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This paper proposes a new algorithm for the unconstrained optimization problem, which is derived as an application of the control theory called Direct Gradient Descent Control. The static optimization problem is solved by using a dynamic controller in which the convergence speed can be greatly accelerated. The major idea is to consider the objective function F(x) and its time derivative dF(x(t))/dt as the evaluation criteria, and to apply the gradient descent method. It is verified by simulation that the proposed dynamic mathematical programming has a very great capability to converge to the optimal solution. It is also interesting to note that the method has to a certain extent the ability to find not only local optimal solutions, but also global optimal solutions. This paper improves the basic algorithm of dynamic mathematical programming so that it is suited to global optimization. The new algorithm generates movement toward the global optimal solution by utilizing two different trajectories with interaction (the chaotic trajectory and convergence trajectory). It is verified by simulation that the new algorithm functions as a global optimization procedure with a high success probability. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(6): 20–27, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20094 [ABSTRACT FROM AUTHOR]

This paper formulates the modified least-squares method presented by Mullis in a general form so that weighting can be applied. Then, all algorithm is proposed with which a least-squares approximation can be derived for an IIR digital filter, by solving iteratively a system of equations. The method is extended to a complex Chebyshev approximation that minimizes the maximum magnitude of the complex error, by multiplying the weight, which is newly derived in this paper, with the modified least-squares error. The method is compared with a conventional complex Chebyshev approximation by means of a computer simulation and the effectiveness of the proposed method is demonstrated. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(7): 28–36, 1998 [ABSTRACT FROM AUTHOR]

This paper presents an analysis of a multirate complex recursive weighted least squares (MC-RLS) algorithm based on an analytic signal. Conventional adaptive filters for multiple sinusoid extraction have been based on lattice filter structures or gradient methods because of their low computational cost and/or low sensitivity to quantization errors. On the other hand, the RLS algorithm is easy to introduce assuming time-variant quantities in the algorithm when sinusoid frequencies have the time-varying property. However, the relationship between the tracking capability and the quantization error of the least-squares (LS) algorithm in the transversal structure has not been reported. In addition, an improvement algorithm for these errors have not been reported. In this paper, we shall describe a new RLS algorithm in a transversal filter structure with a superior transient property, reduced sensitivity to quantization errors, and low computational cost. First, an analytic signal-based autoregressive model is introduced and the MC-RLS algorithm is shown. Then, using an excess mean-square error of the MC-RLS algorithm, the tracking capability shown to be unaffected by the analytic transform and the decimation. In addition, the floating-point error and the computational cost of the MC-RLS algorithm are analyzed. It is shown that both floating-point error and computational cost are smaller than those of conventional RLS algorithms that use real signals. [ABSTRACT FROM AUTHOR]

This paper considers the complex coefficient transfer function with transmission zeros on the imaginary axis and presents a method to realize such a transfer function by a reactance network including imaginary resistors with double resistor termination. Using the obtained network and the reference network for the complex-wave digital filter, the complex digital filter with transmission zeros on the imaginary axis can easily be extended, which is important in practice. In this paper, Brune's method modified by Belevitch as well as Fujisawa's method extended by Morimoto et. al. are improved and the realizability condition is relaxed. Then, several construction examples are shown an the features of construction methods are compared and discussed. [ABSTRACT FROM AUTHOR]

This paper studies the chaotic oscillations in a dissipative system generated by a second-order direct-form II digital filter with a 2's complement adder. The locus of this chaotic oscillation is absorbed into the parallel lines comprising the Cantor-like set on the state space. In this paper, with respect to the chaotic oscillation, the initial value dependence of the locus, the output distribution, and the fractal dimensions of the locus on the state space are investigated as the fundamental nature of the chaos. Also, by considering this filter as the two-dimensional mapping, the mechanism generating the Cantor-like attractor is studied. From this study, it is shown that the 2's complement adder characteristic has functions for stretching and folding of the state space causing the chaos. Also, the coefficient dependence of the Cantor-like attractor is studied and the relationship between the fractal dimensions of the locus and the coefficient are presented. [ABSTRACT FROM AUTHOR]

This paper proposes a method of derivation for the linear-phase biorthogonal wavelet functions with an arbitrary regularity, based on the finite impulse response (FIR) half-band digital filter. Within the range of the orthogonal wavelet functions at present, the Haar function is the only one that satisfies the linear-phase property. In the image processing and other applications, the linear-phase property is more important than the orthogonality. From such a viewpoint, the biorthogonal wavelet functions are proposed, for which the orthogonality condition can be relaxed and the linear-phase property can be emphasized. In its derivation, however, mathematical sophistication is involved and the range of the derived function is considerably limited. With the development of the wavelet transform in recent years, it has become more important to select the base function flexibly according to the purpose of the processing and it is desired to establish a derivation method for the more general biorthogonal wavelet function with a higher degree of freedom. This paper presents a derivation method for the more general biorthogonal wavelet function with an arbitrary regularity. The method is based on the half-band digital filter, and the flat response is added to the filter composing the wavelet function. Then the regularity condition for the function is considered, and the amplitude square-error is used as the evaluation function. Finally, several design examples are shown for the linear-phase wavelet function derived by the proposed method. [ABSTRACT FROM AUTHOR]

This paper aims at estimation of the state of the knowledge (understanding) of the individual learner by executing a test composed of a small number of items. The following approach is proposed: (1) a teacher model is introduced, and the inference process for the understanding state of the learner is represented using the Bayesian network; (2) as the network information of the items based on the teacher model, EVINI (expected value of item network information) is proposed. As the test information, EVTIN (expected value of test information with network) is proposed; and (3) a strategy for item selection based on EVINI is proposed. The following advantages are realized in practice: (1) only a small amount of data is required to construct the model; (2) the goal of inference is to know the understanding state of the individual learner, and the result provides the feedback from an educational viewpoint; (3) the knowledge of the teacher about the domain can be utilized in the inference process, which helps to improve the prediction efficiency; and (4) it is easy to add or modify the knowledge of the teacher model. In this paper, the proposed technique is applied to the real data, as the inference example of the method. The strategy for presenting the items is compared to item response theory, and discussions are made from the theoretical viewpoint. [ABSTRACT FROM AUTHOR]

This paper notes the fact that the recording code often takes the form of a multitrack code, as well as the fact that the k-constraint in the (d, k)-constraint is considerably relaxed, which increases the capacity. Then the paper proposes a systematic construction algorithm for the fixed block-length multitrack (d, k) code and discusses the coding characteristics. A simple idea is applied in the code construction to apply the (d, ∞) code to all tracks except for one in order to reflect the relaxation of the k-constraint on the improvement of the coding rate. The (d, ∞) code is applied to the left track if the vector obtained by the elementwise logical sum of the code words satisfies the k-constraint and, if not, the (d, k) code is applied. The author has already proposed a systematic construction algorithm for the efficient fixed block-length (d, k) code. This paper discusses mainly the systematic construction algorithm and the coding characteristics for the fixed block-length (d, ∞) code, based on the unique ordering technique of the binary sequence by the Schalkwijk algorithm, as the systematic construction algorithm for the fixed block-length multitrack (d, k) code based on the forementioned idea. The coding rate and the coding efficiency are examined, and the result indicates that the characteristics are very close to those of the (d, ∞) code. [ABSTRACT FROM AUTHOR]

This paper summarizes the research result up to the present concerning the generic framework FITS for ITs. FITS is composed of six building blocks, which are teaching-material-independent, and the scheduler to realize the flexible teaching process. By developing the generic framework reflecting the essential task structure of ITS, the manpower needed in developing ITS can be reduced. This paper describes the design philosophy of the generic framework FITS and the mechanisms of the building blocks using the case of the teaching of geography as an example. [ABSTRACT FROM AUTHOR]

In the probabilistic graph, SAT reliability may be defined as the probability that there exists at least one path consisting only of successful edges from s (source vertex) to every other vertex. The SDP method enumerates Boolean product terms corresponding to each of the minimal sets of edges (tree or cutset) whose success or failure results in successful or failed graph operation. The method then generates the reliability formula by transforming a Boolean sum of products into art equivalent form in which all terms are disjoint. However, this method has disadvantages in that in the process of transformation an intermediate product term should be compared with partially formed disjoint terms to determine the tern to be retained or dropped, and the amount of computation time is dominated by the number of comparisons. This paper defines an optimal SAT reliability formula which is the one with a minimal number of product terms. Next, the expected property and ordering of the minimal. sets for generating the optimal formula are discussed and some conditions are presented to obtain an optimal one whose number of terms is equal to the number of minimal sets. Furthermore, this paper proposes an optimal method which has a fundamental operation to enumerate spanning trees by edge reductions (open- or short-circuiting) and derives an optimal formula such that the number of terms in the SAT reliability formula is equal to the number of spanning trees and each term of the formula can be determined from a spanning tree and its particular chords without use of Boolean algebra. Since every term is determined directly without comparisons at a time when a tree is generated, it seems Lo result in less computation time and remarkable saving of the memory space compared with the SDP method using a set of minimal cutsets. [ABSTRACT FROM AUTHOR]

In the analysis of a discrete nonlinear system, one of the important problems is to derive a steady solution for the nonlinear difference equation characterizing the system. However, the study for the solution method of the difference system has not been sufficient, and examples of the methods being applied to the parametric oscillation are few. This paper presents a method which derives the steady solution for the quasi-linear difference equation containing a periodic parametric excitation in its weakly nonlinear function with small parameter ∊. In this method the harmonic balance and the averaging methods used in the solution of the continuous nonlinear differential equation are ape plied to the discrete system. Since the non-linear term in the equation is bounded by ∊, the discrete waveform in the steady state is almost sinusoidal. This paper presents numerical examples for the solutions by the two methods, assuming the solution as the discrete oscillation corresponding to the sinusoid of the continuous system. As a result, the same solution is obtained by either method. Comparing the result with the output waveform obtained directly by the numerical calculation for the fundamental equation, the validity of the approximate solution by the proposed method was verified. [ABSTRACT FROM AUTHOR]

This paper proposes an iterative approximation technique of log-magnitude response for IIR filters. Minimization of the mean-square error between a desired log-frequency response and that of an IIR filter leads to a nonlinear problem. In this paper, the least squares problem on the logarithmic scale is approximated by the iteration of a weighted least squares problem on the linear scale. The weighting function is updated using the result of the previous iteration so that the weighted error on the linear scale approximates the squared error on the logarithmic scale. The filter coefficients at each iteration step can efficiently be obtained using a fast recursive algorithm for a set of linear equations. Several design examples are presented, which show that the iterative algorithm converges after one or two iterations in practice and the weighted error at convergence gives a good, estimate of the mean-square error on the logarithmic scale. An example is also presented, where both log-magnitude and phase responses are approximated simultaneously. [ABSTRACT FROM AUTHOR]

This paper discusses the eigenvalue problem for the real symmetric matrix, especially the determination of the largest eigenvalue. The largest eigenvalue is the maximum extremum of the objective function called the Rayleigh quotient and can be determined by the steepest descent method. It is known, however, that the steepest descent method suffers from slow convergence because it converges linearly. Especially, when the largest and the nest largest eigenvalues have very close values, the convergence is particularly slow. This paper analyzes this situation and shows that the convergence can be accelerated by combining the steepest descent method with a technique called shaking. Finally, it is demonstrated by a numerical example that the convergence is accelerated drastically by the proposed technique. [ABSTRACT FROM AUTHOR]

This paper is concerned with the mathematical formulation of electron beam processing systems. The mathematical model of stochastic electron beam processing systems proposed here takes randomness of material into consideration. In electron beam processing, the melting surface moves over time as a result of evaporation and melting material so that the melting surfaces become a so-called free boundary. Therefore, the problem considered in this paper is among the free boundary problems, e.g., the Stefan problem. The difference between the problem proposed here and the Stefan one is that the term related to the intensity of the electron beam appears in the problem proposed by the author. For a system with a free boundary, variational inequality is an analytical method. Since this paper deals with the stochastic system with the free boundary, a system is formulated by the stochastic variational inequality of a new type, which is an extension to the stochastic system of a usual variational inequality. The uniqueness and existence properties of the solution of the stochastic variational inequality are also studied. The mathematical security of the model of the stochastic electron beam processing system is guaranteed. [ABSTRACT FROM AUTHOR]

In VLSI layout design, a “floor plan” is often derived prior to solving the placement problem. The floor plan is obtained by dividing the square representing the chip into several rectangular rooms, to which modules are assigned, and then the locations of the module and interconnects are approximately determined. In floor plan study, the use of slice structures is common. Recently, however, a method of converting the sequence-pair, as a representation of the rectangular packing, to the floor plan has been proposed. Hence, it is now possible to list all floor plans with general configurations including the nonslice structure. However, in such a method there is the deficiency that an “empty room” without an assigned module may be generated. In the present paper, an adjacent solution is proposed for effective search of only the general configuration floor plan without empty rooms by using the simulated annealing method. An ingenious technique for effectively deriving this adjacent solution is described. The diameter of this solution space is proven to be of polynomial size. Also, the proposed solution space is experimentally compared with the solution space of slice structures. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(6): 28–38, 2005; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/ecjc.10003 [ABSTRACT FROM AUTHOR]

Mean-field Boltzmann machine learning is recognized as a practical method to circumvent the difficulty that Boltzmann machine learning is very time-consuming. However, its theoretical meaning is still not clear. In this paper, based on information geometry, we give an information-theoretic interpretation of mean-field Boltzmann machine learning and a clear geometrical explanation of the approximation used there. Based on this interpretation, computer simulations for evaluating the effectiveness of mean-field Boltzmann machine learning are carried out for two-unit Boltzmann machines. The necessity of geometrical analysis in demonstrating the effectiveness of mean-field Boltzmann machine learning is discussed. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(8): 30–39, 1999 [ABSTRACT FROM AUTHOR]

In analog filters with monotonic amplitude characteristics, there exists a significant difference in the flatness between Butterworth filters and L filters. However, there are no reports on low-pass analog filters with characteristics that are intermediate of those two, that is, in which the amplitude is monotonic and the flatness is arbitrary. In this paper, by means of Jacobi polynomials, a mathematically closed transfer function of such a filter is proposed. The proposed transfer function incorporates those of Butterworth filters and L filters. Also, this transfer function can be realized at arbitrary order for both even and odd orders. © 1999 Scripta Technica, ElectronComm Jpn Pt 3, 82(8): 21–29, 1999 [ABSTRACT FROM AUTHOR]

In the design of two channel perfect reconstruction filter banks, most of the conventional methods optimize the frequency response of each filter to meet the perfect reconstruction condition. However, quantization of the filter coefficients results in some errors in the frequency response, so it is not guaranteed that the perfect reconstruction condition is still satisfied. In this paper, we present a new method for designing biorthogonal FIR linear phase filter banks with structurally perfect reconstruction. From the perfect reconstruction condition, we first describe a class of structurally perfect reconstruction implementations. Since the proposed filter banks structurally satisfy the perfect reconstruction condition, the design problem becomes the magnitude approximation of the analysis or synthesis filters. Design of these filters can be reduced to the design of half-band filters. We then give a new method to design FIR linear phase half-band filters with arbitrary flatness. Therefore, the proposed filter banks can be designed easily by using the proposed method. Additionally, the magnitude responses of the low- and high-pass filters can be arbitrarily controlled by using two different half-band filters. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(1): 1–8, 1999 [ABSTRACT FROM AUTHOR]

In this paper, we propose a model of the human head and eyeballs that naturally simulates the movement of its line of sight in computer graphics. We first measure the actual trajectory characteristics of head movement for several angles. From previous research and the data we obtained, we find that moving the head with a sigmoidal angular velocity is an optimal feature. A mathematical moving model of the head and eyeballs based on our finding is proposed. We create several movements, such as furtive, weird, astonished, and glancing facial expressions, by changing the model parameters. We also present a simple and practical model. Finally, we discuss our proposed model based on our evaluation of subjective tests on the model. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(1): 41–50, 1999 [ABSTRACT FROM AUTHOR]

In applications such as subband coding, the coding gain is a useful evaluation measure for representing the bit-rate reduction performance of the subband filter for the object of coding. It is widely used in the estimation of coding performance and the design of subband filters. To estimate the coding gain requires knowledge of the probability density distribution of the object of coding and the decomposed subband series. Identification of the probability density function, however, is in general difficult. Consequently an approximation is often used in the estimation of the coding gain, where it is assumed that the probability density distributions of the object of coding and all subband series are the same. Thus, estimation of the coding gain contains an error for data, such as images, where this assumption is not satisfied. This paper notes that the probability density distribution of the subband decomposed image can be well approximated by a generalized Gaussian distribution and proposes a method for a more accurate estimation of the coding gain in the orthogonal wavelet transform attained by a variety of subband filter, using the higher-order statistics of the object of coding. The coding gain is estimated for several objects of coding. Comparing the result to the actually measured value, it is shown that the accuracy of estimation is greatly improved in the proposed method, compared to the method based on an approximation. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(1): 58–67, 1999 [ABSTRACT FROM AUTHOR]

Challenge-response type human identification using uniform mapping was proposed as a scheme that is robust against peeping at the input process and in which provers do not need any extra devices, like IC cards. However, this method still has some indeterminacy concerning issues of security or properties. In this paper, we evaluate the properties and resistance against peeping attacks of challenge-response type human identification using uniform mapping. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(1): 79–86, 1999 [ABSTRACT FROM AUTHOR]

In this paper we have introduced a nonfuzzy α-multiobjective linear fractional programming problem, for an α set up to satisfy the DM as much as possible and such that the elements of the coefficient vectors are equal to or greater than α. These vectors are formed with membership degrees of the fuzzy number membership functions involved in the block angular linear fractional programming problem with fuzzy parameters. Simultaneously, we provide for the fuzzy goals of the DM with respect to each objective function by the use of membership functions also containing nonlinear functions. Furthermore, we propose an interactive decision-making method that determines an approximate M-α-Pareto optimal solution in the minimax sense for reference membership values set up by the DM subjectively; if the DM is not satisfied with it, this method elicits a DM satisfying solution from the M-α-Pareto optimal solutions by interactive upgrading of the membership values and/or the α value. With respect to the minimax problem used to determine the M-α-Pareto optimal solution, this one could be determined by application of the Dantzig-Wolfe decomposition principle and the Ritter partitioning procedure, since the techniques introduced here produce block angular problems with only coupling constraints and block angular problems with coupling constraints and coupling variables. The applications of the proposed interactive decision-making technique to actual decision-making conditions are left for future investigation. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(12): 45–54, 1998 [ABSTRACT FROM AUTHOR]

This paper deals with multiobjective 0–1 programming problems having block angular structure. We propose an interactive fuzzy rule-satisfying method in order to obtain satisfactory solutions that take into account objective functions expressed by the decision maker in fuzzy form. In the proposed method, a membership function corresponding to each fuzzy object of the decision maker is specified by interaction with the decision maker. Subsequently, the Parato optimum solution, closest in the minimax sense to a reference point set by the decision maker in the membership function space, is derived by using a genetic algorithm. If satisfaction is not reached, the reference point is updated interactively so that the solution eventually derived is satisfactory to the solution maker. Since the minimax problem solved in this interactive process is a single-object 0–1 programming problem with block angular structure, a genetic algorithm is employed that contains a decomposition process for solving the problem by means of a special configuration. By means of simple numerical experiments, the effectiveness of the proposed method is demonstrated. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(8): 10–17, 1998 [ABSTRACT FROM AUTHOR]

Some methods for synthesizing a protocol specification from a given service specification have been proposed using various computational models. However, the existing methods cannot treat service specifications including both complex control flows and system variables. In this paper, we propose a method for synthesizing a protocol specification automatically from a pair consisting of a service specification and a resource allocation. In our method, service specifications are described in an extended model of Petri nets, which can treat system variables. We have developed a pair consisting of a synthesis system and an execution system, and applied them to CSCW (Computer Supported Cooperative Work). © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(8): 18–26, 1998 [ABSTRACT FROM AUTHOR]

This paper derives a renormalization formula defined on the parameter space where mapping behavior is preserved, together with the equivalent potential function. In contrast to the universal function given by Feigenbaum, the behavior near the critical point is governed by the potential function. There are several interesting features which are shared by Feigenbaum's universal function, such as the representation of the critical point in terms of the unstable fixed point of the potential function, but the mapping differs from the scaling. The one-dimensional mapping is considered as an example, and the critical point and the scaling, which are major constants characterizing chaos from the potential function, are calculated precisely. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(8): 41–51, 1998 [ABSTRACT FROM AUTHOR]

This paper proposes the optimal design for the separable-denominator two-dimensional digital filter, using the genetic algorithm (GA). The design proposed is for the specification in the frequency domain. The simple GA, which is the most basic among GA, is used in the proposed optimal design. The parameters of the transfer function of the separable-denominator two-dimensional digital filter are encoded into bit sequences, and then GA is applied to design the filter. By the use of the separable-denominator transfer function, the stability of the filter is completely guaranteed. The approximation error of the proposed method is compared to that of the conventional method through design examples. The convergence of GA is discussed. It is shown that the proposed optimal design can easily cope with the modification of the design specification of the two-dimensional digital filter. It is shown also that the filter can be designer using the maximum error or the absolute error sum as the error evaluation function in addition to the mean-square error. [ABSTRACT FROM AUTHOR]

This paper presents a design and implementation method for the linear phase two-channel perfect reconstruction finite impulse response (FIR) filter banks with arbitrary filter lengths. This method is labeled a weighted Lagrange-Newton method; it is obtained by introducing the least squares weighting function into the Lagrange-Newton method. Filter banks with good stopband attenuation (equiripple stopband) can be designed using this method. Furthermore, a new method is presented that makes the filter banks with a lattice structure using the property of a polyphase component matrix. The filter banks can achieve perfect reconstruction in spite of coefficient quantization. [ABSTRACT FROM AUTHOR]

During the past few years, there been a series of paper published on the theory of the natural observation method. As one of the important application of this theory, the problems of acceptance and generation of a general waveform are discusses here. The case of polynomial waveforms and its corresponding theory was published previously. A great extension of the theory which general waveforms is presented here and its full picture is clarified. [ABSTRACT FROM AUTHOR]

Given a set of paths on a tree, the graph with vertices corresponding to the paths, where the corresponding vertices are connected by an edge when two paths intersect, is called the path graph. Given a set A of finite intervals on a straight line, the graph with vertices corresponding to the intervals belonging to A, where an edge is provided when two intervals intersect, is called the interval graph. In this paper, it is shown that the problem to decide whether or not a given path graph can be converted to an interval graph by adding K or less edges is NP-complete. [ABSTRACT FROM AUTHOR]

One of the important features that characterize the physical random field or the image texture is Taylor's correlation length. However, there has not beet presented a clear-cut theory as to the foundation of the correlation length from the viewpoint of probability theory or statistical theory. Another aspect is that the feature is one-dimensional, and, therefore, the application to the random field is limited to the isotropic random field. This paper defines the nth order statistical number of degrees of freedom as the equivalent number of uncorrelated points in the square finite region in the homogeneous random field. From the definition, the correlation area and the correlation length are derived. The correlation area is referred to as the average area of the region statistically affected by an arbitrary point on a two-dimensional field. The correlation length represents the effective distance between adjacent independent or uncorrelated points on the line parallel to the x- or y- axis. The first-order correlation length is the same as the conventional Taylor correlation length. The first-order correlation area is a natural extension of Taylor's correlation length to the two-dimensional random field. The correlation length along the principal axis, which is independent of the definition of the coordinate axis, is also derived. Those features are based on the theory of statistics and are expected to be useful for the analysis of the actual random physical field and the texture analysis of the image. [ABSTRACT FROM AUTHOR]

Advances made in electronic computers allows the limit value of the sequence to be determined much more easily now than in the past. However, a problem still arises frequently in which it is difficult to determine the limit value with a high accuracy when a tremendous calculation is required in the determination of each term of the sequence. This paper proposes a theoretical method to estimate the limit value of the sequence with a high accuracy from the viewpoint of the recognition theory. By examining the gradual change of the sequence, the character inherent to the sequence is derived. By utilizing the character, the limit value can be estimated with a high accuracy directly from a small number of terms of the sequence. Lastly, the effectiveness of the proposed estimation method is demonstrated by simple examples. [ABSTRACT FROM AUTHOR]

The theory of natural observation, an approach analysis which replaces Fourier analysis, has been divided into two types: the neighboring type; and the equilibrium type. These types have theoretical systems that are derived from different starting points; theoretically, they have mutual close relations. The purpose of this paper is to elucidate the close relations between these two types. First, it is shown that the set of fundamental observed values defined for one side of types is uniquely derivable from the other, and also that the mathematical form of the derivation maintains duality. Next, an infinite number of invariant determinants are constructed from the set of fundamental observed values, and they are proved to be independent of type. [ABSTRACT FROM AUTHOR]

Much of the previous research has aimed at constructing a theory of statistics in statistical parameter spaces, treating probability distributions as points in space. Such a theory requires that the probability distribution have the same function form and does not apply to distributions with different forms. In this paper, this deficiency is removed by the use of statistical parameter spaces of joint probability distributions. [ABSTRACT FROM AUTHOR]

The inverse Gaussian distribution is related closely to the Gaussian distribution as is suggested by its name. It is used not only in mathematical statistics but also in various fields such as engineering to describe various phenomena and to make quantitative analysis. Schrödinger derived the cumulant generating function for the first-passage time of the Brownian motion with a drift. Then Tweedie extended Schördinger's result and found that the cumulant-generating function for the time to travel for a unit distance and the cumulant-generating function for the distance traveled in the unit time are in the relation of the inverse function. Tweedie found also that the same relations exist between the binomial distribution and the negative binomial distribution as well as between Poisson distribution and gamma distribution. He called one of those the inverse of other. The study of the inverse Gaussian distribution was developed further by Wasan, Johnson and Kotz; Folks and Chhikara; et al. This paper discusses the first-passage time distribution of the Wiener process the origin of the inverse Gaussian distribution, the inverse Gaussian distribution itself and its properties, the generalized inverse distribution, and the application of the inverse Gaussian distribution. [ABSTRACT FROM AUTHOR]

This paper presents a least-squares adaptive equalizer that provides good performance even in al ill-conditioned environment where the channel distortion is rather severe. Using complex-valued tap coefficients and halving the order of the transversal equalizer result in a substantial reduction in the condition number of the input correlation matrix composed of input signals to the equalizer. The input and output signals for the equalizer are transformed into analytic signals. Then a sampling operation of decimation by a factor of two is performed. Adaptive filtering is performed based on complex arithmetic. Compared with commonly used real-valued adaptive equalizers, accuracy of the estimation of tap coefficients is improved substantially and the computational burden per time is reduced. Computer simulations will show the effectiveness of the proposed adaptive equalizer. [ABSTRACT FROM AUTHOR]

The floating-point representation is employed widely in the digital control system due to its features of large dynamic range and high accuracy. However, a sufficient study has not been made on the quantitative evaluation of the quantization error because of the difficulty of the analysis. From such a viewpoint, this paper considers the general digital control system and discusses the evaluation method for the control error and the performance deterioration of the control system due to the quantization in the A-D and D-A converters, as well as the arithmetic operations in the controller. The difference equation for the error of the state of the digital control system is derived, and the quantitative evaluation of the error (i.e., the mean and the variance) is proposed based on the equation. It is noted that there is a freedom in the order of computation in the control operation in the digital controller, and the computation error depends on the order of computation. Consequently, a matrix is newly defined to specify the order of computation, and a method is proposed for the analysis of the control error considering the order of computation. In the proposed method, the error can be evaluated for the general digital control system without specifying the object of analysis. The usefulness is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

In the problem solving of the arithmetical word problems, the process until the solution method is identified as the most important. It is necessary to design and develop the basic functions for exercise problem support in an intelligent tutoring system (ITS), such as problem solving, problem generation, and problem explanation, aiming at the support for the identification of the solution method. In this study, those three basic functions are realized based on the problem-solving method MIPS (model of indexing in problem solving). This paper describes the problem-solving module, the problem-generation module and the problem-explanation module. The problem-solving module not only solves the arithmetical word problem but also generates the cognitive description of the identification process for the solution method. The problem-generation module can generate the problem which specifies what students should do in the identification process. The problem explanation module can indicate the equivalence and difference between any two problems concerning the identification process. [ABSTRACT FROM AUTHOR]

It is known that the active RC filter which simulates the LC ladder filter has lower element-sensitivity. However, recently, many such types of filters have been proposed. In this paper, a method of realization by low- pass filter simulation-type active RC circuit is described. First, it. is proposed that an LC filter to be simulated be realized by adding resistors in parallel to L's and in series to C's of the conventional LC filter. Such a filter has the transmission zeros on the negative real axis of the S-plane, thus the conventional transfer function can no longer be used. Next the derivation method of the transfer function for this filter will be presented. Then the realization of the LCR filter obtained by the active IC circuit using a reduced number of voltage followers will be described. Finally, the synthesis and experiment of a fifth-order Chebyshev low-pass filter will be given. The effectiveness of the synthesis method is confirmed by the fact that the analysis of the clement sensitivity by computer shows that in the passband it is below about 50 percent that of the leapfrog type circuit. [ABSTRACT FROM AUTHOR]

In residue number system digital signal processing, one major problem is the scaling operation. The general scheme for scaling has traditionally been to convert the number into an MRS (mixed radix system) format and then perform the scaling. This method ins eludes problems such as the large number of hardware stages in the processing circuit and constraints on the selection of the scale number. This paper proposes a new method, where a direct modification of the Chinese remainder theorem is utilized to remedy the above problems. In the proposed scheme, the scale number can be set as a divisor of the module, and the residue number after scaling is determined by the operations in each residue number system. Using these changes, the memory capacity of the ROM is reduced and the RON can be designed with 2 stages. Through these improvements the scaling speed of the circuit will also be improved. [ABSTRACT FROM AUTHOR]

This paper considers the design of transmitter and receiver FIR digital filters with partial response of class II and V for data transmission, The filters are required to band-limit the transmitting and receiving signal, while maintaining the overall impulse response with zero intersymbol interference (ISI). Two cases are considered: 1) the case where the transmitter itself has the zero ISI impulse response; and 2) the case where the transmitter and receiver filters are matched. In the former, the length of the filter is set to be equal to the number of samples between two zero-cross points, which are at a certain symmetrical distance from the center of the ideal impulse response. Then a linear-phase transfer function is derived with an equiripple approximation to the ideal amplitude frequency response. In the approxiamtion, the weight in the stopband is set as less than 1, and ISI of less than 1 percent is obtained. In the design of the matched filter pair, the overall order is set in the same way as in the former. Applying the Herrman-Schuessler design method for the minimum phase-shift filter in the frequency domain, the transfer function is derived. To realize ISI of less than 1 percent, it suffices to set the weight in the stopband less than 5 times in the passband. Although an effort was made to decrease ISI by successive approximation with the mirror zeros as the parameters, only a slight improvement was obtained. In either case, class V requires approximately a twice higher order than class II to realize the same attenuation and ISI. [ABSTRACT FROM AUTHOR]

This paper presents a quantitative discussion on the stability of the second-order periodic difference equation, which characterizes the discrete periodic time-varying system. The periodic parameter discrete system, which corresponds to Mathieu's equation in the continuous system, is represented by a second-order linear difference equation with a small parameter E in the varying term. The parameter E plays an important role in the determination of the stability. By applying McLachlan's method, the expression for the boundary between the stability and the instability can be determined analytically with regard to the parameters contained in the equation. For the case where the periodic parameter of the difference equation is represented as a sum of two even functions, the boundary between stability and instability is determined. The stability can be analyzed in a similar way for the case where the periodic parameter is represented as a sum of N even functions in Fourier series. [ABSTRACT FROM AUTHOR]

This paper presents a new method for designing orthonormal wavelet filter banks using the Remez exchange algorithm. It is well known that orthonormal wavelet bases can be generated by paraunitary filter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary filter banks. From the orthonormality and regularity of wavelets, we derive some conditions that must be satisfied for FIR paraunitary filter banks, and investigate the relationship between the filter coefficients and their zeros. According to the relationship, we apply the Remez exchange algorithm in the z-domain directly and formulate the design problem in the form of a linear problem. Therefore, we can easily get a set of filter coefficients by solving the linear equations. Optimal solutions with an arbitrary regularity can be obtained after using an iteration procedure. In the proposed method, the main advantage is that less computational complexity is required as compared with the conventional methods. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(6): 1–8, 1998 [ABSTRACT FROM AUTHOR]

By introducing topological structures in a discrete space, the authors are constructing a discrete geometry and are researching its applications in image processing. In this paper, by using only the topological structure of a discrete space, the authors introduce the concept of digital straight line segments. The nature and characteristics of this concept are examined and its relevance demonstrated. It is found that line segments can be defined universally on various spaces and topological structures. It is also possible to characterize and study their individual natures. By using these results, algorithms for generating line segments in many kinds of spaces can be considered and their correctness verified. © 1998 Scripta Technica. Electron Comm Jpn Pt. 3, 81(2): 34–45, 1998 [ABSTRACT FROM AUTHOR]

This paper presents a global bifurcation scenario for chaotic dynamical systems that solve optimization problems. First, a chaotic dynamical system is constructed by a discretization of the gradient-descent dynamical system of the objective function. With an increase in the discretization parameter, local minimum solutions of the objective function bifurcate into chaotic attractors through a period-doubling bifurcation. The chaotic attractors are initially localized in the state space and eventually merge into a single global chaotic attractor via a series of crises. On the global chaotic attractor which visits a variety of local minima, “chaotic search” for a global minimum is realized. On the basis of the bifurcation scenario, we provide a guideline for tuning the bifurcation parameter value which gives rise to an efficient “chaotic search.” We also consider the efficiency of the “chaotic simulated annealing” algorithm in the light of its annealing schedule. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(2), 1–12, 1998 [ABSTRACT FROM AUTHOR]

Given, a graph G = (V, E), with two vertices s and t specified as the origin and destination, respectively; a positive integer K called the obstruction number; and (positive) weights l (·) on the edges; then, two players P1 and P2 play a game with the following rules. P1 starts from s, and tries to arrive at t by tracing an edge on each move. P2 cuts in his turn, P2 cuts some edges. The maximum total number of edges that P2 can cut is K during the game. It is assumed that both P1 and P2 can see the whole graph. P1 tries to minimize the sum of traveled edge weights (called the path length), and P2 tries to maximize the path length. This paper shows that the path length when the two players do their best can be determined in O(nk-l (m + n log n)) (m = |E| n = (|V|) time. It is also shown that the problem of deciding whether or not the path length when the two players do their best is not greater than a certain positive integer is P-SPACE-complete, even if the weight on each edge is 1. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(2): 13–23, 1998 [ABSTRACT FROM AUTHOR]

Real control objects often include time delays in the path between the input and the output or in the internal signal channel. In such cases, in order to stabilize the system, it is necessary to consider time-delay systems as a mathematical model of the control object. Expressing the state equation of a time-delay system as a 2D system, we can investigate the stability of the closed-loop system by the 2D matrix Lyapunov equation (MLE). We can also derive the 2D algebraic Riccati equation (ARE), which gives the delay-independent solution of the optimal regulator for time-delay systems. If this 2D ARE has a block diagonal positive-semidefinite solution, the solution to the optimal regulator for time-delay systems is given by the state feedback, and simultaneously the value of the linear quadratic cost function becomes a minimum. The solution to the proposed 2D ARE in this paper can be obtained by the positive-definite solution to the 1D ARE for discrete-time systems and continuous-time systems, with a partial amendment of the weighting matrix of the linear quadratic cost function. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 1–12, 1998 [ABSTRACT FROM AUTHOR]

A criterion based on the minimum MSE (mean square error) is given to determine the number of signals mixed with white Gaussian noise in order to estimate their frequencies based on the modified minimum square error method using a higher-order linear prediction model (CLS). Being different from the usual autoregression (AR) model of linear prediction, the method has the advantage of iterative reduction of noise by subtraction of noise variances from diagonal elements of the correlation matrix of observed signal disturbed by noise at the instance of taking an inversion. But it needs precise estimation of both the rank of the correlation matrix and variances of noise by using only observed signals. In this paper, the following three points are made: (1) the analytic method to determine the order of eigenvalues which minimizes MSE criterion derived from eigenvalue analysis; (2) the formula which must be satisfied by noise variances; and (3) the iterative algorithm which gives simultaneous solution for rank order determination of the correlation matrix and estimation of noise variances. Finally, numerical examples are given to show the usefulness and correctness of the proposed MSE criterion, and some comparisons with other methods are made. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 13–23, 1998 [ABSTRACT FROM AUTHOR]

The minimum width drawing problem is a problem in which a rooted tree T and an integer B are given, and it must be decided whether or not there exists a drawing of T with width B or less satisfying the specified condition. This problem is widely investigated for the case of an ordered rooted tree. This paper discusses the computational complexity of the minimum width drawing problem for a rooted unordered tree. As the first step, several constraints are introduced for the placement of vertices, and eight sets of constraints are defined. It is shown for each of the eight constraint sets that the minimum width drawing problem is NP complete, whichever integer coordinate system or real coordinate system is used. It is also shown in the case of the integer coordinate system that the problem is NP complete, even if the number of children of each vertex is limited to three or less. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 32–41, 1998 [ABSTRACT FROM AUTHOR]

This paper discusses the concept of the minimal value set. Based on the number of connected components of the minimal value set, the unimodal function (number of connected components = 1) and the multimodal function (number of connected components ≧ 2) are defined. Several properties are derived from the relation between the connected level set and the minimal value set, and the unimodal region of a certain minimal value set is defined. Three theorems concerning the minimal value set are derived, as follows. (1) The set of local minimal points includes the minimal value set. (2) The minimal value set includes the set of minimal points in the narrow sense. (3) The unimodal function includes the quasi-convex function. The probability that the multistart method, where the local optimization technique is applied to the multiple candidate points, finds the global minimal point, as well as the necessary condition for the local optimization technique so that the points on the unimodal region containing the global minimal point converge correctly to the global minimal point, are discussed. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 42–51, 1998 [ABSTRACT FROM AUTHOR]

This paper discusses error spectrum shaping for 2D state-space digital filters. In order to reduce cost by reducing the total number of parameters, a method of analytic design is proposed in which the error feedback coefficient is specified by a diagonal matrix. The proposed algorithm has the feature that the optimal error feedback coefficient can be designed analytically in closed form by minimizing a quadratic form. The validity of the proposed algorithm is demonstrated with a numerical example. The noise reduction effect where the subdecimal part of the optimal coefficient is rounded by the power of 2 is also demonstrated. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 79–90, 1998 [ABSTRACT FROM AUTHOR]