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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]

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]

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]

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]