Abstract
In acoustic multi-channel equalization techniques, such as complete multi-channel equalization based on the multiple-input/output inverse theorem (MINT), relaxed multi-channel least-squares (RMCLS), and partial multi-channel equalization based on MINT (PMINT), the length of the reshaping filters is generally chosen such that perfect dereverberation can be achieved for perfectly estimated room impulse responses (RIRs). However, since in practice the available RIRs typically differ from the true RIRs, this reshaping filter length may not be optimal. This paper provides a mathematical analysis of the robustness increase of equalization techniques against RIR perturbations when using a shorter reshaping filter length than conventionally used. Based on the condition number of the (weighted) convolution matrix of the RIRs, a mathematical relationship between the reshaping filter length and the robustness against RIR perturbations is established. It is shown that shorter reshaping filters than conventionally used yield a smaller condition number, i.e., a higher robustness against RIR perturbations. In addition, we propose an automatic non-intrusive procedure for determining the reshaping filter length based on the L-curve. Simulation results confirm that using a shorter reshaping filter length than conventionally used yields a significant increase in robustness against RIR perturbations for MINT, RMCLS, and PMINT. Furthermore, it is shown that PMINT using an optimal intrusively determined reshaping filter length outperforms all other considered techniques. Finally, it is shown that the automatic non-intrusively determined reshaping filter length in PMINT yields a similar performance as the optimal intrusively determined reshaping filter length.
Highlights
The microphone signals recorded in many hands-free speech communication applications, such as teleconferencing, voice-controlled systems, or hearing aids, do contain the desired speech signal and attenuated and delayed copies due to reverberation
In order to increase the robustness against room impulse responses (RIRs) perturbations, partial multi-channel equalization techniques, such as relaxed multi-channel least-squares (RMCLS) [23] and partial multi-channel equalization based on multiple-input/output inverse theorem (MINT) (PMINT) [24], have been proposed
We have analytically shown that using a shorter reshaping filter decreases the condition number of the convolution matrix, increasing as a result the robustness against RIR perturbations
Summary
The microphone signals recorded in many hands-free speech communication applications, such as teleconferencing, voice-controlled systems, or hearing aids, do contain the desired speech signal and attenuated and delayed copies due to reverberation. In [33], it has been analytically shown that decreasing the reshaping filter length increases the robustness for MINT and PMINT only if the multi-channel convolution matrix of the RIRs is a square matrix. It is analytically shown that decreasing the reshaping filter length increases the robustness of MINT, RMCLS, and PMINT independently of the dimension of the (weighted) multi-channel convolution matrix of the RIRs. A mathematical relationship between the reshaping filter length and the condition number of the (weighted) multi-channel convolution matrix of the available RIRs, the sensitivity of equalization techniques to RIR perturbations, is derived. The reshaping filter g can be constructed based on different design objectives for the EIR c
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