The quasi-stationary response of linear systems to modulated waveforms

A major consideration in communications is the transmission of modulated waveforms through linear systems. The engineer usually wants the modulation to be preserved, for it is the modulation that carries the transmitted information. This paper presents a straightforward method for relating distortion of the modulation to readily computed characteristics of the linear system and the input signal. Through a simple integration by parts, the response is broken up into 1) a quasi-stationary term that preserves the characteristics of the modulation, and 2) a correction term that represents the distortion. Examples of the application of the results to both AM and FM signals through linear time-invariant systems and FM waves through first order time-variant systems are presented. A fairly extensive bibiliography of the basic problem is also presented.