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

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

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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.

Inspec keywords: gradient methods; precoding; transient response; FIR filters; equalisers; lattice filters; linear systems; nonlinear systems

Other keywords: finite linear equation system; low misconvergence probability; augmented nonlinear system; bicepstrum. theory; V.92 high-speed modem standard; lattice filter system; minimum-phase-all-pass decomposition; finite impulse response system; real-time MP-AP decomposition algorithms; preequalisation technique; gradient-adaptive algorithms; compound precoding stabilisation

Subjects: Interpolation and function approximation (numerical analysis); Codes; Communication channel equalisation and identification; Filtering methods in signal processing

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