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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]