2.1 INTRODUCTION

The studies of Italian mathematician Vito Volterra (1860 1940) pioneered and developed the branch of mathematics known as functional analysis. His first paper on the subject of functionals was published in 1887, and his collected works were published in the volume Theory of Functionals and of Integro-Differential Equations in 1936. The current usage of Volterra Theory in systems engineering is due to Norbert Wiener, who hypothesized that a time-invariant nonlinear system could be modeled by a series of Volterra functionals, provided that the nonlinearities in the system were not too strong. Wiener also proposed a method of identifying the kernels of the Volterra functionals using white noise. The development of Wiener's methods are well presented by Schetzen [1], who provides a thorough introduction into the use of Volterra series, though sadly this volume is now out-of-print.

The Volterra theory was picked up and applied to nonlinear circuits and communications systems by Rome Air Development Center in the 1960s [2], and sparked some interest leading to classic publications on the application of Volterra methods to nonlinear systems analysis [3, 4]. The development and application of these theories dwindled in the 1970s as improvements in devices and device technology brought about faster improvements in the circuit and system linearity than did the application of the theoretical analysis. Volterra theory was "rediscovered" in the 1980s as distortion in communications circuits again became a serious problem: low-noise, high-frequency devices...