Volterra Transfer Functions from Pulse Tests for Mildly Nonlinear Channels.

Multichannel communications systems are often mildly nonlinear, hence they are characterizable by the Volterra series. The methodology described herein represents a numerical implementation of an RADC in-house concept formulation for pulse testing linear and quadratic Volterra systems. This analytic formulation, in terms of the appropriate convolutions, expressed the linear and quadratic responses to square pulse input waveforms. These responses contain, in canonic form, the system poles and residues which are then determined by suitable identification methods and algorithms to provide the Volterra Transfer functions. In this paper we describe a method for determining the Volterra transfer-functions H1 s1 and H2 s1, s2 from pulse tests. The method involves two transient tests in the laboratory, followed by analysis by the computer. The latter consists of a pole determination using the pencil-of-functions method, and b computation of the residues by a least-squares technique. Advantages of the method include the rapidity of the laboratory tests, as contrasted with traditional frequency-scan approaches, and the explicit determination of the transfer functions. Furthermore, the method is readily extendible to H3 s1, s2, s3 and even to higher order transfer functions, although the computations grow very rapidly for these cases. Author