The Use of Functionals in the Analysis of Non-linear Physical Systems†

ABSTRACT This report is an attempt to develop a method of analysis applicable equally to linear or non-linear systems. The main method discussed is the expansion of the input-output relation in a functional power series–an idea first due to Volterra for general functional relationships and to Wiener in its application to non-linear communication problems. The report attempts to present a systematic development of this idea. The last part of the report discusses analogous expansions in a series of terms orthogonal with respect to input statistics.