A structural view of asymptotic convergence speed of adaptive IIR filtering algorithms. I. Infinite precision implementation

An ordinary differential equation (ODE) approach is used to study the focal convergence speed of adaptive IIR filtering and system identification algorithms of various structures: the direct form, the transform domain, and the lattice. The eigenvalue spreads of the associated information matrices for the algorithms are calculated and compared. Their limits as the unknown system poles approach the unit circle are obtained. For each of the three basic structures, two basic types of adaptive algorithms have been studied: the simple constant gain (SCG) type and the Newton type. It is found that the Newton-type algorithms for the direct form and the lattice have the best local convergence speed, regardless of the unknown system pole locations. For the transform-domain Newton type algorithms, however, local convergence speed depends on the orthogonality of the transformation. It is found that SCG-type algorithms are suitable for identifying poles that are well inside the unit circle