On the determination of the optimal pole position of Laguerre filters

摘要

As is known in the literature, at each stationary point of the squared error (SE) curve of a Laguerre filter at least one of a pair of certain Laguerre coefficients (weights) vanishes. The author describes a very efficient way to compute the derivatives of each one of these coefficients with respect to the pole position of the Laguerre filter. The knowledge of these derivatives makes possible the computation of high-order approximations to the coefficients in question, such as truncated Taylor series and Pade approximants. The zeros of these approximations are usually good estimates of the location of the stationary points of the SE curve nearer to the center of the approximation. In this way, the position of these stationary points, in particular local minima, can be estimated without resorting to a numerical search algorithm. Both continuous time and discrete time Laguerre filters are discussed, excited either by an impulse or by an arbitrary signal. The authors illustrate the main results of the paper with a numerical example.