A fast orthogonalized FIR adaptive filter structure using recurrent hopfield-like network

Abstract

Transversal FIR adaptive filters with LMS like adaptation algorithms have been widely used in many practical applications because their computational cost is low and the transversal structure is unconditionally stable. However the slow convergence rate of transversal filters with LMS adaptation algorithms may restrict their use in several practical applications. To increase the convergence rates of transversal filters, several algorithms based on the Newton Rapson method, such as the recursive least square algorithm, has been proposed. It provides the fastest convergence rates, although its computational cost is in general high, and its low cost versions, such as the Fast Kalman algorithm are, in some cases, numerically unstable. On the other hand, in real time signal processing, a significant amount of computational effort can be saved if the input signals are represented in terms of a set of orthogonal signal components. This is because the representation admits processing schemes in which each of these orthogonal signal components are independently processed. This paper proposes a parallel form FIR adaptive filter structure based on a generalized subband decomposition, implemented in either, a digital or analog way, in which the input signal is split into a set of orthogonal signal component. Subsequently, these orthogonal signal components are filtered by a bank of FIR filters whose coefficient vectors are updated with a Gauss-Newton type adaptive algorithms, which is implemented by using modified recurrent Neural Network. Proposed scheme reduces the computational cost avoids numerical stability problems, since there is not any explicit matrix inversion. Results obtained by computer simulations show the desirable features of the proposed structure.