Deconvolution of the Glottal Pulse Using a Finite-Difference Solution of the Acoustical Klein-Gordon Equation

Deconvolution of the glottal-pulse waveform from the speech signal remains an active field of research although dating back over half a century. In the main, existing approaches use classical inverse filtering frequency-domain methods to estimate both the vocal-tract and glottal-pulse waveforms. In this paper, we adopt a new approach which takes advantage of two relatively recent developments: firstly, the physical modeling of the speech process by means of the Klein-Gordon wave equation of relativistic quantum mechanics and, secondly, a finite-difference calculation of this equation to find the impulse response of the vocal tract. This approach allows accurate parameterisation of the impulse response which simplifies the blind deconvolution. Results show considerable improvement compared with existing algorithms when applied to synthetic speech where the ground truth is known.