A novel multidelay adaptive algorithm for Volterra filters in diagonal coordinate representation [nonlinear acoustic echo cancellation example]

In this contribution, we present a novel algorithm for the efficient computation of the output of Volterra filters in diagonal coordinate representation (DCR), while allowing for different memory length for each kernel. This is achieved by extending partitioned block filtering methods for fast convolution in the discrete Fourier transform (DFT) domain to Volterra filters. It is shown that the DCR is particularly favorable for modeling the cascade of a Volterra filter followed by a linear filter, as required for applications such as nonlinear acoustic echo cancellation. To obtain a corresponding adaptive structure of the proposed approach, we introduce a generalization of a known DFT-domain adaptive algorithm for linear systems to Volterra filters.