Resonators in series and parallel

A transfer function that creates multiple formants can be formed by simply multiplying several second-order filters together. Hence the transfer function for the vocal tract is given as 

These equations show the main advantage of the formant technique, namely that, for a given set of formant values, we can easily create a single transfer function and difference equation for the whole oral tract. In a similar fashion, a nasal system can be created, which likewise links the values of the nasal formant to a transfer function and a difference equation. 

This formulation is known as a serial or cascade formant synthesiser and was the first type to be developed. Note that the relative amphtudes of the formants are determined 

Synthesis techniques based on vocai-tract modeis 

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