On reduced computational methods for global IIR filtering

A reduced computation, recursive implementation for a globally convergent optimal infinite-impulse-response (IIR) filter design method previously proposed by the authors (1990) is presented. Both methods use homotopy continuation methods to find the filter parameter estimates at the absolute minimum of the least-square (LS) performance surface. The guarantee that the absolute minimum is found using the original method requires that all real and complex-valued stationary points of the LS error surface be found, where the number of these points increases as the number of impulse response samples used in the estimate is increased. The modifications reduce the number of solutions that need to be found while maintaining the guarantee that the absolute minimum of the LS error surface is found. The number of minima are determined by using a p-homogeneous homotopy function and the fundamental theorem of algebra. Single-solution homotopy functions then are used to iteratively refine the parameter estimates at the minima as additional impulse response samples are incorporated into the estimate. The homotopy paths terminating at all local and global minima of the LS error performance surface can be tracked simultaneously, resulting in potentially real-time implementation