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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]

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]

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]