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This paper describes a method of configuration of a complex RiCR filter with coupled Chebyshev characteristics. The frequency shift method is a well-known method of obtaining a complex filter from a real filter, in which the transfer characteristic of the real filter is shifted along the frequency axis. The complex coupled Chebyshev filter obtained by the frequency shifting of a coupled Chebyshev filter has an excellent attenuation characteristic, but the number of constituent elements for active realization is large and the circuit is complex. In the proposed method, the complex coupled Chebyshev filter is first transformed to a complex RiCR filter so that the number of constituent elements for active realization is reduced and the circuit is simplified. In this paper, a method is presented for transforming the complex coupled Chebyshev filter to a complex RiCR filter. The attenuation characteristics and the numbers of constituent elements of the complex filter designed by the proposed method, the complex coupled Chebyshev filter, and the conventional complex RiCR filter, are compared for confirmation of the effectiveness of the proposed method. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(5): 12–20, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20212 [ABSTRACT FROM AUTHOR]

This paper discusses a routing scheme for an autonomous distributed wireless network (mobile ad-hoc networking) using an ultra-wideband (UWB) system. The UWB system is a kind of spread-spectrum communication system which has the function of measuring the distance between the transmitter and the receiver with high accuracy. Using this distance measurement function, the received energy per bit is kept constant by adjusting the spreading factor according to the transmission distance. This paper considers a packet-forwarding scheme based on the above feature of the UWB system, where the spreading factor is adjusted according to the distance between the transmitter and the receiver. The objective is to realize higher throughput than in single-hop transmission by using multihop transmission which controls the maximum transmission distance. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(2): 22–30, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20082 [ABSTRACT FROM AUTHOR]

Recently, the present authors have applied the FDTD (Finite-Difference Time-Domain) method to acoustic problems. FDTD is one of the finite-difference methods in the time domain used in electromagnetic problems. However, in this method, phase errors cannot be neglected in a large-scale propagation analysis such as indoor acoustic propagation and they cause problems in the analysis. In order to reduce the phase error, Cole has invented the NS-FDTD (Non-Standard FDTD) method for electromagnetic problems. However, the numerical dispersion and stability condition are not described in Cole's paper. Also, the definition is given only for a cubic lattice. In this paper, an application of the three-dimensional NS-FDTD method to acoustic problems is attempted. Further, the method is extended to a rectangular lattice. The numerical dispersion and stability condition of the present method are derived. As a result, it is shown that the present method has much higher accuracy than the FDTD method. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(9): 15–24, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1115 [ABSTRACT FROM AUTHOR]

It is known that an IIR filter can provide an excellent amplitude characteristic that is of lower order than an FIR filter. Further, the IIR filter using all-pass circuits can realize an identical characteristic with fewer multipliers than in the conventional IIR filter. In this paper, a configuration and design method are given for a two-channel filter bank consisting of IIR filters with all-pass circuits. Lossless transforms and lossy transforms using these filter banks are proposed. One lossless transform is the S transform based on the Haar transform, but there is a problem that correlation remains in the output signals. In this paper, in place of the Haar transform in the S transform, a lossless transform based on two-channel integer IIR filter banks consisting of delay lines and all-pass circuits is proposed. On the other hand, the Haar transform is the only lossy transform based on the two-channel FIR filter bank that offers linear phase and orthogonality. Also, there are no design methods and no proof of effectiveness in applications of the two-channel IIR filter bank with both characteristics for image coding. In this paper, a two-channel orthogonal linear-phase IIR filter bank with a parallel structure of the all-pass circuits is proposed in order to maximize the coding gain, with the order of regularities as the constraint. Finally, the proposed methods are applied to stationary image coding and the effectiveness of the present method is shown. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(7): 1–9, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10001 [ABSTRACT FROM AUTHOR]

Checkerboard distortion is the kind generated in the sampling rate converter using a digital filter. In this paper, such distortion is studied in the continuous-time domain. The distortion is newly defined in the problem of interpolation by a continuous interpolation function and conditions for avoiding the checkerboard distortion are derived. Further, it is shown that a digital filter that does not generate checkerboard distortion can be created by an appropriate sampling to the continuous interpolation function satisfying the conditions in this paper. The relationship between the continuous interpolation function with time scale transform and the checkerboard distortion is studied. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(12): 59–68, 2001 [ABSTRACT FROM AUTHOR]

This paper proposes an efficient algorithm for finding all solutions of nonlinear resistive circuits. As a computational method of finding all solutions of nonlinear equations, interval analysis is well known, and the Krawczyk algorithm is one of the most typical algorithms of interval analysis. However, the Krawcyzk algorithm is extremely inefficient for circuit equations whose nonlinearity is very great. In this paper, several techniques are proposed for improving the computational efficiency of the Krawczyk algorithm for circuit equations. These techniques exploit the special structure of the circuit equations such as separability or partial linearity. It is shown that the computation time of the Krawczyk algorithm is substantially decreased by using the proposed techniques. © 1997 Scripta Technica, Inc Electron Comm Jpn Pt 3, 80(7): 28–36, 1997 [ABSTRACT FROM AUTHOR]

When unidirectional errors and symmetric errors occur in the channel, it is well known that codes capable of correcting up to t symmetric errors and detecting all t + 1 and greater unidirectional errors, i.e., t-error correcting/all unidirectional error detecting (t-EC/AUED) codes, are effective. Furthermore, constant weight codes with t-error correcting capability are known as t-EC/AUED codes with high coding rate. Recently, Bose and Rao have proposed a single error correcting constant weight code with high coding rate that is realizable with relatively simple encoding and decoding operations. In this paper, a new construction method for single error correcting constant weight codes is proposed. The encoding and decoding operations are not too complex, and it is possible to achieve coding rates even higher than those of the Bose-Rao codes. Furthermore, with the construction method proposed in this paper, not only in comparisons restricted to constant weight codes, but also in comparisons to previous codes that are known as high rate codes, it is possible to construct codes with the same error correcting capability that have even higher coding rates. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(7): 55–64, 1997 [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]

The adaptive line embracer eliminates noise from a sinusoidal signal with the unknown frequency buried in the noise and extracts the sinusoidal signal. The performance of the adaptive line embracer is represented by the signal-to-noise improvement figure. The signal-to-noise improvement figure increases as the bandwidth of the adaptive line figure increases is made narrower. The convention adaptive line enhancer, however, contains an incompatible problem in that the convergence of the adaptive coefficient is deteriorated when the signal-to-noise improvement figure is by narrowing the bandwidth. This paper proposes the adaptive line enhancer with the discriminated structure to solve this problem. The adaptive line enhancer with the discriminated structure is composed of two parts. One is the (frequency) estimator that estimates the frequency of the unknown sinusoidal signal, and the other is the (sinusoidal signal) discriminator that discriminates the unknown sinusoidal signal from the noise. The estimator is the conventional adaptive line enhancer, and the bandwidth is determined so that the convergence of the adaptive coefficient is the fastest. The discriminator is the narrowband bandpass filter where the center frequency is controlled by the adaptation coefficient. This paper the optimal design method for each of those paths, and the effectiveness of the method us verified by a computer simulation. [ABSTRACT FROM AUTHOR]

This paper considers the oscillators coupled in the form of a ring through resistors. It is described for the case of five oscillators that, for the symmetrical solutions, the analysis based on the conjugate class in group theory is useful. Major problems in tie coupled oscillators are the existence of the synchronized periodic solution and its stability. In the case of the weakly nonlinear system, the problems of the synchronized periodic solution and the stability are almost answered by techniques that include mode analysis. In the case of the strongly nonlinear system, on the other hand, the periodic solutions with symmetry have been classified mostly based on the subgroup in the group theory when the number of coupled oscillators is less. When the number of oscillators is increased, however, the number of subgroups becomes tremendous, which makes systematic analysis difficult. This paper uses the conjugate class and shows that tie symmetrical solutions can be classified systematically. It is also shown that the approximate periodic solution with symmetry can be approximately determined by the averaging based on the symmetry. [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]

It is known that the quadrature mirror filter (QMF) bank used for subband coding cannot avoid the aliasing effect for adaptive signal processing or spectral estimation, etc. A new class of filter banks is desired for these applications where the effect of aliasing also be considered. In this paper, a new class of filter bank is reported which has alias-free characteristics at equally spaced frequency points. This filter bank is called frequency sampling filter bank, and it consists of nonrecursive FIR filters. This paper also reports design methods for two types of the filter banks, keeping in mind the reduction in amount of calculation for practical implementation. In one method, all channel filters of the filter bank are determined by complex exponential modulation of a prototype filter. The other method determines the channel filters by cosine or sine modulation of a prototype filter. Both designs have the forementioned aliasing characteristics, and an efficient structure based on polyphase configuration is possible. [ABSTRACT FROM AUTHOR]

The information storage algorithm of a Hopfield-type network is a kind of self-correlation learning. This algorithm needs the condition in which vectors of learning patterns cross at right angles to each other. This paper proposes n method to make this condition easier. To this purpose, threshold is used. An investigation of how to decide quantity is included. This paper discusses a network with units whose state is 1 or 0. Fixing method of threshold has not been proposed before to this type of network. It is, therefore, proposed in this research; the goal is to facilitate learning patterns. [ABSTRACT FROM AUTHOR]

This paper describes a stepped flexural mode quartz crystal resonator. The objective of this paper is to determine the resonant frequency, the motional series resistance R1, and the Q value of the stepped flexural mode tuning fork-type quartz crystal resonator. The equation of motion is presented for a flexural mode resonator with nonuniform cross section with rotary inertia, and shear force is taken into consideration. Then, since the flexural mode quartz crystal resonator can be thought of as having two clamped-free beams, the vibrational displacement computed from the boundary condition of clamped-free ends and the condition of continuity of different cross sections are used to derive the frequency equation by Galerkin's method. In addition, the transcendental equation can be derived from the boundary conditions and the continuity condition. Further, from these relationships, the frequency constant (f·l1) and the resonant frequency are determined as functions of the width ratio W21 (width w2/-width w1) and the length ratio L21 (length l2/length l1). As a result, it is shown that the frequency can be lowered without increasing the length of the resonator. These relationships are compared with the experimental results. It is shown that both agree very well. Hence, the present analysis results are effective for arbitrary frequency design. Finally, the typical values of the electrical equivalent circuit parameters are given. It is shown that, as L21 is increased, the motional series resistance R1 increases and the Q value decreases, although the characteristics are sufficient as a resonator. At the same time, the structure is resistant to vibration. [ABSTRACT FROM AUTHOR]

This paper considers digital filters with hypercomplex coefficients. Filters of this type can reduce the order of filters to one-fourth the one with real coefficients. It is reported that the first-order digital filter with hypercomplex coefficients can realize the fourth-order digital filter with real coefficients which can be expressed by a second-order all-pass filter with complex coefficients. This paper considers also generalization including the foregoing special case and shows that the first-order digital filter with hypercomplex coefficients can realize an arbitrary-order digital filter with real coefficients less than 4. Arbitrary higher-order digital filter with real coefficients can be realized by parallel connection or cascade connection of first-order digital filters with hypercomplex coefficients. This paper considers the following three different realizations: (a) realization by parallel connection: (b) realization by cascade connection of real part; and (c) realization by cascade connection. We find that case (b) is the most low sensitive. Finally, stability criteria of hypercomplex digital filters of first-order are suggested. [ABSTRACT FROM AUTHOR]

This paper considers the set of waveforms for which the weighted power-of-p (1 < p < +∞) integral of the Fourier spectrum is bounded. Since different weight functions can be used in different frequency bands, as long as they are positive, the restriction of the waveform by the power-of-p integral is sufficiently general. It is assumed that the waveform belonging to such a set is added to several given linear time-invariant filters. A theory of the optimum approximation of the original waveform is established using the sampling sequences of the corresponding outputs. The measure of the original waveform is established using the sampling sequences of the corresponding outputs. The measure of the approximation error is defined as the upper limit of the absolute value of the difference between the original and the approximating waveforms when the original waveforms are changed one by one over the whole set of waveforms. Considering the sampling points, which substantially affect the approximation at a fixed time t, a theorem is presented which indicates that there exists a waveform which has zero value at all such sampling points and has the absolute value of the approximation error which reaches the above upper limit. It is shown also that a similar result can be established for the multidimensional waveform. In this paper, it is shown that the proposed method of linear approximation is better than any other approximation using the same sample values, including the nonlinear signal processing, as long as the forementioned set of waveforms and the measure for the approximation error are considered. [ABSTRACT FROM AUTHOR]

This paper proposes a design method for the FIR two-channel perfect quadrature mirror filter (QMF) with the linear phase. The two-channel perfect QMF can be designed by Vetterli's method, where a system of equations representing the condition for the perfect reconstruction of the signal is solved. The filter designed by this method, however, does not, in general, have good frequency characteristics. This paper presents the design for the two-channel QMF with a perfect reconstruction and a good amplitude characteristic. The method is based on Vetterli's method, and a constraint to approximate the amplitude charac- teristic in the frequency domain is added to the condition of perfect reconstruction in time domain. Then Remez' algorithm is applied to the derived system of equations. The construction of the two-channel perfect QMF, when the coefficient is quantized, also is discussed. Furthermore, a method is shown in which the two-dimensional (2-D) perfect QMF is designed by applying the McClellan transformation to the obtained 1-D QMF. The condition for the McClellan transformation for the perfect reconstruction is derived. [ABSTRACT FROM AUTHOR]

This paper considers the case where hysteresis is given by the Preisach model and discusses the stability analysis for the periodic solution in the nonautonomous system containing hysteretic elements. The behavior of the system containing hysteretic elements is affected by the history of the system until it arrives at the steady state. In this paper, it is shown first that even periodic solutions with the same hysteretic loop may have different variational systems for the steady-state solution if the histories until arriving at the steady state are different, Next, two kinds of stability criteria are considered based on the difference of the history up to the steady state and the stability against the external disturbance is investigated. The dependence of the stability of the solution on the bifurcation of the periodic solution also is discussed. Finally, examples of numerical analysis are presented to verify the result of discussions. [ABSTRACT FROM AUTHOR]

Given an absolutely square-integrable waveform handpass limited to the interval |ω| ≤ ω0, ω0 > 0, and regularly spaced sample points tn = nτ0, (τ0 = π/ω1, ω1 > ω0i n = 0, ± 1, ± 2, . . .), the interpolation formula which corrects errors in the sample values of the original waveform is not uniquely determined. In this paper, we derive several theorems which establish the relation between the interpolation functions and a two-variable function of angular frequency ω and time t called the generating function of the sampling theorem. First, we show that these interpolation functions may be considered as functions of time with coefficients obtained from the Fourier series expansion of the generating functions with respect to the angular frequency ω. This theorem depends on another already established theorem, for which a brief proof is given in the Appendix, for the reader's convenience, in the case that the relation is defined on a vector space. Next, under the condition that the generating function is absolutely continuous, we consider the problem of determining a generating function that minimizes the sum of the squares of the weighted interpolation functions. We show that the sum of the squares of the weighted interpolation functions as a measure provides a bound on the magnitude of the interpolation functions and also measures the rate of decrease. In this paper, under two conditions, which are satisfied in the sampling theorem, a generating function in the sampling theorem is determined which minimizes the above-mentioned measure of the interpolation functions. Using these arguments, we also derive generating functions which minimize various weighting measures related to the interpolation functions Ψn(t), such as when the weights are squares, (2k)-th powers, and (1 + n2τ02). [ABSTRACT FROM AUTHOR]

This paper shows that the learning identification (the normalized LMS) algorithm can be expressed by a first-order IIR lowpass filter having rapidly varying coefficients as a function of output signal to be sent to an unknown system to be estimated. Based on the expression, this paper studies the estimation error of adaptive filters obtained by the learning identification algorithm. It is pointed out that the mean of estimation error given by the conventional analysis corresponds to the output fluctuation which can be computed by replacing varying coefficients of the lowpass filter with its arithmetic mean. However, the output fluctuation is affected by the time constant specified by the coefficients of the lowpass filter and it has a characteristic that it increases rapidly when time constant is short and decreases slowly when it is long. This means that the actual estimation error becomes larger than the result given by the conventional analysis. According to the analysis shown in this paper, it can be seen that the estimation error consists of elements for which the portion increased by the effect of time constant become fewer anti-proportionally to the number of the tap, and those elements which increase at a constant rate independently of the number of the tap. It was shown also by simulation using white noise that the difference between the estimation error obtained in actual estimation operation which occurs when the number of the tap is small and the result given by the conventional analysis can be explained well by the analysis by simulation using white noise. [ABSTRACT FROM AUTHOR]

This paper considers the 2-fl separable-denominator digital filter, and discusses its real-time and parallel-processing-oriented realization. The aim of this paper is to employ a large number th processors concurrently, and to realize a real-time processing minimizing the data throughput delay by applying pipeline processing. More precisely, the case where the poles of the 2-D separable- denominator transfer function are composed of real and complex poles is considered, and two new methods of realization are presented based on the Roesser-type local state-space model, which is suited to the real-time processing. It is shown that the data throughput delay in those methods is equal to the time for two multiplications and one addition, or the time for one multiplication and two additions. The processor factor and the efficiency in each realization are investigated, and the effectiveness of the realization methods are verified from the viewpoints of real-time processing and paralle processing. [ABSTRACT FROM AUTHOR]

In a previous paper, the authors proposed a design method for representing the window function by the C-spline function, which is a linear combination of the B- spline functions. By using that design method, a window function is obtained which has the same mainlobe bandwidth and the highest sidelobe level as the Hanning window or Blackman window, but a faster sidelobe fall-off. However, the design method for the new window function is not practical due to the fact that the description of the design specification is premature and the optimal dimension is not specified. This paper aims at the realization of a practical design method by improving those points. A design method is proposed in which the specification for the high-frequency range is given in terms of the sidelobe fall-off, and the specification for the low-frequency range is given in terms of the desired frequency characteristics in the logarithmic scale, together with the tolerable approximation error, represented by the mean-square error. The optimal dimension is determined, in the iterative approximation increasing the dimension to reduce the error in regard to the desired frequency characteristics, as the minimum dimension that reduces the err- or to the tolerable value. The usefulness of the proposed design method is demonstrated by a design example for the window function, which has a better characteristic than those of Kaiser-Bessel, Gauss and Hanning windows. [ABSTRACT FROM AUTHOR]

This paper proposes a time-varying parameter estimation of a minimum realization ARMA lattice model. The model consists of four types of elementary sections. Since each elementary section has only a design parameter after normalization, its characteristics can be represented more compactly. To estimate time-varying characteristics, several methods with the constant weighting factor have been proposed. This paper shows the limits of the methods using the constant weighting factor and proposes an estimation method with a new variable weighting factor. The new method directly weights observed signals and can arbitrarily change the weighting factor at any time. [ABSTRACT FROM AUTHOR]

This paper considers the switched (S) network obtained from the bipolar network by replacing each transistor by its Ebers-Moll model and further replacing the diode in the model by the switch and the voltage source. The switching (S) control is proposed as a method to determine the operational state of such a network; S control is a method where the S network is analyzed under the assumed switching state S-, and the new switching state P is determined based on the result of analysis. The procedure is iterated until S+ = S- is valid. However, the analysis by S control contains several problems in its execution, such as the singularity problem, where the coefficient matrix of the network equation becomes singular, or the limit cycle problem, where several S states are circulated. This paper presents a method of analysis for the S network, where virtual capacitors and inductors are added between switch terminals, and the solution is obtained as the steady-state solution obtained by the numerical integration of the state equation. The singularith problem is dissolved by the proposed method. It is shown also that some networks, in which the limit cycle phenomenon arises by the conventional method, can be analyzed by the proposed method without the problem. By appropriately setting the values of the capacitors and inductors in the proposed method, the calculation of the inverse matrix can be eliminated in the numerical integration steps, and the high-speed computation composed only of the additions and multiplications of matrices can be realized. [ABSTRACT FROM AUTHOR]

Recently, for signal processing such as echo cancellation and equalization it is required to develop IIR-adaptive digital filters. This paper proposes a new-type IIR- adaptive algorithm based on the orthogonalization method, considers the convergence of the algorithm, and verifies its effectiveness by simulation. White's algorithm is one of IIR-adaptive algorithms reported thus far and Feintuch's algorithm is known as its approximation algorithm. This paper also derives an IIR-adaptive algorithm using both Feintuch's algorithm and the orthogonalization method, First, it can be shown that a generalized algorithm (IIR-LI) of IIR-learning identification method based on previous heuristic methods can be derived using the idea of Feintuch's algorithm and the conjugate gradient method. Next, a new IIR-adaptive algorithm (IIR-AACG) based on the orthogonalization principle of the conjugate gradient method is presented. Further, by applying the orthogonalization method to a past input vector sequence we derive an IIR-Affine projection algorithm (1IR-AP). Finally, these algorithms are compared by computer simulation to verify the effectiveness of the orthogonalization method. [ABSTRACT FROM AUTHOR]

This paper discusses how to reduce the number of states in the main decoder placed in an SST Viterbi decoder for general rate 1/2, constraint length K, and quick look-In codes. Presented are three different cell configurations for which state elimination is possible if an MAP estimation method is applied for branch metric computation. It is shown that for each of these cell cone figurations, a considerable portion of decoder states can be eliminated without any accompanying performance degradation. It Is clarified also that, by transforming encoder states to syndrome former states (i.e., dual states)1 these cell configurations can be mapped to those discussed in Schalkwijk's paper. [ABSTRACT FROM AUTHOR]

gggggAssume that an n × n dot matrix is stored in consecutive n words of a computer with one word being n bit. This paper discusses eight operations to rotate or transpose the dot matrix in horizontal/vertical! slant direction. As is well known, such operations form a group. This paper presents a unified description of the algorithms, and it is shown that all eight algorithms can be derived by suit- ably setting the constants in the unified algorithm. Then it is shown that the algorithms can be transformed to each other by simple transformation rules for the constants, and those transformation rules are shown to form a group. The foregoing algorithms for the dot matrix are not unique, and there can be different descriptions for the algorithm producing the same result. Consequently, there can be various versions of the eight algorithms as well as versions of transformation rules. This paper shows that one of the two groups formed by the transformation rules is isomorphic to the group of algorithms, but the other is not isomorphic. [ABSTRACT FROM AUTHOR]

This paper shows that when a single-step numerical method to integrate ordinary differential equations admits some symmetries, an infinite number of numerical solutions can be obtained from a single one without a further numerical experiment. When this property is obtained, trajectories to be integrated numerically can be confined in advance which may lead to a reduction in the number of experiments. Here, by symmetry is meant invariance of difference equations under an action of a Lie group. However, it is not necessarily easy to judge if a scheme admits a symmetry. This paper illustrates a combination of a backward Euler method and a forward one, whereby a symmetry is attached automatically to any invariant (first integral). Kepler motion is treated as an example. For this system, the integration scheme introduced here conserves three angular momenta which produce a symmetry composed of all three-dimensional rotations. By means of this symmetry group, one numerical solution produces a three-parameter solution by way of linear transformations. It is shown also that the numerical values calculated directly by the scheme and those obtained from another solution by means of a symmetry agree with each other with sufficient accuracy. [ABSTRACT FROM AUTHOR]

This paper considers the software which is used discretely with regard to time, such as the usual software for numerical computation, and proposes a model for the reliability analysis in the development stage. Also, the ease of the software test is considered in which two debuggers attempt to detect the bugs in the software. A discussion is made from the viewpoint of Bayes' theory. The case of two debuggers is as follows. Two software engineers execute the test independently for the same software. The detected bugs are compared later, including their overlaps, to acquire a larger amount of information. Based on the model for analysis proposed in this paper, a formulation is presented for the determination of the release of the software, i.e., the time to terminate the test. Numerical examples are presented, providing discussions on the features of the model considered in this study as well as on its usefulness. [ABSTRACT FROM AUTHOR]

This paper proposes a new construction method for 2-D IIR digital filters with all-pass subfilters as components. Recently, numerous studies have been made to construct digital filters by combining all-pass characteristics. This paper is based on the construction by a parallel connection of an all- pass subfilter and delay element, which can realize approximately the linear phase characteristic. First, the basic design for 1-D digital filters as well as its properties are described. Then the theory for the 1-D case is extended to the 2-D case, and a new construction method for 2-D digital filters with low-pass characteristics with circular symmetry is shown. The proposed method features the following. The phase characteristic is approximately linear in the passband. The filter can be realized with a smaller number of multipliers than in the traditional method. The coefficient sensitivity is low. [ABSTRACT FROM AUTHOR]

This paper proposes a method to approximate transfer functions of magnitude and delay digital equalizers for transmission channels with bandpass characteristics. In this method, an extrapolation band is added to the equalization band on the unit circle on the z-plane, and the resulting extended approximation band is mapped on the overall unit circle on the auxiliary complex plane. In the magnitude equalization, the allpole type transfer function is used for the approximation to have a loss from the extended approximated band. On the auxiliary complex plane, the desired characteristics are squared and inverted. Then the extrapolation characteristics are determined, and the inverted desired characteristics are expanded into Fourier cosine series. This series is transformed inversely into the z-plane to determine the denominator of the transfer function. If the extrapolation characteristics are determined improperly, the resulting transfer functions may become unrealizable. This paper proposes a method of determining the extrapolation characteristics so that it always gives realizable transfer functions. In the delay equalization using the auxiliary complex plane, the approximation cannot be performed in a straight forward manner. In the proposed method, the delay characteristics are treated graphically and the inverted characteristics are expanded into Fourier cosine series. After inverse transformation into the z-plane, the inverse of the series is expanded into the Fourier series and truncated in some length to give the transfer function [ABSTRACT FROM AUTHOR]

This paper considers approximation formulas of the n-dimensional wave f(X) expressed by the sum of sampled values of f(X) multiplied by certain n-dimensional waves called interpolation functions. A systematic discussion is made to determine whether or not the approximate function converges to the original wave f(X). In this paper it is assumed that the interpolation functions satisfy the causality in regard to a certain axis in the n-dimensional space Rn. Usually, that axis is considered to be the tine axis. These discussions are important from the theoretical viewpoint, since it is closely related to the problem as to whether or not interpolation functions can be realized as impulse responses of physically realizable time-in- variant linear circuits. The set of sampling points is defined as a set of vertices obtained by sampling periodically all the vertices of the n-dimensional parallel polyhedra periodically arranged in the space Rn. This definition of the set of sampling points Includes most of the important arrangements of the sampling points, such as the hexagon and octagon lattices in the two-dimensional plane. In this paper, it is assumed that the interpolation functions have supports, which are parallel translations of each other. The functional forms of the interpolation functions may be different. The set of f(X) considered in this paper is defined as the set of n-dimensional waves whose Fourier spectra have the weighted power-of-p norm (p > 1) smaller than the specified positive value. It is shown first that, under the condition that the squared-sum of the interpolation functions is bounded, the considered approximate expression does not in general converge to the original wave. It is shown that if the I ore-going condition is relaxed, an approximate expression can be found with the impulse response of a causal time-invariant linear network as the interpolation function, which converges to the original wave. [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]

Several methods have been proposed to determine a high-resolution NNR spectrum from limited data. This paper attempts to improve and extend the NMR spectrum estimation method using a complex Kalman filter, which was pro- posed previously by Nishlyama and Mita. In the proposed NMR spectrum estimation using the Kalman filter, extra data were required in addition to that to be used in the spectrum estimation, in the approximate determination of the spin-spin relaxation time. Hence, the previously reported NMR spectrum estimation is not based strictly on the same condition as that of the discrete Fourier transform. This paper improves this point, and the extra data are obtained by extrapolation by the AR model. This makes it possible to compare the method with the discrete Fourier transform based on the same number of data. It is shown that when the spectrum is limited to a certain frequency band, the proposed method gives an NMR spectrum with twice higher frequency resolution by reducing the effect of the spin-spin relaxation time and the effect of discrete approximation. In the proposed method, the spin-spin relaxation time of the nucleus, corresponding to the frequency resolution that is twice higher than usual, is determined by a linear interpolation of the spin-spin (relaxation time which is obtained approximately by discrete Fourier transform. [ABSTRACT FROM AUTHOR]

This paper proposes a new method of constructing the multirate FIR digital filter with arbitrary passband, using real-coefficient filters for the decimator and interpolator composing the multirate filter. It is already known that the bandpass filter can easily be realized using the complex-coefficient filter. In such a construction, however, the processing of the analytic signal is required using Hubert transform, which makes the whole system somewhat complex. From such a viewpoint, this paper presents a method of constructing the multirate bandpass digital filter using the real-coefficient filter. Another method is also presented, where the multirate lowpass filter with arbitrary passband can be constructed by combining the complementary response and a lowpass filter. The multirate method is effective in realizing a narrowband response, but may not be useful in realizing a relatively wideband response. By the proposed method, the latter can easily be realized drastically reducing the number of multiplications. Similar methods can be applied to highpass and bandstop filters. [ABSTRACT FROM AUTHOR]

This paper presents a unified theory for the nonuniform sampling theorem for the low-pass band-limited waveform. In most practical cases, the mean interval of the sampling points is in the so-called oversampling state. One can also assume that there exists a certain period in the sampling point sequence. Those properties of the sampling point sequence are assumed in this paper. Yen has derived a sampling theorem for the case where the sampling-point sequence has a period. In his theorem, however, the interpolation function has a spectrum which is a stepwise discontinuous function, not suited to the realization of the interpolation function by a digital or other similar filters. One of the greatest features of the sampling theorem proposed in this paper is that the interpolation function has a continuous spectrum. The problem has been discussed by one of the authors for the case where the sampling frequency and the band-end frequency of the waveform are in an integer ratio. In this paper, the sampling theorem is derived in a unified and integrated form without imposing such a condition. The variance of the approximation error is also derived for the case where a statistically independent additive error is superposed on the sampled value, and it is shown that the proposed sampling theorem is better in that respect. The discussion is extended to the multidimensional band-limited waveform, and a sampling theorem is shown which has an interpolation function with a continuous spectrum. [ABSTRACT FROM AUTHOR]

This paper studies the analysis and minimization of roundoff noise in separable denominator multidimensional (SD M-D) digital filters on the basis of state-space representations. First, the roundoff noise in SD M-D digital filters is analyzed and the !2-norm dynamic range constraint is discussed. Using the results, a synthesis method of optimal realizations (with respect to roundoff noise) is proposed. Further, the simple relation between balanced realizations and optimal realizations of SD M-D digital filters is obtained and an efficient method for synthesizing optimal realizations from balanced realizations is proposed. In addition, this paper also proves that optimal realizations are free of overflow oscillations under zero input conditions. Finally, the synthesis procedure is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

It is known that a leapfrog-type digital filter obtained by simulating an LC ladder filter terminated with resistors on both ends is a digital filter with a low coefficient sensitivity. In this paper, an analog circuit to be simulated is chosen as a distributed circuit in which the real frequency and the discrete variable correspond rigorously. By means of an equivalent transformation, a leapfrog-type digital filter is constructed in which no delay free loop is generated. In this method, an LC ladder circuit expressed in terms of the Richard variable p is transformed to the circuit expressed in terms of the WI variable y. The digital filter is configured by stimulation of the relationship between the node voltage and series branch current in each element of LC ladder circuit. However, if the configuration is based on general distributed LC ladder circuits, a delay-free loop is always generated and configuration becomes unstable. As a solution to this problem, unit elements are introduced in this paper. It is shown that a realizable signal-flow graph can always be obtained if stub circuits are used as the original circuit. The basic section necessary to circuit configuration is presented. Finally, as a practical example, the present method is used for design of a fourth-order bandpass filter. The results are described and compared with those by other configurations. [ABSTRACT FROM AUTHOR]

One of the important problems of watermarking techniques is the weakness against geometrical distortions because of synchronization loss. In this paper, we propose an image compensation scheme against geometrical distortions in order to extract watermarks correctly. Our scheme collects the feature points in an image so as to recover the distortions caused by geometrical distortion attacks. Such feature points are selected by the local maximal value of partitioned regions which can be obtained by several filtering operations. Based on the computer simulated results, we have searched the optimal filtering operation and interpolation, and then studied the validity of our scheme. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(12): 1– 9, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20235 [ABSTRACT FROM AUTHOR]

The YUV 4:2:0 format is a representative format for color images in international standards. In this format, both color difference components U and V reduce the number of pixels in the horizontal and vertical directions by one-half. Consequently, this reduction degrades the color difference components. At a relatively high bit rate, the degradation produced by reducing the number of pixels is often worse than the degradation that depends on the coding. Thus, processing to compensate for the degradation due to the format transform becomes necessary. The pixels of the color difference components reduced once on the encoding side are determined by interpolation on the decoding side. The typical interpolation methods are bilinear interpolation, bicubic interpolation, and interpolation by a finite impulse response (FIR) filter. When these interpolation methods were applied to interpolate the color difference components in the YUV 4:2:0 format, blur and lower saturation were produced in the colors in the color difference components returned to the original number of pixels. In this paper, we propose a method that uses information in the luminance component not having a reduced number of pixels to interpolate the color difference components in the YUV 4:2:0 format. Consequently, color blurring is prevented in the edges of the image, and an objective is to improve the saturation in the entire image. We based the proposed method on bilinear interpolation and bicubic interpolation, and formulated an interpolation method using the luminance component as an extended form. The proposed method and the bicubic interpolation are compared in both objective and subjective evaluations, and demonstrate the effectiveness of the proposed method. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(9): 1–10, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20218 [ABSTRACT FROM AUTHOR]

In connection with the method of selecting among sensors connected by a network those sensors that can efficiently acquire information on the object, this paper presents a discussion in a form that explicitly treats the existence of communications delay when the information is received via a network. First, we propose a calculation algorithm that is scalable with respect to the increase in the number of the sensors when the information from several sensors is combined by a Kalman filter and the communications delay is taken into account. When several sensors have different communications delays and these delays change so that the sensor information arrival is unrelated to the actual time, the information is correctly combined. Next, we propose a method for selecting an appropriate sensor when state estimation by this algorithm is performed. This method makes use of the cross-information previously used as a reference for sensor selection. However, the reduction of the information content due to communications delay, affecting the estimated value for the present time, can be expressed quantitatively. These algorithms are verified by numerical experiments and their effectiveness is demonstrated. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(5): 21–31, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20211 [ABSTRACT FROM AUTHOR]

In this paper, we propose a new adaptive filter and adaptive nonlinear predictor to implement the nonlinear prediction of speech signals to solve the problem of impulse-shaped residual errors in the linear prediction. While using order statistics processing, we add an improvement that keeps time information about the input signal to the LMS-L filter proposed by Pitas and Venetsanopoulos. Tests using synthesized speech show that the proposed nonlinear predictor has superior prediction performance to the Volterra series predictor and not just the linear predictor. However, even with this proposed nonlinear predictor, the prediction accuracy degrades in experiments using real speech. Therefore, we propose a new iterative method to conquer this problem. The iterative method pays attention to the periodicity of the speech, reuses the speech data, and obtains a prediction accuracy similar to when using many data samples. In experiments on real continuous speech, the proposed predictor improved prediction accuracy by using the iterative method, and the effectiveness of the method was confirmed. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(11): 28–42, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20148 [ABSTRACT FROM AUTHOR]

Recently, approximation problems for FIR digital filters in the complex domain have been studied extensively. This class of problems minimizes the absolute value of the complex error of the filter studied and the desired response. Hence, the problem is to approximate amplitude and phase. However, in the waveform transmission, the group delay to indicate the delay of the wave is more important than the phase characteristic. To date, the phase approximation has been used as an indirect approximation of the group delay. Hence, the designed group delay characteristic is substantially degraded from the desired group delay. In the present paper, the group delay error is included in the performance function as a performance parameter of the least squares method. By deriving the least square error with repeated transformation of the desired response, a direct approximation of the group delay is realized and both the amplitude and the group delay are optimized. Finally, by numerical simulation, the method is compared with the conventional ones and the effectiveness of the present method is demonstrated. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(11): 20–27, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20169 [ABSTRACT FROM AUTHOR]

An upper bound equation for the bit error rate of serially concatenated trellis coded modulation was proposed, but required an extremely large memory space for the numerical calculations and encountered problems in the execution. In this paper, we propose a method able to perform these numerical calculations. We also analyze the interleaver gain based on the upper bound equation. The results clearly show that a larger interleaver gain is obtained than the prediction from the result of serially concatenated convolution codes. We also present a guide for obtaining a large interleaver gain. This guide can be used even when the codes are limited in a code search, and the results of code searches are presented. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(9): 21–32, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20156 [ABSTRACT FROM AUTHOR]

This paper considers chirp pulse microwave CT (CP-MCT), in which the chirp pulse and signal processing technology are used to estimate the internal structure and temperature variation of biological objects. A method is developed in which the CT image to be acquired by actual measurement can be derived by numerical computation. The aftereffect function between the transmitting and receiving antennas is calculated by a Gaussian pulse and the FDTD method. After convolution of the function with the input chirp pulse signal on the time axis, the measured signal at a point is constructed by the same signal processing as in real measurement. This computation is repeated for each point on the translation-scanning axis. The projection data are acquired and the CT image is generated. The validity of this computation procedure, which is called the aftereffect function method, is demonstrated by comparing the resolution and the measured temperature variation in actual measurements with the results of a simulation computation. Using the aftereffect function method, the point-spread function of an imaging system which is difficult to measure, can be derived. An analytical model for the human head is constructed. Simulations are performed for the attenuation distribution and the temperature variation distribution. Based on the results, the feasibility of the biological imaging by CP-MCT is discussed. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(9): 53–63, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20190 [ABSTRACT FROM AUTHOR]

According to the boundary surface control principle, it is possible to reflect the flow of acoustic energy at a boundary if a boundary surface with impedance 0 can be formed by controlling the sound pressure and the particle velocity at an arbitrary position in space. If this principle is used in such a way that a boundary surface is formed only in the direction not intended for radiation of the sound, then a directional speaker system can be realized. In the conventional design method of the directional speaker array system, in order to achieve sharp directivity in the low frequencies, it is necessary to enlarge the array length. On the other hand, in our proposed system, it is easy to achieve sharp directivity in the low frequencies, since the boundary surface control principle can achieve high performance in the low frequencies. Moreover, by changing the control sound source spacing for each bandwidth, rather flat characteristics can be obtained over the entire control range. In this paper, the basic characteristics constituting guidelines for system design and the effect of control are confirmed by numerical calculations and experiments. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(2): 1–9, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20122 [ABSTRACT FROM AUTHOR]

Character recognition systems, which employ a machine to recognize handwritten or printed characters, are prone to recognition errors in the cases of characters which are similar in shape. For example, the numerical character 7 is frequently mistaken for 9, and vice versa. In contrast, the characters 7 and 4 are not similar in shape, and 7 is unlikely to be mistaken for 4, or vice versa. Therefore, the rate of recognition error between these characters will be low. By considering this type of error model, this paper defines a new q-ary asymmetric error and proposes a method for constructing single q-ary asymmetric error locating codes. It also presents an evaluation of the code, demonstrating its superiority to the conventional single q-ary symmetric error correcting code. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(3): 77–87, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1156 [ABSTRACT FROM AUTHOR]

When the characteristics of non-Gaussian time series, such as biological signals, are described, higher-order spectra such as the bispectrum must be referenced in addition to the power spectrum. To obtain estimates having few statistical fluctuations, parametric estimation methods of these spectra should be established. In recent years, a simple discretization method (SDM) has been proposed as a numerical solution based on iterated integral transform of the stationary joint density probability function and the higher-order spectra of nonlinear autoregressive models like a neural network autoregressive model. However, the SDM requires an amount of calculation memory that increases exponentially with respect to the lag order of corresponding models. In order to overcome this drawback, the tensor product expansion method (TPEM) where the joint probability density function is expanded as the sum of single-variable functions was proposed. This method can suppress the increase in the required memory capacity to a linear increase. A numerical example has shown where the TPEM calculated the bispectrum more accurately than the SDM with an equivalent amount of memory. However, the relationship between the performance of tensor product expansion and the dependence properties of the target time series has not as yet been investigated. In this paper, we study the property dependence of the time series in the TPEM and point out the problem of worsening calculation accuracy for a time series in which values at each time instant highly depend on each other. As the solution, we propose a new method that introduces a linear coordinate transform in state space where the joint probability density function undergoes the tensor product expansion. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(1): 19–28, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10103 [ABSTRACT FROM AUTHOR]

The 1/f spectra that appear in electroencephalogram data are among the characteristics that appear in the wide range of self-organizing phenomena encompassing both physical and sociological phenomena. The fact that they appear across the various objects suggests that the underlying cause of the 1/f spectra can be elucidated by using a simplified model that does not depend on the detailed structure of the objects. This paper, treating the electroencephalogram as a macro-quantity of neuron activities, demonstrates the existence of a self-similar solution through the spatial-temporal coarse-graining of a neural network, which is a simplified model of the brain. The self-similar solution in fact leads to the derivation of a 1/f spectrum. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(1): 72–81, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10016 [ABSTRACT FROM AUTHOR]

Recently, simulation has become important in the field of acoustics. As an acoustic simulation method, the FDTD (Finite-Difference Time-Domain) method has been proposed. However, when this method is applied to a large-scale propagation analysis such as indoor acoustic propagation, the phase error cannot be neglected and causes a problem in the analysis. Therefore, a highly accurate method of analysis that can reduce the phase error is strongly desired. In the present paper, a three-dimensional FDTD(2, 4) method with second- and fourth-order accuracy in time and space is formulated as a highly accurate method of analysis. Also, the numerical dispersion and stability condition, which are important for understanding the characteristics of the method, are derived. It is demonstrated that the present method provides much greater accuracy than the FDTD method. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(11): 30–37, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10076 [ABSTRACT FROM AUTHOR]