A FLOATING-POINT ARITHMETIC ERROR ANALYSIS OF DIRECT AND INDIRECT COEFFICIENT UPDATING TECHNIQUES FOR ADAPTIVE LATTICE FILTERS

This paper shows how finite precision arithmetic effects can deleterio usly manifest themselves in both the stochastic gradient and the recur sive least squares adaptive lattice filters. Closed form expressions a re derived for the steady-state variance of the accumulated arithmetic error in a single adaptive lattice coefficient using a floating-point stochastic arithmetic error analysis. Emphasis is placed on the compu tational form or the time-recursive adaptive lattice coefficients. The analytical results show that the performance of adaptive lattice filt ers using a direct updating computational form is less sensitive to fi nite precision effects than that of adaptive lattice filters using an indirect updating computational form. This is shown to be the result o f an accumulated arithmetic error that is reduced in the directly upda ted filter coefficients by the division of an unnormalized residual po wer estimate. In addition, a method for reducing the self-generated no ise is presented. Experimental results obtained on a 32-b floating-poi nt hardware implementation of the adaptive lattice filters and with co mputer simulations are included to verify the analytical results descr ibing the effects of finite precision on adaptive lattice filters.