The LF Model in the Frequency Domain for Glottal Airflow Modelling without Aliasing Distortion

Abstract

Many of the commonly used voice source models are based on piecewise elementary functions defined in the time domain. The discrete-time implementation of such models generally causes aliasing distortion, which make them less useful for certain applications. This paper presents a method which eliminates this distortion. The key component of the proposed method is the frequency domain description of the source model. By deploying the Laplace transform and phasor arithmetic, closed-form expressions of the source model spectrum can be derived. This facilitates the calculation of the spectrum directly from the model parameters, which in turn makes it possible to obtain the ideal discrete spectrum of the model given the sampling frequency used. This discrete spectrum is entirely free of aliasing distortion, and the inverse discrete Fourier transform is used to compute the sampled glottal flow pulse. The proposed method was applied to the widely used LF model, and the complete Laplace transform of the model is presented. Also included are closed-form expressions of the amplitude spectrum and the phase spectrum for the calculation of the LF model spectrum.