Perturbation Analysis of Digital Eigenfilters

Eigenfilter design has been shown to be an effective approach for digital filters since its occurrence in 1987. Many extensions have also been proposed since then. As noted by Vaidyanathan, the inclusion of the alpha parameter provides an extra degree of design freedom. However, the effect this design tradeoff parameter remains unexplored. In this paper, we present a technique to characterize the effect of alpha. Based on the theory of perturbation analysis of linear operators, we are able to analytically determine the resultant approximate eigenvector when alpha is varied from its nominal operating point. The accuracy of the approximation depends on the variation parameter epsiv and the nonlinearity related to the linear operator under investigation. Examples are provided to demonstrate the feasibility of this analysis approach.