A novel memoryless nonlinear gradient algorithm for a second-order adaptive IIR notch filter
Adaptive IIR notch filters have been widely studied for many years. However, not many efforts have been made to pursue new algorithms which work better than the plain gradient algorithm but have a little increase in complexity. In this paper, we employ the gradient linearization, Taylor series expansion and calculus of variations to derive a memoryless nonlinear gradient function for a second-order adaptive IIR notch filter, which improves the estimation performance considerably. Theoretical expressions for the stability bounds on the step size parameter and the steady-state coefficient variance of the proposed algorithm using the memoryless nonlinear gradient function are also derived. Extensive simulations indicate the significant improvement that may be achieved using the new algorithm, and verify the closed-form analytical results.
Abstract Characterizing the spatial variation of allele frequencies in a population has a wide range of applications in population genetics. This article introduces a new nonparametric method, which provides a two-dimensional representation of a structural parameter called the genetical bandwidth, which describes genetic structure around arbitrary spatial locations in a study area. This parameter corresponds to the shortest distance to areas of significant allele variation, and its computation is based on the Womble's systemic function. A simulation study and application to data sets taken from the literature give evidence that the method is particularly demonstrative when the fine-scale structure is stronger than the large-scale structure, and that it is generally able to locate genetic boundaries or clines precisely.