Volterra filter equalization: a frequency domain approach

The equalization of nonlinear systems is an important application of Volterra filters. The pth-order inverse is one of the important approaches of Volterra equalization, but the existence of Volterra filter equalization and the convergence and error bound using the pth-order approximation equalizer instead of the Volterra equalizer are not reported yet. We discuss the above problems. The concept of local l ₂ stability for the Volterra filter is introduced, and the algorithmic formula of the pth-order inverse is presented by using the multi-dimension z-transform. Finally, the existence of Volterra filter equalization and the convergence and error bound using the pth-order approximation equalizer instead of the Volterra equalizer are discussed. The proposed algorithms are corroborated with a simulation example