This paper addresses the problem of estimating the parameters of multivariate ARMA processes by using higher-order statistics called cumulants. The main objective in this paper is to extend the idea of the q-slice algorithm in univariate ARMA processes to multivariate ARMA processes. It is shown for a multivariate ARMA process that the MA coefficient matrices can be estimated up to postmultiplication of a permutation matrix by using the third-order cumulants and of an extended permutation matrix by using the fourth-order cumulants. Simulation examples are included to demonstrate the effectiveness of the proposed method.

This paper introduces some modelling methods of time-varying stochastic process and its linear/nonlinear adaptive identification. Time-varying models are often identified by using a least square criterion. However the criterion should assume a time invariant stochastic model and infinite observed data. In order to adjust these serious different assumptions, some windowing techniques are introduced. Although the windows are usually applied to a batch processing of parameter estimates, all adaptive methods should also consider them at difference point of view. In this paper, two typical windowing techniques are explained into adaptive processing. In addition to the use of windows, time-varying stochastic ARMA models are built with these criterions and windows. By using these criterions and models, this paper explains nonlinear parameter estimation and the property of estimation convergence. On these discussions, some approaches are introduced, i.e., sophisticated stochastic modelling and multi-rate processing.

In order to realize a continuous-time system model in digital computers, we must construct a discrete-time system model simulating the continuous-time processes in some characteristic aspect. Though many discretization methods have been proposed, they do not necessarily provide a discrete-time system in which input, state and output are identical with the sampled values of the original continuous-time system. The isomorphism discretization that all of the input, state and output of a continuous-time system can be recovered from the corresponding discrete-time system is crucial for our analysis. This paper aims at guaranteeing the isomorphism between a continuous- and a discrete-time system models (fluency system model) which were proposed by the authors. The isomorphism of input space had been already shown in the previous works by one of the authors. In this paper, by showing the isomorphism of the state function and output spaces, the aim will be achieved.

It is an important problem whether or not we can reject the disturbances from distributed parameter circuit. In order to analyze this problem structurally, it is necessary to investigate the basic equation of distributed parameter circuit in the framework of state space. Since the basic equation has two parameters for time and space, the state value belongs to an infinite-dimensional space. In this paper, the disturbance-rejection problems with incomplete state feedback and/or incomplete state feedback and feedforward for infinite-dimensional systems are studied in the framework of geometric approach. And under certain assumptions, necessary and/or sufficient conditions for these problems to be solvable are proved.

When measuring the ejection fraction for the evaluation of the ventricular pumping function by means of the thermodilution technique, the slow response a conventional thermistor has caused it to be considered unsuitable, and fast thermistors have been proposed as an alternative. However, in this paper we propose improving the time-domain response of a conventional thermistor using a signal processing technique composed of a series of first-order high-pass filters which is known as the natural observation system. We considered the rise time of the thermistor in response to a step temperature change to effect correction for the measurement of the ejection fraction. The coefficients of the natural observation system were calculated by minimizing the square error between the step-response signal of the thermistor and the band-limited reference signal. In an experiment using a model ventricle, the thermodilution curve obtained from a conventional thermistor was improved using the proposed technique, thus enabling successful measurement of the ejection fraction of the ventricles.

We discuss estimation error as a basic problem in formant estimation in the analysis of speech of very short-time duration in the glottal closure of the vowel. We also show in our simulation that good estimation of the first formant is almost impossible with the ordinary method using a waveform cutting. We propose a new method in which the cut waveform, as a discontinuous function of finite time, is mapped to a continuous function defined in the whole time domain; and we show that using this method, the estimation accuracy for low frequency formants can be greatly improved.

An adaptive method analyzing analytic speech signals is proposed in this paper. The method decreases the errors of finite precision on calculation in a method with real coefficients. It is shown from the results of experiments that the proposed method is more useful than adaptive methods with real coefficients.

Wave digital filters are a class of digital filters. They are equivalent to commensurate transmission line circuits synthesized with uniform, lossless, and commensurated transmission lines. In order to extend their applications to physical wave phenomena including quantum electronics, it is necessary to consider a generalized distributed line whose velocity of energy flow has frequency characteristics. This paper discusses a generalized distributed circuit, and we obtain two types of lines, lossless and cut-off. In order to analyze these lines, we discuss signal flow graphs of steady state voltage and current. The reflection factors we obtain here are the same as that for an active power or a diagonal element of a scattering matrix, which is zero in conjugate matching. By using this reflection factor, we obtain band-pass filters synthesized with the cut-off lines. We also describe an analysis method for nonuniform line related to Riccati differential equation.

In the band-limited signal space, the mutual relation between continuous time signal and discrete time signal is expressed by the sampling theorem of Whittaker-Someya-Shannon. This theorem consists of an orthonormal expansion formula using sinc functions. In that formula, the expansion coefficients are identical to the sample values of signals. In general, the bandlimited signal space is not always suited to model the signals in nature. The authors have proposed a new model for signal processing based on finite times continuously differentiable functions. This paper aims to complete the sampling theorem for the spline signal spaces, which corresponds to the sampling theorem of Whittaker-Someya-Shannon in the band-limited signal space. Since the obtained sampling theorem gives the simplest representation of signals, it is considered to be the most fundamental characterization of spline functions used for signal processing. The biorthonormal basis derived in this paper is considered to be a system of delta functions at sampling points with some continuous differentiability.

Fluency approach is to deal with staircase, polygonal and band-limited signals as those in a unified series of signal spaces of which characteristics vary with the parameter of degree. Scaling functions and their duals have been obtained which fulfill a part of the requirements to constitute a multiresolutional analysis in this approach. The purpose of the present paper is to derive general formulae to express wavelets and their duals which fulfill the rest of the requirements. It is the first step to have a general expression of every possible wavelet in selecting a wavelet. The degree is limited to be arbitrary positive oddintegers so far in this paper. The genaral formulae derived in this paper are in the form of linear combinations of the sampling functions, which are scaling functions, and their duals. These formulae can be also regarded as a reduced version of the conditions for multiresolutional analysis in terms of sampling functions and their duals. The general formulae provide a start point for selecting a wavelet which decides characteristics of a multiresolutional analysis in the fluency approach. Some criteria for the concrete selection for each purpose of multiresolutional analysis and a formula for the even-degree cases are yet to be aquired in the future.

Reduction of the complexity of the NLMS algorithm has received attention in the area of adaptive filtering. A processing cost reduction method, in which the component of the weight vector is updated when the absolute value of the sample is greater than or equal to the average of the absolute values of the input samples, has been proposed. The convergence analysis of the processing cost reduction method has been derived from a low-pass filter expression. However, in this analysis the effect of the weignt vector components whose adaptations are skipped is not considered in terms of the direction of the gradient estimation vector. In this paper, we use an arbitrary value instead of the average of the absolute values of the input samples as a threshold level, and we derive the convergence characteristics of the processing cost reduction method with arbitrary threshold level for zero-mean white Gaussian samples. From the analytical results, it is shown that the range of the gain constant to insure convergence and the misadjustment are independent of the threshold level. Moreover, it is shown that the convergence rate is a function of the threshold level as well as the gain constant. When the gain constant is small, the processing cost is reduced by using a large threshold level without a large degradation of the convergence rate.

Myoelectric (ME) signals during dynamic movement suffer from motion arifact noise caused by mechanical friction between electrodes and the skin. It is difficult to reject artifact noises using linear filters, because the frequency components of the artifact noise include those of ME signals. This paper describes a nonlinear method of eliminating artifacts. It consists of an inverse autoregressive (AR) filter, a nonlinear filter, and an AR filter. To deal with ME signals during dynamic movement, we introduce an adaptive procedure and fuzzy rules that improve the performance of the nonlinear filter for local features. The result is the best ever reported elimination performance. This fuzzy rule based adaptive nonlinear artifact elimination filter will be useful in measurement of ME signals during dynamic movement.

In this paper, the relationship between the recursive least square (RLS) method with a U-D decomposition algorithm and ARMA lattice filter realization algorithm is presented. Both the RLS method and the lattice filter realization algorithm are used for the same applications, such as model identification, etc., therefore, it is expected that the lattice filter algorithm is in some ways related to the RLS. Though some of the proposed lattice filter algorithms have been derived by the RLS method, they do not express the relationship between RLS snd ARMA lattice filter realization algorithm. In order to describe the relation clearly, a new structure of ARMA lattice filter is proposed. Further, based on the relationship, a method of model identification with frequency weighting (MIFW), which is different from a previous method, is derived. The new MIFW method modifies the lattice parameters which are acquired without a frequency weighting and obtain the parameters of an ARMA model, which is identified with frequency weighting. The proposed MIFW method has the following restrictions: (1) The used frequency weighting is FIR filter with a low order. (2) By using the parameters of the ARMA lattice filter with ARMA (N,M) order and the frequency weighting with L order, the new ARMA parameter with the frequency weignting is with ARMA(N-L,M-L) order. By using the proposed MIFW method, the ARMA parameters estimated with the frequency weighting can be obtained without starting the computation again.

In many applications involving the processing of noisy signals, it is desired to know the noise variance. This paper proposes a new method for estimating the noise variance from the signals of autoregressive (AR) and autoregressive moving-average (ARMA) systems corrupted by additive white noise. The method proposed here uses the low-order Yule-Walker (LOYW) equations and the lattice filter (LF) algorithm for the estimation of noise variance from the noisy output measurements of AR and ARMA systems, respectively. Two techniques are proposed here: iterative technique and recursive one. The accuracy of the methods depends on SNR levels, more specifically on the inherent accuracy of the Yule-Walker and lattice filter methods for signal plus noise system. The estimated noise variance is used for the blind indentification of AR and ARMA systems. Finally, to demonstrate the effectiveness of the method proposed here many numerical results are presented.

This paper shows that a convolution property holds for sixteen members of a sinusoidal unitary transform family (DCTs and DSTs), on condition that an impulse response is an even function. Instead of the periodicity of an input signal assumed in the DFT case, DCTs require the input signal to be even symmetric outside boundaries and DSTs require it to be odd symmetric. The property is obtained by solving the eigenvalue problem of the matrices representing the convolution. The content of the property is that the DCT (or the DST) element of the output signal is the product of the DCT (or the DST) element of the input signal and the DFT element of the impulse response. The result for the well-known DCT is useful for a strongly-correlated signal and two examples demonstrate it.

This paper describes a new method of approximating ideal Hilbert transformers by using time reversal techniques. As is well known, an ideal Hilbert transformer is not physically realizable because it is not causal. Nevertheless, it is extremely imprortant conceptually in the area of digital signal processing. In this paper, we propose a method to approximately implement such a Hilbert transformer. The method divides the impulse response of the ideal Hilbert transformer into two parts, i.e., causal and noncausal parts. Although a causal filter is physically realizable, a noncausal filter is not realizable. A noncausal filter is realized using time reversal techniques for input signals to the filter, and then the Hilbert transformer can be approximately implemented by the parallel connection of causal and noncausal filters.

We develop a convergence theory of the simple genetic algorithm (SGA) for two-bit problems (Type I TBP and Type II TBP). SGA consists of two operations, reproduction and crossover. These are imitations of selection and recombination in biological systems. TBP is the simplest optimization problem that is devised with an intention to deceive SGA into deviating from the maximum point. It has been believed that, empirically, SGA can deviate from the maximum point for Type II while it always converges to the maximum point for Type I. Our convergence theory is a first mathematical achievement to ensure that the belief is true. Specifically, we demonstrate the following. (a) SGA always converges to the maximum point for Type I, starting from any initial point. (b) SGA converges either to the maximum or second maximum point for Type II, depending upon its initial points. Regarding Type II, we furthermore elucidate a typical sufficient initial condition under which SGA converges either to the maximum or second maximum point. Consequently, our convergence theory establishes a solid foundation for more general GA convergence theory that is in its initial stage of research. Moreover, it can bring powerful analytical techniques back to the research of original biological systems.

This paper presents techniques for generating the input patterns for locating logic design errors (PLE's) by Boolean function manipulation based on binary decision diagrams (BDD's). One PLE has one Boolean variable X or and constant values. A primary output of a correct circuit takes value X, while the designed circuit takes either 0 or 1. By using PLE's, the X-algorithms locate single or multiple logic design errors in a combinational circuit. Although PLE's play the most important role in the X-algorithms, the condition under which PLE's exist has not been formalized. This paper gives a formal analysis on the existence condition of PLE's. It is shown that the condition is always satisfied by incorporating another type of PLE. From the condition, an implicit representation of PLE's is derived. In addition, two kinds of approaches are presented for generating PLE's by Boolean function manipulation based on BDD's. One is an approach for generating all the existing PLE's. The other is a heuristic approach to obtain a limited number of PLE's in a short time. Both approaches generate PLE's including don't cares. Incorporating them, a compact representation of PLE is achieved. Experimental results have shown the compactness of the proposed representations and the availability of the pattern generation techniques.

This paper describes the general conditions for perfect signal reconstruction in adaptive blocksize MDCT. MDCT, or modified Discrete Cosine Transform, is a method in which blocks are laid to overlap each other. Because of block overlapping, some consideration must be paid to reconstructing the signals perfectly in adaptive blocksize schemes. The perfect reconstruction conditions are derived by considering the reconstruction signals, on a segment by segment basis. These conditions restrict the analysis/synthesis windows in the MDCT formula. Finally, this paper evaluates two examples of window sets, including windows used in the ISO MPEG audio coding standard.

Relating to the problem of suppressing the immanent redundancy contained in an image with out vitiating the quality of the resultant approximation, the interpolation of multi-dimensional signal is widely discussed. The minimization of the approximation error is one of the important problems in this field. In this paper, we establish the optimum interpolatory approximation of multi-dimensional orthogonal expansions. The proposed approximation is superior, in some sense, to all the linear and the nonlinear approximations using a wide class of measures of error and the same generalized moments of these signals. Further, in the fields of information processing, we sometimes consider the orthonormal development of an image each coefficient of which represents the principal featurr of the image. The selection of the orthonormal bases becomes important in this problem. The Fisher's criterion is a powerful tool for this class of problems called declustering. In this paper, we will make some remarks to the problem of optimizing the Fisher's criterion under the condition that the quality of the approximation is maintained.

The generation and design of a stationary Markov signal are discussed as an inverse problem, in which one looks for a transition probability when a stationary probability distribution is given. This paper presents a new solution to the inverse problem, which makes it possible to design and generate a Markov random signal with arbitrary probability distribution and an exponential correlation function. Several computer results are illustrated in figures.

We present distributed load balancing mechanisms implemented on multiprocessor systems for real time video encoding, which dynamically equalize load amounts among PE's to cope with extensive computing requirements. The loosely coupled multiprocessor system, e.g. a torus connected one, is treated as the objective system. Two decentralized controlled load balancicg algorithms are proposed, and mathematical analyses are provided to obtain some insights of our decentralized controlled mechanisms. We also prove the proposed algorithms are steady and effective theoretically and experimentally.