Adaptive regularized spectral reduction for stabilizing ill-conditioned bone-conducted speech signals

Bone-conducted (BC) speech signals are inherently challenging to analyze due to their wide frequency range, which leads to ill-conditioning in numerical analysis and linear prediction (LP) techniques. This ill-conditioning is primarily caused by the expansion of eigenvalues, which complicates the stability and accuracy of traditional methods. To address this issue, we propose a novel regularized spectral reduction (RSR) method, built upon the regularized least squares (RLS) framework. The RSR method compresses the frequency range of BC speech signals, effectively reducing eigenvalue spread and enhancing the robustness of LP analysis. Key to the RSR approach is a regularization parameter, fine-tuned iteratively to achieve optimal performance. Experimental results demonstrate that RSR significantly outperforms existing techniques in eigenvalue compression, resulting in more accurate LP analysis for both synthetic and real BC speech datasets. These improvements hold promise for applications in hearing aids, voice recognition systems, and speaker identification in noisy environments, where reliable BC speech analysis is critical.