Multi-tube vocal tract model

We will now develop a general expression for the transfer function of a tube model for vowels, in which we have an arbitrary number of tubes coimected together. 

Importantly, for the given sample rate, no extra accuracy is achieved by increasing the number of tubes beyond this value. 

The principle behind finding the N tube transfer function is the same as for the two tube model - start at the lips and apply Equations 11.18a and 11.18b for each tube in turn. This is tedious to perform in the maimer used for the two tube system, but we can use matrix multipUcation to speed up the process. 

We can use the special reflection coefficients at the lips and glottis to model the terminating boundary conditions as before. In the matrix formiflation, this gives 

2 Rabiner and Schafer [368] show that the above can be calculated more easily, and without direct matrix multiplication if we assume that the glottal impedance is infinite. 

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