Frequency domain non-linear adaptive filter

A new non-linear adaptive filter is presented. The algorithm is based on the Volterra series implemented in the frequency domain. For a finite memory of length N, the algorithm converges to the equivalent time domain non-linear adaptive filter as proposed by Roy and Sherman [1]. The frequency domain implementation offers a significant reduction in computation. For the second order Volterra series, the proposed algorithm requires O(N²) multiply-adds for N output points as opposed to an O(N³) for the time domain algorithm. For a large number of taps (≥ 32), the linear version of the proposed algorithm also offers a significant reduction in computation. Another advantage is its fast convergence to the Wiener solution due to the "pseudo-orthogonality" obtained by adapting in the frequency domain.