Power normalized update algorithm for adaptive filters-without divisions

Two power-normalized update algorithms for adaptive filters are described that do not require divisions. The algorithms are based on very simple iterative procedures that approximate divisions. Since neither the quotients nor the dividends change quickly, the division procedures need only be updated once each time the coefficients of the adaptive filter are updated. One algorithm requires three extra multiplications per coefficient and results in adaptive filters with convergence times practically identical to those achieved when actual divisions are used. The second algorithm requires only one multiplication per coefficient instead of a division, yet results in adaptive filter convergence times only slightly larger than those obtained with real divisions. Both algorithms result in adaptive filters only slightly more complex than steepest descent adaptive filters. The algorithms are especially applicable to real-time adaptive filters realized using single-chip digital signal processors or custom ASICs where hard-wired dividers are usually not available and fast convergence is still desired