Gradient-based adaptive algorithm for minimum phase-all pass decomposition of an FIR system

An adaptive filtering algorithm which performs minimum phase-all pass (MP-AP) decomposition of an FIR system is proposed. The minimum phase component of the system is modeled as a lattice filter cascaded with a gain stage. Simulation results on randomly generated FIR systems demonstrate convergence of the algorithm to the correct MP-AP decomposition in 92.6% of cases. The algorithm has the additional advantage that it is capable of detecting misconvergence during or after adaptation. These properties combined make the algorithm a strong candidate for use with compound precoding, a pre-equalization method for high-speed modems.