Signal Theory

Abstract

It is suggested that much of the subject matter now lumped under the heading of "circuit theory" might better be called "system theory," which in turn may be separated into three subdivisions-that which deals with the representation of the physical elements; that which deals with the representation of the signals, and that which deals with the representation of the transformations and relations between the signals and the elements. For the first subdivision, the name "circuit theory" in its original sense is suggested; for the second subdivision, the name "signal theory;" and for the third, the name "operator theory." This paper describes some of the distinctions between the first and second subdivisions. Signal representations are needed for two purposes: To study the transmission properties of a system, and to reveal the information-bearing attributes of a signal. Steady-state (i.e., Fourier) representations are well suited to the first purpose, but representations that explicitly involve temporal parameters are needed for the latter purpose. The expansions of signals in terms of nonsinusoidal components provide one type of representation which has been used extensively in physics but has been little used in the practical analysis of signals. A specific example is given of a filter structure which analyzes the incoming signal in terms of a set of orthogonal functions formed from the exponential componentse^{-t}, e^{-2t}, e^{-3t}, etc., and it is shown how an "ideal" filter, in the sense of Zadeh, may be constructed for separating these components. A practical use of this ideal filter is to measure the nonlinear distortion of an arbitrary dynamical system under transient conditions.