The Second-order Sequential Best Rotation (SBR2) algorithm, used for Eigenvalue Decomposition (EVD) on para-Hermitian polynomial matrices typically encountered in wideband signal processing applications like multichannel Wiener filtering and channel coding, involves a series of delay and rotation operations to achieve diagonalisation. In this paper, we proposed the use of Householder transformations to reduce polynomial matrices to tridiagonal form before zeroing the dominant element with rotation. Similar to performing Householder reduction on conventional matrices, our method enables SBR2 to converge in fewer iterations with smaller order of polynomial matrix factors because more off-diagonal Frobeniusnorm (F-norm) could be transferred to the main diagonal at every iteration. A reduction in the number of iterations by 12.35% and 0.1% improvement in reconstruction error is achievable.

Speech enhancement is important for applications such as telecommunications, hearing aids, automatic speech recognition and voicecontrolled system. The enhancement algorithms aim to reduce interfering noise while minimizing any speech distortion. In this work for speech enhancement, we propose to use polynomial matrices in order to exploit the spatial, spectral as well as temporal correlations between the speech signals received by the microphone array. Polynomial matrices provide the necessary mathematical framework in order to exploit constructively the spatial correlations within and between sensor pairs, as well as the spectral-temporal correlations of broadband signals, such as speech. Specifically, the polynomial eigenvalue decomposition (PEVD) decorrelates simultaneously in space, time and frequency. We then propose a PEVD-based speech enhancement algorithm. Simulations and informal listening examples have shown that our method achieves noise reduction without introducing artefacts into the enhanced signal for white, babble and factory noise conditions between-10 dB to 30 dB SNR.

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