We enhanced the performance of linear prediction (LP) for bone-conducted (BC) speech signals by deriving a regularized version of the modified covariance (MC) method. The spectral estimation accuracy is discussed for the purpose of assessing the performance of LP. Inherently, BC speech has an expanded spectral dynamic range that causes ill-condition in conventional spectral estimation methods. To overcome this problem, we focus on the covariance method and its modified version, the MC method. In the field of numerical analysis, we often face the situation where an ill-conditioned case occurs in finding the solution. To deal with this situation, the regularized least squares method is utilized. Motivated by this idea, we derive the regularized MC (RMC) method in this study for BC speech analysis. The RMC method has the effect of compressing the spectral dynamic range of the input speech signal, and this effect mitigates the ill-conditioned problem of LP. Through experiments, we show that the RMC method provides a more accurate spectral estimation than conventional spectral estimation methods for BC speech where synthetic and real BC speeches are considered. The performance of the RMC method is affected by the setting of the regularization parameter. A way to determine the regularization parameter in practice is experimentally derived. The RMC method with such a setting provides the best performance of spectral estimation for BC speech.

Heaviside proposed the telegrapher’s equations as an alternative to the Maxwell equations. His proposal was groundbreaking and can be considered miraculous. Nothing could be a more accurate solution than this proposal. The following physical properties can be derived from the telegrapher’s equations. The telegrapher’s equations are represented by a circuit diagram consisting of series and parallel elements. Circuits are known to have steady and transient states. These equations also demonstrate that the electromagnetic waves, which are determined by the existence of an electromagnetic field expressed by partial differential equations, propagate at the velocity of light c.