Fundamental Theory of Natural Observation Method with Complete Reconstruction Property by Finite Sum -- Natural Observation Theory of Normal Type.

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]