Convergence performance of adaptive filter having a restricted linear sum of moment of weight and application to design of filter

Abstract

This paper studies an adaptive filter with a restricted linear sum of the moments of tap coefficients and investigates its applications. In general, when a sampled value filter or a digital filter represented by a surface acoustic filter is realized, the maximum absolute values or the variances of the tap coefficients are restricted. In this paper, restrictions on the maximum values or the variances are imposed by means of a restricted linear sum of several moments around an arbitrary positive number, facilitating the realization of the filter. The number of the moments and the weights are determined in such a way that the frequency characteristics of the filter after restriction satisfy the given specifications. The adaptive system consists of an ideal filter without restriction on the tap coefficients and an adaptive filter placed in parallel. The adaptive filter consists of a transversal filter. Its adaptive algorithm is a gradient algorithm with a small amount of processing, with a restricted linear sum of the moments of the tap coefficients. Since the proof of uniqueness of the converged value of the adaptive algorithm and the upper limit of the loop gain in the algorithm are formulated, the filter designer can easily obtain filter parameters with restricted tap coefficients. Finally, verification of the discussed results is rigorously carried out by computer simulations. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(3): 11–20, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20126