A floating-point arithmetic error analysis of direct and indirect coefficient updating techniques for adaptive lattice filters

The ways in which finite precision arithmetic effects can deleteriously manifest themselves in both the stochastic gradient and the recursive least squares adaptive lattice filters are discussed. closed form expressions are 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. The analytical results show that the performance of adaptive lattice filters using a direct updating computational form is less sensitive to finite precision effects than that of adaptive lattice filters using an indirect updating computational form. In addition, a method for reducing the self-generated noise is presented. Experimental results obtained on a 32-b floating-point hardware implementation of the adaptive lattice filters and with computer simulations are included to verify the analytical results describing the effects of finite precision on adaptive lattice filters