Uncertainty in natural observation theory of normal type and an optimum value of the time-constant parameter.

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]