Shortening the order of paraunitary matrices in SBR2 algorithm

The second order sequential best rotation (SBR2) algorithm has recently been proposed as a very effective tool in decomposing a para-Hermitian polynomial matrix R(z) into a diagonal polynomial matrix Γ(z) and a paraunitary matrix B(z), extending the eigenvalue decomposition to polynomial matrices, R(z) = B(z)Γ(z)B(z). However, the algorithm results in polynomials of very high order, which limits its applicability. Therefore, in this paper we evaluate approaches to reduce the order of the paraunitary matrices, either within each step of SBR2, or after convergence. The paraunitary matrix B(z) is replaced by a near-paraunitary quantity B
N
(z), whose error will be assessed. Simulation results show that the proposed truncation can greatly reduce the polynomial order while retaining good near-paraunitariness of B
N
(z).