Structural issues in cascade-form adaptive IIR filters

Adaptive IIR filters implemented in cascade-form are attractive due to the ease with which their stability may be monitored. Four cascade-form structures are compared for use in adaptive filtering with respect to complexity of implementation, error surface geometry, and adaptation speed. The four structures include a cascade of second order pole/zero sections, a cascade of second order all-pole sections followed by a tapped delay line, and two new structures. The latter pair includes a tapped cascade, which is a cascade of second order all-pole sections whose output is constructed as a weighted combination of signals tapped from the cascade. The second new structure is a modification of the tapped cascade that yields orthogonal signals at the taps of the cascade. It is shown that the tapped cascade provides the best overall performance in the respects noted above.