A STRUCTURAL VIEW OF ASYMPTOTIC CONVERGENCE SPEED OF ADAPTIVE IIR FILTERING ALGORITHMS .1. INFINITE PRECISION IMPLEMENTATION

Recently, adaptive algorithms based on alternate structures such as pa rallel and lattice that are more traditional in digital filter design literature have been proposed for system identification and adaptive i nfinite impulse response (IIR) filtering with the objectives of ease o f stability monitoring, improved convergence speed, better numerical p roperty, and possible VLSI implementation due to their modular structu ral nature, as opposed to the direct form algorithms. While the issue of stability for adaptive algorithms has received much study, that of convergence speed has hardly been touched for these structures. Comput er simulations show that many adaptive IIR filtering algorithms do not converge or converge extremely slowly for lightly damped low-frequenc y (LDLF) poles despite their theoretical convergence analysis under id eal conditions. In this paper such a problem is studied analytically u nder infinite precision implementation assumption. Asymptotic converge nce speed of various structures and algorithms is investigated in term s of unknown system pole-zero locations which may often be roughly kno wn a priori. The adverse effects of LDLF poles on convergence speed of various structures and algorithms are analyzed and compared. This is done by studying local eigenvalue spread of appropriate information ma trices associated with each algorithm. It is shown, expectedly, that l ocal convergence speed of the simple constant-gain type algorithms is very susceptible to unknown system pole locations, especially LDLF pol es, whereas Newton type of algorithms are more immune to such effect. More surprising results in terms of convergence speed have also been o btained. For example, the transform-domain algorithms are shown to be inferior to the direct form ones; and, locally most lattice algorithms do not offer much improvement ever the direct form ones. With additio nal consideration in terms of global convergence and stability monitor ing, it is concluded that the normalized lattice structure and its ass ociated appropriate algorithms are more preferable than the others in dealing with LDLF poles.