Analysis and synthesis of the phonatory excitation signal by means of a pair of polynomial shaping functions

The object of the presentation is a polynomial waveshaping model of the phonatory excitation signal. The phonatory excitation signal is the acoustic signal that is generated at the glottis via the vibrating vocal folds and the pulsatile airflow. A waveshaper is an operator that transforms a sinusoid into any desired waveform. The waveshaper is approximated by means of a pair of polynomials whose coefficients are obtained via a constant linear transformation of the Fourier series coefficients of the shape of a cycle of the desired phonatory signal. The properties of the waveshaping model compared to conventional models of the phonatory signal are the following. (i) The model can be linearly fitted to observed glottal waveforms. (ii) The mean value of the model output is zero and the acoustic excitation is zero when the glottis is closed. (iii) The cycle length is controlled via the instantaneous frequency of the driving sinusoid. (iv) The spectral balance of the output is controlled by the amplitude of the driving sinusoid. (v) The waveshaper’s coefficients fall into two categories, i.e. parameters that enable the control of the features of the phonatory timbre on the one hand, and coefficients that encode the default cycle shape (phonatory identity) on the other.