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.     

Some integrals and orthogonal properties for a class of hypergeometric functions

We present three integrals and three orthogonal properties for a class of hypergeometric functions. We employ orthogonal properties to generate a theory concerning infinite series expansions involving our hypergeometric functions.     

A new approach to the epsilon expansion of generalized hypergeometric functions

Assuming that the parameters of a generalized hypergeometric function depend linearly on a small variable ε$\epsilon$, the successive derivatives of the function with respect to that small variable are evaluated at ε=0$\epsilon =0$ to obtain the coefficients of the ε$\epsilon$-expansion of the function. The procedure, which is quite naive, benefits from simple explicit expressions of the derivatives, to any order, of the Pochhammer and reciprocal Pochhammer symbols with respect to their argument. The algorithm may be used algebraically, irrespective of the values of the parameters. It reproduces the exact results obtained by other authors in cases of especially simple parameters. Implemented numerically, the procedure improves considerably, for higher orders in ε$\epsilon$, the numerical expansions given by other methods.     

A new class of hybrid models for time series forecasting

Applying quantitative models for forecasting and assisting investment decision making has become more indispensable in business practices than ever before. Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing forecasters. Both theoretical and empirical findings have indicated that integration of different models can be an effective way of improving upon their predictive performance, especially when the models in the ensemble are quite different. In the literature, several hybrid techniques have been proposed by combining different time series models together, in order to overcome the deficiencies of single models and yield hybrid models that are more accurate. In this paper, in contrast of the traditional hybrid models, a new methodology is proposed in order to construct a new class of hybrid models using a time series model as basis model and a classifier. As classifiers cannot be lonely applied as forecasting model for continuous problems, in the first stage of the proposed model, a forecasting model is used as basis model. Then, the estimated values of the basis model are modified in the second stage, based on the distinguished trend of the residuals of the basis model and the optimum step length, which are respectively calculated by a classifier model and a mathematical programming model. Empirical results with three well-known real data sets indicate that the proposed model can be an effective way in order to construct a more accurate hybrid model than its basis time series model. Therefore, it can be used as an appropriate alternative model for forecasting tasks, especially when higher forecasting accuracy is needed.     

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions, where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998). This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Ganjali, 2009), which contains several lifetime models such as: exponential geometric (Adamidis and Loukas, 1998), exponential Poisson (Kus, 2007) and exponential logarithmic (Tahmasbi and Rezaei, 2008) distributions. The hazard function of our class can be increasing, decreasing and upside down bathtub shaped, among others, while the hazard function of an EPS distribution is only decreasing. We obtain several properties of the WPS distributions such as moments, order statistics, estimation by maximum likelihood and inference for a large sample. Furthermore, the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints. Special distributions are studied in some detail. Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions.     

On the use of variograms for the prediction of time series

We consider the prediction of stationary stochastic processes with non-zero mean. When the covariance of the process is known, but the mean is not, the classical approach is to first estimate the mean from the past data, and then apply an optimal predictor to the zero-mean residuals. Bastin and Henriet [1] showed that an alternative was to use a predictor based on ‘variograms’ rather than covariance information, thus avoiding the estimation of the mean. We show here that the two predictors are identical when the unknown mean is replaced by its minimum variance estimate. We also examine, through simulation, how the two predictors compare when the statistics are unknown.     

Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach

The numerical evaluation of Hilbert transforms on the real line for functions that exhibit oscillatory behavior is investigated. A fairly robust numerical procedure is developed that is based on the use of convergence accelerator techniques. Several different types of oscillatory behavior are examined that can be successfully treated by the approach given. A few examples of functions whose oscillations are too extreme to deal with are also discussed.     

Certain classes of generating functions for the Jacobi and related hypergeometric polynomials

For a certain class of generalized hypergeometric polynomials, the authors first derive a general theorem on bilinear, bilateral, and mixed multilateral generating functions and then apply these generating functions in order to deduce the corresponding results for the classical Jacobi and Laguerre polynomials. They also consider several linear generating functions for these polynomials as well as for some multivariable Jacobi and multivariable Laguerre polynomials which were investigated in recent years. Some of the linear generating functions, presented in this paper, are associated with the Stirling numbers of the second kind.     

A class of discrete orthogonal transforms

For a given N-periodic sequence, a class of log₂N discrete orthogonal transforms ranging from Walsh-Hadamard transform to discrete Fourier transform (DFT) is defined. The power spectra invariant to circular shift of the sampled data for these transforms are developed. Phase spectra, analogous to that of the DFT, for all the discrete transforms are defined and developed. Recursive relations for generating the transform matrices are developed. Generalized expressions for factoring these transform matrices are provided. Based on these matrix factors, efficient algorithms for fast computation of the transform coefficients are developed. By introducing a number of zeros as the elements in the transform matrices, a modified version of the transforms is developed. By using these modified matrices, the power and phase spectra can be computed efficiently. These transforms can be used in the general area of information processing.     

Generic polar harmonic transforms for invariant image representation

This paper introduces four classes of rotation-invariant orthogonal moments by generalizing four existing moments that use harmonic functions in their radial kernels. Members of these classes share beneficial properties for image representation and pattern recognition like orthogonality and rotation-invariance. The kernel sets of these generic harmonic function-based moments are complete in the Hilbert space of square-integrable continuous complex-valued functions. Due to their resemble definition, the computation of these kernels maintains the simplicity and numerical stability of existing harmonic function-based moments. In addition, each member of one of these classes has distinctive properties that depend on the value of a parameter, making it more suitable for some particular applications. Comparison with existing orthogonal moments defined based on Jacobi polynomials and eigenfunctions has been carried out and experimental results show the effectiveness of these classes of moments in terms of representation capability and discrimination power.     

Forecasting nonlinear time series with neural network sieve bootstrap

A new method to construct nonparametric prediction intervals for nonlinear time series data is proposed. Within the framework of the recently developed sieve bootstrap, the new approach employs neural network models to approximate the original nonlinear process. The method is flexible and easy to implement as a standard residual bootstrap scheme while retaining the advantage of being a nonparametric technique. It is model-free within a general class of nonlinear processes and avoids the specification of a finite dimensional model for the data generating process. The results of a Monte Carlo study are reported in order to investigate the finite sample performances of the proposed procedure.     

Subanalytic solutions of linear difference equations and multidimensional hypergeometric sequences

We consider linear difference equations with polynomial coefficients over C and their solutions in the form of sequences indexed by the integers (sequential solutions). We investigate the C-linear space of subanalytic solutions, i.e., those sequential solutions that are the restrictions to Z of some analytic solutions of the original equation. It is shown that this space coincides with the space of the restrictions to Z of entire solutions and that the dimension of this space is equal to the order of the original equation.We also consider d-dimensional (d≥1) hypergeometric sequences, i.e., sequential and subanalytic solutions of consistent systems of first-order difference equations for a single unknown function. We show that the dimension of the space of subanalytic solutions is always at most 1, and that this dimension may be equal to 0 for some systems (although the dimension of the space of all sequential solutions is always positive).Subanalytic solutions have applications in computer algebra. We show that some implementations of certain well-known summation algorithms in existing computer algebra systems work correctly when the input sequence is a subanalytic solution of an equation or a system, but can give incorrect results for some sequential solutions.     

A new approach for automated parts recognition using time series analysisand neural networks

This paper presents a new approach for automated parts recognition. It is based on the use of the signature and autocorrelation functions for feature extraction and a neural network for the analysis of recognition. The signature represents the shapes of boundaries detected in digitized binary images of the parts. The autocorrelation coefficients computed from the signature are invariant to transformations such as scaling, translation and rotation of the parts. These unique extracted features are fed to the neural network. A multilayer perceptron with two hidden layers, along with a backpropagation learning algorithm, is used as a pattern classifier. In addition, the position information of the part for a robot with a vision system is described to permit grasping and pick-up. Experimental results indicate that the proposed approach is appropriate for the accurate and fast recognition and inspection of parts in automated manufacturing systems.     

Learning based brain emotional intelligence as a new aspect for development of an alarm system

The multi criteria and purposeful prediction approach has been introduced and is implemented by the fast and efficient behavioral based brain emotional learning method. On the other side, the emotional learning from brain model has shown good performance and is characterized by high generalization property. New approach is developed to deal with low computational and memory resources and can be used with the largest available data sets. The scope of paper is to reveal the advantages of emotional learning interpretations of brain as a purposeful forecasting system designed to warning; and to make a fair comparison between the successful neural (MLP) and neurofuzzy (ANFIS) approaches in their best structures and according to prediction accuracy, generalization, and computational complexity. The auroral electrojet (AE) index are used as practical examples of chaotic time series and introduced method used to make predictions and warning of geomagnetic disturbances and geomagnetic storms based on AE index.     

基于Volterra级数的一类非线性系统性能评估

化工过程多具有非线性特征,针对用线性系统性能评估方法处理非线性系统会存在过估计的情况,研究了一类叠加线性干扰的非线性系统的性能评估问题。通过使用Volterra级数近似非线性环节,把最小方差性能评估问题转化成一类模型辨识问题,并从辨识误差中得到非线性系统的最小方差估计值。通过数值仿真,将新方法所得结果和现有线性性能评估方法进行了比较,验证了设计算法的优越性。     

Numerical inversion of multidimensional Laplace transforms by the Laguerre method

Numerical transform inversion can be useful to solve stochastic models arising in the performance evaluation of telecommunications and computer systems. We contribute to this technique in this paper by extending our recently developed variant of the Laguerre method for numerically inverting Laplace transforms to multidimensional Laplace transforms. An important application of multidimensional inversion is to calculate time-dependent performance measures of stochastic systems. Key features of our new algorithm are: (1) an efficient FFT-based extension of our previously developed variant of the Fourierseries method to calculate the coefficients of the multidimensional Laguerre generating function, and (2) systematic methods for scaling to accelerate convergence of infinite series, using Wynn's ε-algorithm and exploiting geometric decay rates of Laguerre coefficients. These features greatly speed up the algorithm while controlling errors. We illustrate the effectiveness of our algorithm through numerical examples. For many problems, hundreds of function evaluations can be computed in just a few seconds.     

A distance-based fuzzy time series model for exchange rates forecasting

Fuzzy time series model has been successfully employed in predicting stock prices and foreign exchange rates. In this paper, we propose a new fuzzy time series model termed as distance-based fuzzy time series (DBFTS) to predict the exchange rate. Unlike the existing fuzzy time series models which require exact match of the fuzzy logic relationships (FLRs), the distance-based fuzzy time series model uses the distance between two FLRs in selecting prediction rules. To predict the exchange rate, a two factors distance-based fuzzy time series model is constructed. The first factor of the model is the exchange rate itself and the second factor comprises many candidate variables affecting the fluctuation of exchange rates. Using the exchange rate data released by the Central Bank of Taiwan, we conducted several experiments on exchange rate forecasting. The experiment results showed that the distance-based fuzzy time series outperformed the random walk model and the artificial neural network model in terms of mean square error.     

New algorithms for deriving reduction formulas for hypergeometric series of multiple variables

A Maple-implementation of algorithms for the automatic derivation of hypergeometric series reduction formulas of the most general form is considered. The list of elementary reductions is presented.