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Implementational aspects of both FIR and IIR adaptive niters in fixed-point fractional arithmetic are discussed. Results of the experiments conducted on an 8-bit processor for an FIR algorithm (LMS) and an IIR algorithm (SHARF) are presented. Finite word length effects of such realizations are empirically studied. The various factors that contribute to the excess mean square error and that influence the convergence behaviour of adaptive filters are discussed.

A new class or adaptive infinite impulse response ( IIR) or recursive filter algorithms is obtained by incorporating a simple modification in the correction vectors of some existing algorithms. The resulting class of algorithms explores the inherent parallelism present in their coefficient update equations, and hence the possibility of faster initial convergence. Two IIR filter algorithms are considered for discussion and simulation.

A general infinite impulse response (IIR) or recursive adaptive filter co-efficient vector update equation is given by where μ(k) is the adaptation gain sequence, and f(k) is the correction vector. In this paper, we show that improvements in filter convergence can be obtained by appropriately modifying either μ(k) or f(k). In the former case, we force Dvoretzky conditions (from stochastic approximation theory) on μ(k) during the search period, whereas the latter uses delayed error signals (i e, modified f (k)) resulting in a parallel processing technique.We have incorporated these proposed modifications in recursive least mean square (RLMS) and simple hyperstable adaptive recursive filter (SHARF) algorithms. From simulation studies, it has been observed that the modification on f(k) gave improved results for the SHARF, and the RLMS converged quickly with the modification on μ(k). Results of simulation studies are presented in the form of learning curves and parameter tables.