A STRUCTURAL VIEW OF ASYMPTOTIC CONVERGENCE SPEED OF ADAPTIVE IIR FILTERING ALGORITHMS .2. FINITE PRECISION IMPLEMENTATION

Finite precision (FP) implementation is the ultimately inevitable real ity of all adaptive filters, including adaptive infinite impulse respo nse (IIR) filters. This paper continues to examine asymptotic converge nce speed of adaptive IIR filters of various structures and algorithms , including the simple constant gain type and the New-ton type, but un der FP implementation, A stochastic differential equation (SDE) approa ch is used in the analysis. Such an approach not only greatly simplifi es the PP analysis, which is traditionally very involved algebraically , but it also provides valuable information about the first-order as w eb as the second-order moments that (the latter) are not available usi ng the ordinary differential equation (ODE) approach, Asymptotic conve rgence speed, as well as the convergent values, of the pertinent momen ts of FP errors are examined in terms of unknown system pole-zero loca tions, The adverse effects of lightly damped low-frequency (LDLF) pole s resulting from fast sampling on the local transient and convergent b ehavior of various structures and algorithms are analyzed and compared . The new results agree with the existing ones when reduced to the fin ite impulse response (FIR) case. In particular, the explosive behavior of pertinent error variances of Newton-type IIR algorithms when the f orgetting factor lambda = 1 is also concluded. Computer simulation ver ifies the predicted theoretical results.