Natural observation method for discrete‐time waveforms

Abstract

Tbe 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.

Evaluation of instantaneous power by the aspectum in the theory of the natural observation method

“…(e j2π ⋅ f / f s ) of the fundamental observation filter are shown in Eqs. (11) and (12), respectively [7]. Here f s is the sampling frequency.…”

“…The authors have reported the first examples of the application of waveform analysis based on the natural observation theory to electromagnetic signals [3,4], and have shown that this method is extremely effective for nonsteady irregular signals such as natural electromagnetic fluctuations. In related research, there are few if any application examples, although Iijima and colleagues provided a deep theoretical study [1,2,[5][6][7][8] of the aspectum has been offered theoretically, but no specific examples of its use for actual waveforms are available. Thus, it is important to examine the characteristics of waveform analysis with the aspectum by applying it to known signals.…”

Analysis of atmospheric electric field variation signals using digital natural observation method

“…The natural observation theory [10][11][12][13][14][15][16][17] is a novel approach to signal analysis dealing with instantaneous variation of signals. That is, while Fourier analysis or the maximum entropy method is an analytical tool that decomposes signals into their frequency components [18], in the natural observation method, signals are expanded as series in the gradients (derivatives) of nonperiodic waveforms.…”