A Levinson-type algorithm for a class of non-Toeplitz systems with applications to multichannel IIR filtering

• Published in: IEEE transactions on signal processing 1994-12, Vol.42 (12), p.3309-3320
• Main Authors: Jiqin Pan, Levine, W.S.
• Format: Article
• Language: English
• Subjects: Adaptive filters; Applied sciences; Detection, estimation, filtering, equalization, prediction; Equations; Exact sciences and technology; Filtering algorithms; IIR filters; Information, signal and communications theory; Lattices; Mean square error methods; Nonlinear filters; Poles and zeros; Signal and communications theory; Signal processing algorithms; Signal, noise; System identification; Telecommunications and information theory
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.340769

A very flexible Levinson-type recursion for a class of non-Toeplitz systems of linear equations is demonstrated. A complete solution is expressed as a linear combination of a partial solution and three auxiliary solutions. The class of systems possesses a special structure in that the coefficient matrices can be partitioned into four block Toeplitz submatrices. The number of multiplications and additions required to compute an n-dimensional solution is O(n/sup 2/). The recursion is then applied to multichannel IIR filtering. Specifically, a lattice structure is established for linear minimum mean square error predictors having independently and arbitrarily specified numbers of poles and zeros. Next the recursion is used to develop a fast time and order recursive least-squares algorithm for ARX system identification. The novelty of the algorithm is that it can be used to efficiently determine parameter estimates of a family of ARX models.< >