### Abstract

Spatial information in broadband array signals is embedded in the relative delay with which sources illuminate different sensors. Therefore, second order statistics, on which cost functions such as the mean square rest, must include such delays. Typically, a space-time covariance matrix therefore arises, which can be represented as a Laurent polynomial matrix. The optimisation of a cost function then requires extending the utility of the eigenvalue decomposition from narrowband covariance matrices to the broadband case of operating in a space-time covariance matrix. This overview paper summarises efforts in performing such factorisations, and demonstrated via the exemplar application of a broadband beamformer how thus well-known narrowband solutions can be extended to the broadband case using polynomial matrices and their factorisations.

Original language | English |
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Number of pages | 8 |

Publication status | Accepted/In press - 1 Jun 2020 |

Event | 7th International Conference on Multimedia and Human-Computer Interaction - Prague, Czech Republic Duration: 13 Aug 2020 → 15 Aug 2020 https://mhciconference.com/ |

### Conference

Conference | 7th International Conference on Multimedia and Human-Computer Interaction |
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Abbreviated title | MCHI'20 |

Country | Czech Republic |

City | Prague |

Period | 13/08/20 → 15/08/20 |

Internet address |

### Keywords

- array processing
- broadband beamforming
- sensor processing
- polynomial matrices
- matrix factorisation

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## Cite this

Weiss, S. (Accepted/In press).

*Mathematical tools for processing broadband multi-sensor signals*. Paper presented at 7th International Conference on Multimedia and Human-Computer Interaction, Prague, Czech Republic.