The mathematical foundations of associated expansions for mildly nonlinear systems

We address a large class of nonlinear systems for which a Volterra-like input-output expansion has recently been proved to exist. In this paper it is shown for the first time that a certain associated expansion (whose terms act on functions defined on the entire
t
-axis) (i) exists, (ii) has certain fundamental properties involving almost periodic functions and their spectra, and (iii) is related, via basic propositions concerning asymptotics in the variable
t
, to the original expansion. The results (which, for example, provide an analytical basis for intermodulation-distortion studies for communication satellites) fill a widely recognized gap in the theory of nonlinear systems.