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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 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]

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]