Role of the Positive Real Function in the Signal Processing--Dedicated to the Late Professor Toshio Fujisawa--

Tosiro KOGA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E74-A   No.1   pp.3-13
Publication Date: 1991/01/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: INVITED PAPER

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This paper is intended as clarification of the interrelation between the signal processing and the classical network theory in relation to the modeling, analysis, and synthesis of linear filters and predicters. After preliminary consideration on the positive-reality with regard to historical aspects and interdisciplinary relations between mathematics, an axiomatic approachi is shown to the representation of linear systems. As a result, an alternative derivation is presented for the s-domain as well as the Z-domain representation of respective systems. Next, concerning the representation of a discrete stationary Gaussian process, it is shown that there exists a complete parallelism between the modeling of the process and the Darlington type synthesis of classical networks. Finally, distinction in the problem statement between the signal processing and the classical synthesis is clarified, and it is shown that an underlying decisive problem concerning the spectral analysis can be solved from the view-point of classical network theory, which bears on the concept of positive-reality.