructing three-dimensional realizations of stationary and intrinsic Gaussian random fields, (ii) conditioning these realizations to a set of data and (iii) back-transforming the Gaussian values to the original attribute units. Such programs can deal with simulations over large domains and handle anisotropic and nested covariance models.The quality of the proposed programs is examined through an example consisting of a non-conditional simulation of a spherical covariance model. The artifact banding in the simulated maps is shown to be negligible when thousands of lines are used. The main parameters of the univariate and bivariate distributions, as well as their expected ergodic fluctuations, also prove to be accurately reproduced.     

A Mathematica program for the two-step twelfth-order method with multi-derivative for the numerical solution of a one-dimensional Schrödinger equation

In this paper, we present the detailed Mathematica symbolic derivation and the program which is used to integrate a one-dimensional Schrödinger equation by a new two-step numerical method. We add the fourth- and sixth-order derivatives to raise the precision of the traditional Numerov's method from fourth order to twelfth order, and to expand the interval of periodicity from (0,6) to the one of (0,9.7954) and (9.94792,55.6062). In the program we use an efficient algorithm to calculate the first-order derivative and avoid unnecessarily repeated calculation resulting from the multi-derivatives. We use the well-known Woods-Saxon's potential to test our method. The numerical test shows that the new method is not only superior to the previous lower order ones in accuracy, but also in the efficiency. This program is specially applied to the problem where a high accuracy or a larger step size is required.

Program summary

Title of program: ShdEq.nbCatalogue number: ADTTProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTTProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputer for which the program is designed and others on which it has been tested: The program has been designed for the microcomputer and been tested on the microcomputer.Computers: IBM PCOperating systems under which the program has been tested: Windows XPProgramming language used: Mathematica 4.2Memory required to execute with typical data: 51 712 bytesNo. of bytes in distributed program, including test data, etc.: 45 381No. of lines in distributed program, including test data, etc.: 7311Distribution format: tar gzip fileCPC Program Library subprograms used: noNature of physical problem: Numerical integration of one-dimensional or radial Schrödinger equation to find the eigenvalues for a bound states and phase shift for a continuum state.Method of solution: Using a two-step method twelfth-order method to integrate a Schrödinger equation numerically from both two ends and the connecting conditions at the matching point, an eigenvalue for a bound state or a resonant state with a given phase shift can be found.Restrictions on the complexity of the problem: The analytic form of the potential function and its high-order derivatives must be known.Typical running time: Less than one second.Unusual features of the program: Take advantage of the high-order derivatives of the potential function and efficient algorithm, the program can provide all the numerical solution of a given Schrödinger equation, either a bound or a resonant state, with a very high precision and within a very short CPU time. The program can apply to a very broad range of problems because the method has a very large interval of periodicity.References: [1] T.E. Simos, Proc. Roy. Soc. London A 441 (1993) 283.[2] Z. Wang, Y. Dai, An eighth-order two-step formula for the numerical integration of the one-dimensional Schrödinger equation, Numer. Math. J. Chinese Univ. 12 (2003) 146.[3] Z. Wang, Y. Dai, An twelfth-order four-step formula for the numerical integration of the one-dimensional Schrödinger equation, Internat. J. Modern Phys. C 14 (2003) 1087.     

On a finite element method for the equations of one-dimensional nonlinear thermoviscoelasticity

A computationally uncoupled numerical scheme for the equations of one-dimensional nonlinear thermoviscoelasticity is proposed. The scheme makes use of the finite element method for the space variable and the different method for the time variable. The existence and uniqueness of the approximate solutions are proved, and bounds of the error are analyzed.     

Reconstruction of a discontinuous function from a few fourier coefficients using bayesian estimation

The goal of this paper is the application of spectral methods to the numerical solution of conservation law equations. Spectral methods furnish estimates of the firstn Fourier coefficients of the solution. But since the solutions of conservation law equations can have discontinuities, the estimate of the solution by summing the firstn terms of the Fourier series will haveO(1/n) error, even if the Fourier coefficients are known to high accuracy. But if the solution could be accurately reconstructed from its Fourier coefficients, spectral methods could be used effectively in these problems. A method for doing this is to assume a probability distribution for functions. Functions which are smooth away from the discontinuity are assumed to be likely, and those which are not smooth away from the discontinuity are assumed to be unlikely. Then a reconstruction algorithm is chosen by minimizing the expected error over all algorithms. It is possible to put the smoothness assumptions mentioned earlier into an infinite-dimensional Gaussian probability distribution, and then the minimum-error algorithm is well-known and fairly simple to construct and apply. If the Fourier coefficients of the reconstructed function are known exactly, then this approach gives very good results. But when used with Fourier coefficients obtained from a spectral approximation to Burgers' equation, the results were much less impressive, probably because the coefficients were not known very accurately. It is possible to construct filters that reconstruct a function using Legendre or Chebyshev coefficients for information instead Fourier coefficients. It is found that the performance of these filters is similar to the Fourier case.     

A computer program for the simulation of landform erosion

A computer implementation of a stochastic model describing changes in a landform during lithologically controlled erosion is described. The model is a Markov chain in two dimensions where the noise component depends upon the underlying lithologies. A surface at any elevation above the present level can be reconstructed according to the characteristics of any of four generally accepted geomorphic theories. Erosion then proceeds until the desired reduction in elevation is achieved. The resulting surface then can be compared to an expected surface, such as the present one, and a measure of fit obtained. About 4096 geomorphically significant option combinations are available, including: isostatic adjustment to erosion, epeirogenic uplift, treatment of the landform parameters as random variables, and criteria for ending the simulation. A technique for validation based upon the random topology model of R. L. Shreve is included. An example covering about 5000 km² in the central Appalachians is described.     

Stability of the totally implicit finite difference scheme for the one-dimensional diffusion equation with a moving boundary

We analyze the totally implicitO(h ² k) finite difference method applied to a linear unidimensional diffusion equation with a boundary moving with constant velocity. The related physical problem is the solidification of a finite column filled with a binary mixture, in the quasiequilibrium regime. By advancing the boundary along the pathh/k=velocity of the interface, a simple algorithm is obtained which is shown to be consistent and unconditionally stable for any value of the interfacial segregation factor and of the Peclet number.