Approximate Kalman Filtering for the Harmonic plus Noise Model

We present a probabilistic description of the Harmonic plus Noise Model (HNM) for speech signals. This probabilistic formulation permits Maximum Likelihood (ML) parameter estimation and speech synthesis becomes a straightforward sampling from a distribution. It also permits development of a Kalman filter that tracks model parameters such as pitch, harmonic amplitudes, and autoregressive coefficients. We focus here on pitch tracking for which the estimator is highly non-linear. As a result it is necessary to develop an approximate Kalman filter that goes beyond extended Kalman filtering. 1. THE HARMONIC PLUS NOISE MODEL Since the work of McAulay and Quatieri [1] speech has been repeatedly modeled as the sum of harmonic sinusoids in additive noise. Based on this model speech synthesis and morphing with high perceptual quality has been achieved among other applications (see references in [2, 3]). In the Harmonic plus Noise Model (HNM) the observed data y(t) is the sum of a harmonic component h(t), which captures the voiced portion of the speech spectrum while a colored noise component, n(t) captures the unvoiced portion of speech y(t) = h(t) + n(t) : (1) The harmonic and noise processes are defined as