Fundamental theory of natural observation method with complete reconstruction property by finite sum‐natural observation theory of normal type

Abstract

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 characteristic 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 a 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 taansform with that of a conventional filter bank. Furthermore, a criterion for determining observation parameters in 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.

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

“…As shown in Fig. 1, the fundamental observation filter includes one low-pass filter (LPF), (M -1) bandpass filters (BPF), and one high-pass filter (HPF) [6]. The diagram indicates that the filter's band shifts from low to high frequency band as the order m increases.…”

“…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]. In addition, the notion of the aspectum has been offered theoretically, but no specific examples of its use for actual waveforms are available.…”

“…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.…”

On the uncertainty principle in natural observation transforms of normal type

“…Initially the neighboring type was proposed and then the equilibrium type, which has a close connection with the neighboring type. Subsequently, the normal type [12,13] was proposed as a new type that can make waveform observations with finite number of observed values. The authors investigated the uncertainty relation in the natural observation transform so as to gain knowledge about its observation resolution [14].…”