A LEVINSON-TYPE ALGORITHM FOR A CLASS FOR NON-TOEPLITZ SYSTEMS WITH APPLICATIONS TO MULTICHANNEL IIR FILTERING

A very flexible Levinson-type recursion for a class of non-Toeplitz sy stems of linear equations is demonstrated. A complete solution is expr essed as a linear combination of a partial solution and three auxiliar y solutions. The class of systems possesses a special structure in tha t 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(n2). The recursion is then appl ied to multichannel IIR filtering. Specifically, a lattice structure i s established for linear minimum mean square error predictors having i ndependently and arbitrarily specified numbers of poles and zeros. Nex t the recursion is used to develop a fast time and order recursive lea st-squares algorithm for ARX system identification. The novelty of the algorithm is that it can be used to efficiently determine parameter e stimates of a family of ARX models.