A general theory of linear signal transmission systems

✍ Scribed by L.A. Zadeh

• Publisher: Elsevier Science
• Year: 1952
• Tongue: English
• Weight: 956 KB
• Volume: 253
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(52)90836-3

✦ Synopsis

The analysis and synthesis of signal transmission systems are usually conducted either in the time domain or in the frequency domain. In this paper a more general approach based on the resolution of signals in terms of some suitable, but otherwise arbitrary, set of component signals is outlined. A signal transmission system is characterized by a so-called characteristic function, of which such commonly used descrilative functions as the impulsive response, unit step response, and the system function are special cases. The general input-output relations are interpreted in geometrical terms by using the function space approach. The concept of ideal filter is introduced via the idempotent property of projections in function space, and the significance of this concept is indicated. Stability, operational symbolism, product relation, and inverse systems are briefly discussed. ' N, Nz " = " ' K, K 2 K3=Kd'K ' FIG. 2. Physical interpretation of the product relation.

An explicit expression for the product can readily be obtained by referring to Fig. 2 and noting that for the particular case where the input