Statistical-Mechanical Analysis of Adaptive Volterra Filter for Time-Varying Unknown System

The Volterra filter is a digital filter that can describe nonlinearity. In this work, we analyze the dynamic behaviors of an adaptive signal processing system with the Volterra filter and a time-varying unknown system by a statistical-mechanical method. Specifically, assuming the self-averaging property with an infinitely long tapped-delay line, we derive simultaneous dif-ferential equations that describe the behaviors of the macroscopic variables in a deterministic and closed form and obtain the exact solution by solving them analytically. In addition, the validity of the derived theory is confirmed by comparison with numerical simulations.