### Abstract

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 T(z) and a paraunitary matrix B(,z), extending the eigenvalue decomposition to polynomial matrices, R-(z) = B(z)T(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 BN(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 BN(z).

Original language | English |
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Title of host publication | 2007 6th International conference on information, communications & signal processing |

Place of Publication | New York |

Publisher | IEEE |

Pages | 1396-1400 |

Number of pages | 5 |

ISBN (Print) | 9781424409822 |

DOIs | |

Publication status | Published - 2007 |

Event | 6th Conference on Information, Communications, and Signal Processing - , Singapore Duration: 10 Dec 2007 → 13 Dec 2007 |

### Conference

Conference | 6th Conference on Information, Communications, and Signal Processing |
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Country | Singapore |

Period | 10/12/07 → 13/12/07 |

### Keywords

- hermitian matrices
- polynomial matrices
- eigenvalues
- eigenfunctions
- paraunitary matrices
- SBR2 algorithm

## Cite this

Ta, C. H., & Weiss, S. (2007). Shortening the order of paraunitary matrices in SBR2 algorithm. In

*2007 6th International conference on information, communications & signal processing*(pp. 1396-1400 ). IEEE. https://doi.org/10.1109/ICICS.2007.4449828