On multidimensional HARF and SHARF algorithms

Recently, a multidimensional (k-D) hyperstable adaptive recursive filter (HARF) algorithm, which converges in a “volumewise´ sense but not in the usual sense, was introduced in the literature. As an extension to that paper, we present a new k-D HARF algorithm which converges in the usual sense and faster than the one previously reported. This new formulation of k-D HARF algorithm is much easier to understand and it is a more natural way of extending 1-D HARF algorithm to k-D. Furthermore, for the first time, we introduce a k-D version of 1-D (SHARF) algorithm and provide simulations which show the potential applications of the new k-D HARF and k-D SHARF in system identification and noise cancellation. Finally, we compare the performance of these three different adaptive schemes