Lossless pole-zero modeling of speech signals

The authors establish a theory for lossless pole-zero modeling of speech signals for the description of nasal sounds. The theory is based on a generalized vocal tract tube model which consists of the main vocal tract, the oral tract, and the nasal tract. A pole-zero type transfer function, which turns out to be a generalized version of the existing all-pole type transfer function, is derived. Fundamental properties of the generalized vocal tract model are investigated, employing the concept of discrete-time reactance. A procedure for evaluating the reflection coefficients for the model is outlined. The assumption of losslessness in the modeling leads to the following two properties. First, the combination of two lattice structures representing the oral and the nasal tracts form one larger lattice structure when viewed at their joint point called the branch boundary. Second, the oral and the nasal tract render respective discrete-time reactances whose convex combination generates the discrete-time reactance at the branch boundary. The first property enables the combined reactance to be computed, and the second helps separate it into its components