In comparison with adaptive finite impulse response (FIR) filters, adaptive infinite impulse response (IIR) filters offer the potential to implement an adaptive filter meeting desired performance levels, as measured by mean-square error, for example, with much less computational complexity. | Williamson . Adaptive IIR Filters Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 23 Adaptive IIR Filters Geoffrey A. Williamson Illinois Institute of Technology Introduction The System Identification Framework for Adaptive IIR Filtering Algorithms and Performance Issues Some Preliminaries The Equation Error Approach The LMS and LS Equation Error Algorithms Instrumental Variable Algorithms Equation Error Algorithms with Unit Norm Constraints The Output Error Approach Gradient-Descent Algorithms Output Error Algorithms Based on Stability Theory Equation-Error Output-Error Hybrids The Steiglitz-McBride Family of Algorithms Alternate Parametrizations Conclusions References Introduction In comparison with adaptive finite impulse response FIR filters adaptive infinite impulse response IIR filters offer the potential to implement an adaptive filter meeting desired performance levels as measured by mean-square error for example with much less computational complexity. This advantage stems from the enhanced modeling capabilities provided by the pole zero transfer function of the IIR structure compared to the all-zero form of the FIR structure. However adapting an IIR filter brings with it a number of challenges in obtaining stable and optimal behavior of the algorithms used to adjust the filter parameters. Since the 1970s there has been much active research focused on adaptive IIR filters but many of these challenges to date have not been completely resolved. As a consequence adaptive IIR filters are not found in commercial practice in anywhere near the frequency that adaptive FIR filters are. Nonetheless recent advances in adaptive IIR filter research have provided new results and insights into the behavior of several methods for adapting the filter parameters and new algorithms have been proposed that address some of the problems and open issues in
