Operational Analysis of Variable-Delay Systems

An operational method of analysis of variable-delay systems such as delay modulators and variable-path communication systems is developed in this article. The output of a variable-delay system is related to its input by a delay operator which has the usual exponential form, but differs from the conventional (time-invariant) delay operators in that the time delay is a function of time. Special consideration is given to systems in which the variation in time delay is due to motion of the receiver or transmitter (source) or both. Such systems-referred to as type-R, type-S and type-RS systems, respectively-are analyzed in general terms. An operational relation is obtained for the correlation function of the output of a type-R system, and the result is applied to the determination of the correlation function of a frequency-modulated sound wave.