A Simple Algorithm for Adaptive Allpass-FIR Digital Fil- ter Using Lattice Allpass Filter with Minimum Multipliers

Adaptive infinite impulse response (IIR) digital filter implemented using a cascade of second order direct form allpass filters and a finite impulse response (FIR) filter, has the property of its poles converging to those of the unknown system. In this paper we implement the adaptive allpass-FIR digital filter using a lattice allpass filter with minimum number of multipliers. We then derive a simple adaptive algorithm, which does not increase the overall number of multipliers of the proposed adaptive digital filter (ADF) in comparison to the ADF that uses the direct form allpass filter. The proposed structure and algorithm exhibit a kind of orthogonality, which ensures convergence of the poles of the ADF to those of the unknown system. Simulation results confirm this convergence. key words: adaptive filter, lattice IIR filter, allpass filter, orthogonality, residue theorem