Nonlinear digital filter realization by distributed arithmetic

It is assumed that a nonlinear shift-invariant digital filter is represented by a truncated discrete Volterra series. A matrix notation, based on the properties of the Kronecker product of matrices, is derived for the nonlinear operator of order K in the Volterra expansion. The matrix notation shows how the well-known distributed arithmetic, originally proposed for linear digital filters, can be adopted for the realization of nonlinear operators. The characteristics of combinatorial and memory-oriented structures are compared, and the problem of complexity reduction is discussed.