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It is fundamentally important in waveform recognition to provide a method for systematic description of the changing nature of the given waveform at an arbitrary time. This paper presents a solution to this problem based on the natural observation method proposed by the author. After the definition of the instance is introduced, regulating the infinitesimal time interval at the time of interest, the instantaneous derived waveform series is derived from the input waveform by successive observations. A set of practical analysis methods has been studied theoretically for determining the mathematical structure of the instantaneous waveform for the observations. [ABSTRACT FROM AUTHOR]

When the linear prediction coefficients (LPC) are used as a feature parameter of speech, a problem in speech recognition is the variation of LPC due to the difference of the speaker and the effect of the preceding or succeeding utterances. Because of this variation, LPC is distributed in a certain region in the LPC space. This paper proposes a method which approximated the region of distribution by a linear manifold model described in [1], and recognizes the category permitting the variation of LPC. The method is applied to the vowel recognition of CV syllable, and its usefulness is verified experimentally. It is shown first by spectrum analysis experiment that the linear manifold model is useful in the approximation of the variation of the vowel spectrum due to the preceding consonant. Second, a recognition experiment is carried out based on the model, and it is shown that the recognition rate can be improved by a simple model of linear manifold which is suited to computation. [ABSTRACT FROM AUTHOR]

A lattice filter has several advantageous properties for adaptive applications. The gradual increase of the degree of estimation by the regular repetition of the adaptation module is particularly advantageous for hardware realization. In this paper, this adaptation module is called a lattice element and a method is proposed for the design of adaptive filters using such lattice elements. The efficiency of this method is demonstrated by the derivation of orthogonalizing and biorthogonalizing filters. The operation of these filters is tested by computer simulation and some problems arising at higher-order filters are pointed out. [ABSTRACT FROM AUTHOR]

Observation of the waveform is a fundamental problem common to the problem treating various waveforms such as the voice. This paper attempts to provide a rational answer to this problem. Originally, the theory has been developed with the assumption of a simple condition called the natural observation condition. As a result, a simple and complete observation system has been developed which consists of only one original function and two observation types. Traditionally, the concept of a running spectrum has been known for the observation problem of waveforms. In such a concept, the temporal transition of the short-term spectrum is studied. From this viewpoint, the present method is an extension of the concept and places a new theoretical foundation in a rational manner so that unclear points and self-contradictions of the previous theory are corrected. [ABSTRACT FROM AUTHOR]

This paper describes a method of non-stationary analysis based on the geometrical orthogonal projection with least-squares estimation for a linear model. In the past, local stationary analysis and adaptive methods which successively estimate the parameters have been used for this purpose. How- ever, in application to the nonstationarity case as in biomedical signals these methods have the disadvantage that it is difficult to see the physical significance of the parameters. In consideration of this, the present paper defines the backward prediction error space (Ens) consisting of the backward prediction error vector in each dimension and proposes to handle the nonstationarity by expanding the property into the orthogonal states in each dimension. The backward prediction error vectors constitute an orthogonal system in the least-squares estimation and the reflection coefficient is the parameter directly related to this system. The orthogonality can be interpreted in direct relation to the independence of physical functions. As a measure of the non-stationarily, the angle between the vectors is adopted in the BPES. When the parameters which were optimum in the stationary interval are applied to an arbitrary interval, the angle is an exact expression of the discrepancy due to the nonstationarity. By an example of analysis of biomedical signals it is verified that the angle is useful in evaluation of the nonstationarity, especially of that arising from the change of orders. Thus, it is anticipated that the deterministic non- stationary analysis by BPES will provide new information about biological systems. [ABSTRACT FROM AUTHOR]

This paper provides a method of estimating a rotation center to analyze kinematically the movement of a rigid body moving periodically in a two-dimensional (2-D) space. The rotation center, which is derived from an axis point of the human jaw joint, is defined as a point which moves reciprocally in periodic movement. Accordingly, it is called the reciprocating point. Separating a path of the reciprocating point by its turning point, we can divide the path into two parts—the forward path and the backward path. Both paths are identical and hence it appears that any position in one path has its counterpart in the other path. We show that if we have a function corresponding to a pair of positions mentioned in the foregoing, we can estimate the reciprocating point. Then we derive an algorithm which approximates successively the function and the reciprocating point alternatively. This algorithm is proved to be effective for estimating an axis point of the jaw joint. [ABSTRACT FROM AUTHOR]

This paper describes a problem of estimating a kinematically characteristic point of a rigid body moving in a three-dimensional (3-D) space. We call this point the 1-D characteristic point and denote it by P1. The point P1 is characterized by its motion range which forms a curved line. Hence, if the rigid body moves periodically, we can specify P1 as a point which moves reciprocally. This paper proposes a method of estimating P1. By projecting the orbit of a point onto three planes orthogonal with each other, we reduce this estimation problem to that of solving a set of quadratic equations, and we then provide one of its solutions. In addition, we clarify how measurement errors of the motion propagate to an estimation of P1. [ABSTRACT FROM AUTHOR]

In the problem of measuring three-dimensional positions and motion of a rigid body, methods to determine the three-dimensional position from its optical projection data on a two-dimensional plane have been widely used. We have proposed a method using positional relations among the marked points and applied it to three-dimensional movement measurement of the human law. If the positions of three marked points on a rigid body are known, measuring these positions requires only one projection datum at each point to determine the three- dimensional position of the points, since the degree of freedom of a rigid body is six. A previous paper presented formulation of the problem in general form, its solution and theoretical analysis of stability of solution, as well as observation method. This paper analyzes the effect of error associated with measurement on estimating the position of marked points at implementation. Error propagation equations are derived effective for design of measuring instruments. The optimum measuring method is obtained from the viewpoint of error propagation using the result. [ABSTRACT FROM AUTHOR]

In the problem of estimating three-dimensional positions of a rigid body from projection data of marked points fixed set to it onto a two-dimensional plane. We propose a method using positional relations among the marked points. To estimate the positions of the marked points by optical measurement, multiple projection data are generally used at each point. In measuring multiple points attached on a rigid body, it is possible to estimate three-dimensional positions of the points from only a single projection datum at each point, if the position of each point on the rigid body is known. In this paper, the problem formulated ks of three marked points (the least necessary number to estimate the position of a rigid body). The solution is given by an iterative approximation. Furthermore, the relation between the measurement method and the convergence of the iterative approximation is analyzed. Observation is best obtained from tilts point of view. An instrument to measure three-dimensional movement of the human jaw is introduced. [ABSTRACT FROM AUTHOR]

Previously, in the processing of CT projection data, it was assumed that the measured values are independent at each point. Here it is shown that the actual data have a dependent property, which is called the redundancy of the projection data. It is shown that the redundancy is effective for the reduction of the noise sensitivity of the re- construction formula. This paper evaluates the effect qualitatively and experimentally in comparison with the convolution method, which is the mainstream of the present reconstruction procedure. The reconstruction formula (formula II), which was derived in a previous paper to reduce the noise sensitivity utilizing the redundancy, is compared with the convolution method. The analytical comparison with the mean-square error as the evaluation measure, as well as the visual comparison of the actually reconstructed examples, are performed. [ABSTRACT FROM AUTHOR]

This paper discusses the relations between Coulomb's gauge conditions, boundary conditions on the peripheral surface, symmetrical boundary surface and the surface between media of different materials. It is demonstrated that the gauge conditions are indispensable to describe fully the boundary conditions and the necessity and meanings of gauge conditions are discussed theoretically. [ABSTRACT FROM AUTHOR]