Analysis of Finite Word Length Effect in Two Dimensional Volterra Filters

The Volterra filter is a nonlinear filter with the filter structure that follows the expansion of Volterra series (multi-dimensional convolutions). In this research the effects of finite word length in terms of signal-to-noise ratio (SNR) is being analyzed in two-dimensional volterra digital filters. The voterra filter are of great interest nowadays for the study of nonlinear system theory because of its most important and uncommon property that its output is linearly dependent on the coefficients of the filter itself and that allows the extension of the principles of the optimum linear filter theory to the optimum nonlinear volterra filter theory. The given theoretical analysis is derived mainly by considering effect of round-off error. A statistical approach is used, which permits the computation of the statistics of the errors at the output of the filters. Output SNR is defined, and appropriate expressions are derived.