A structural view of asymptotic convergence speed of adaptive IIR filtering algorithm. II. Finite precision implementation

For pt.I see ibid., vol.41, no.4, p.1493-1517, 1993. Finite precision (FP) implementation is the ultimately inevitable reality of all adaptive filters, including adaptive infinite impulse response (IIR) filters. This paper continues to examine the asymptotic convergence speed of adaptive IIR filters of various structures and algorithms, including the simple constant gain type and the Newton type, but under FP implementation. A stochastic differential equation (SDE) approach is used in the analysis. Such an approach not only greatly simplifies the FP analysis, which is traditionally very involved algebraically, but it also provides valuable information about the first-order as well as the second-order moments that (the latter) are not available using the ordinary differential equation (ODE) approach. The asymptotic convergence speed, as well as the convergent values, of the pertinent moments of FP errors are examined in terms of unknown system pole-zero locations. The adverse effects of lightly damped low-frequency (LDLF) poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared. The new results agree with the existing ones when reduced to the finite impulse response (FIR) case. In particular, the explosive behavior of pertinent error variances of Newton-type IIR algorithms when the forgetting factor λ=1 is also concluded. Computer simulation verifies the predicted theoretical results