Optimal linear separation and deconvolution of acoustical convolutive mixtures

This thesis addresses the problem of the optimal inversion of a linear acoustical convolutive mixing process by means of multichannel linear filtering. In most real-world acoustical scenarios, a number of sound emitting sources are encountered, which may be simultaneously active. When perceiving the sound of these sources by direct listening or from microphone recordings, the original undistorted signal of a single source is not accessible, but rather a mixture of the superposed sources. Furthermore, the source signals are reverberated due to multipath propagation. Propagation and mixing of the sources is characterized by a convolutive mixing process and can be completely described by a matrix of acoustical impulse-responses (AIRs). Reverberation, the superposition of several sources, and additive background noise account for a reduced speech intelligibility in case of speech sources, and for a reduced sound fidelity in general. Several multichannel algorithms exist which aim at a separation and deconvolution (dereverberation) of the sources. The most prevalent linear multichannel filtering techniques are beamforming and blind algorithms. In adverse and highly reverberant environments the performance of these methods is limited, and it is not clear, whether the limitations arise from the particular linear algorithm, or if the setup and physical environment fundamentally limits the performance of any linear filtering method. A theoretical and practical ‘best-case’ performance analysis for linear multichannel filtering methods in the least-squares optimal sense is presented in this thesis. The term ‘best-case’ implies that the convolutive mixing process is known, i.e., the matrix of AIRs are given. Insights gained by the analysis may serve as an upper bound for any practical