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This paper considers waveform observation by the normal-type natural observation transform, and discusses the instantaneous relation between the waveform to be observed and the normal-type basic observed value sequence. The relation is similar to the uncertainty relation in the Fourier transform. Although the global uncertainty relation in the normal-type natural observation transform is clearly formulated already, the result is still insufficient for the theory of natural observation, where the instantaneous handling of the waveform has to be formulated. From such a viewpoint, the relation shown in this paper is significant, as a basic property in the instantaneous handling of the waveform by the theory of natural observation. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(8): 61–70, 2000 [ABSTRACT FROM AUTHOR]

The natural observation transform is a new formulation of the time waveform as a transform, when a waveform is observed in the short-term (instantaneous) region specified by the time-constant parameter at an arbitrary time. The basic observed value sequence not only includes the considered time, but also the information extracted from the waveform in the region specified by the time-constant parameter. Based on the above property of the natural observation transform, the object of the transform is not the input waveform itself, but the waveform appearing in the region specified by the time and the time-constant parameter. This paper notes this situation, and discusses the uncertainty that exists between the behavior of the waveform, which is the object of the normal natural observation transform in the whole time region, and the aspect in which the basic observation values are distributed in the sequence for the whole time region. Based on the result of investigation, the optimality criterion for the time-constant parameter is proposed using the equivalent time-constant, and a method of determining the optimal value is shown. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(8): 30–38, 2000 [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 similarity method is an effective matching method for pattern recognition, especially for character recognition. However, for waveform recognition in the time domain, it cannot make enough allowance for possible deformations of waveforms and therefore does not show good performance. In this paper, we improve the allowance of the simple similarity by using the pluralizing method. To apply the pluralizing method, waveforms are expressed in the expansion formula with the natural observation theory of normal type. The effectiveness of pluralized simple similarity is verified by a simulation of speaker-independent vowel recognition. Another improvement considering speaker individuality is also mentioned. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(12): 1–9, 1997 [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]

Natural observation theory was developed in order to make reasonable observations of waveforms under natural observation conditions. This paper aims to clarify the observation characteristics of the theory of neighboring type from the viewpoint of an uncertainty principle. The new concept of equivalent time constant is introduced as a means for representing the uncertainty principle. The representation of the certainty principle in terms of the equivalent time constant has the advantage of representing the uncertainty principle of the Fourier transform more accurately. The uncertainty principle of the natural observation transform of neighboring type is derived by using the representation formula in which the equivalent time constant plays an essential role. This paper gives a detailed presentation of the uncertainty principle and provides a new insight to the set of fundamental observed values of the neighboring type in relation to the resolution of waveform observations. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(7): 11–19, 1997 [ABSTRACT FROM AUTHOR]

A theory of natural observation methods was originally formulated for two-complementary systems; neighboring type and equilibrium type. This paper introduces a new system, normal-type system, that is different from the forementioned two types. One characteristics feature of the normal-type natural observation method is its ability to reconstruct an original waveform from the sum of a finite number of observation values. The natural observation theory of a normal type evolves naturally under the condition that waveform and its power component can be expressed in the sum form. These meanings are discussed by comparing a frequency response of the normal-type natural observation transform with that of a conventional filter bank. Furthermore, a criterion for determining observation parameters I order to realize the natural observation of normal type under a given tolerance of error is described. It is believed that the proposed theory offers new insights into systematization of the natural observation theory. [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 natural observation method provides a procedure to analyze the time-varying characteristics of the continuous-time waveform with mathematical rigor and can resolve the fundamental problem encountered in Fourier analysis method. In this paper, for discrete-time waveforms a discrete natural observation method is proposed which has characteristics similar to those for the continuous natural observation method. Similar to the continuous natural observation theory of normal type, the discrete natural observation theory is introduced by requiring that the waveform values and the power component can be expressed in terms of sum forms. The discrete natural observation method is complete by itself as a discrete type, and not only is it similar in nature to those of the continuous type but also can be shifted naturally to the continuous type as the sampling interval vanishes. [ABSTRACT FROM AUTHOR]

During the past few years, there been a series of paper published on the theory of the natural observation method. As one of the important application of this theory, the problems of acceptance and generation of a general waveform are discusses here. The case of polynomial waveforms and its corresponding theory was published previously. A great extension of the theory which general waveforms is presented here and its full picture is clarified. [ABSTRACT FROM AUTHOR]

Advances made in electronic computers allows the limit value of the sequence to be determined much more easily now than in the past. However, a problem still arises frequently in which it is difficult to determine the limit value with a high accuracy when a tremendous calculation is required in the determination of each term of the sequence. This paper proposes a theoretical method to estimate the limit value of the sequence with a high accuracy from the viewpoint of the recognition theory. By examining the gradual change of the sequence, the character inherent to the sequence is derived. By utilizing the character, the limit value can be estimated with a high accuracy directly from a small number of terms of the sequence. Lastly, the effectiveness of the proposed estimation method is demonstrated by simple examples. [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]

Often, in handwriting a character, a natural expansion or contraction occurs even if the writer intends to write the character in a specified size. This paper considers the expansion-contraction phenomenon which appears statistically in drawing a figure in general. A theoretical investigation is presented from the theory of probability, and the shape of the probability distribution governing the phenomenon is analyzed mathematically. The approach also gives an answer from the viewpoint of the theory of probability to the problem where the length is expanded or contracted unintentionally, even if a constant length is intended. This paper shows a typical mathematical approach in which the determination of the shape of the probability density function is reduced to the solution of the special functional equation. It is considered to be interesting also from the viewpoint of the theory. [ABSTRACT FROM AUTHOR]

A few years ago a fundamental theory on natural observation of waveforms was published as the foundation of a new effective method instead of Fourier analysis. In this papers a natural observation filter is proposed based on the theory. The filter has a typical property with regard to perfect reconstruction for a certain characteristics waveform group. The algebraic relation between the structure of the filter and the corresponding waveform group is theoretically clarified. The result of the present paper is expected to be applicable for recognition problems of various waveforms. [ABSTRACT FROM AUTHOR]