Gradient-adaptive algorithms for minimumphase-all-pass decomposition of a finite impulse response system

Adaptive algorithms which perform minimum-phase-all-pass (MP-AP) decomposition of a finite impulse response system are proposed. The first algorithm models the MP component of the system as a lattice filter cascaded with a gain stage. The algorithm has a low misconvergence probability, and is capable of detecting misconvergence during or after adaptation. Two further algorithms are proposed based on the theory of the bicepstrum. One adaptively solves a finite linear system of equations and the other an augmented nonlinear system. The first has an error sensitive to the proximity of the system zeros to the unit circle, whereas the second, although more computationally intensive, may approach the exact MP-AP decomposition given a sufficient number of iterations. These real-time MP-AP decomposition algorithms have applications in the stabilisation of compound precoding, which is a pre-equalisation technique included as an option in the V.92 high-speed modem standard.