Search

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]

In natural observation theory, input waveforms are observed using natural observation transforms. Especially in the case of the neighboring type, the effect of the uncertainty principle as it applies to a natural observation transform was clarified by using the equivalent time constant. This paper aims to characterize natural observation transforms of normal type in waveform observation from the point of view of the uncertainty principle. Besides the equivalent time constant, the average degree index is introduced to represent the uncertainty principle. It describes a relation between the equivalent time constant and the variance in the observation degree. This paper gives a new insight into the set of fundamental observed values of normal type from the point of view of observation resolution. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(7): 45–54, 1998 [ABSTRACT FROM AUTHOR]

The natural observation theory was originally developed for continuous-time waveforms, and subsequently for discrete-time waveforms. The theories are classified as neighboring, equilibrium, and normal types. However, the derivation of the theory for discrete waveforms was somewhat mathematical and its physical principles for waveform observation were not discussed in sufficient detail. This paper aims to improve the derivation method thoroughly by making the physical principles clear. As a result, the theory of natural observation methods for discrete-time waveforms is formulated by minimizing problems with simple observation error criteria. The natural observation methods derived from the principle are equivalent to the previous ones, although the principles are different from each other. The principles make the physical meanings clear as a basis for developing the theory. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(8): 31–35, 1997 [ABSTRACT FROM AUTHOR]

The theory of natural observation has been proposed as a new method of analysis to replace the Fourier analysis method. It was systematized as a theory with two major types-the neighboring type and the equilibrium type. Especially, although the nucleus of the theory is of standard form, the description with regard to the starting point of the theory in the past has not always been plain and comprehensible. This paper is a radical improvement in this regard and was written to clarify the origin of the theoretical development. Although the previously published theories are not completely revised, this paper is considered significant from the viewpoint of clarification of the base of the theoretical development. [ABSTRACT FROM AUTHOR]

With regard to the theory of natural observation proposed as a new method of waveform analysis and although papers by the author have already been published over the last few years, this paper attempts a generalization based on the theory. As a result, the theory of natural observation can largely be divided into the neighboring type and the equilibrium type. Further, it was clarified that the previous theories belong to the neighboring type. In the treatment of acoustic vibration waveforms such as voice, the hitherto not discussed equilibrium type is desirable. Also, based on the forementioned theories, the general form of natural observation transformation is proposed anew as a substitute for Fourier transformation and, in particular, the standard form thought to be useful hereafter is shown concretely. [ABSTRACT FROM AUTHOR]