ACOUSTIC TUBE MODELING OF SPEECH PRODUCTION
For many years, Gunnar Fant directed the Speech Transmission Laboratory in Stockholm. He performed X-ray measurements to determine the shape of the human vocal tract during phonation. In 1970 (based to a great extent on his doctoral thesis) his book Acoustic Theory of Speech Production  was published. It contained detailed information on vocal tract shapes.
For each phoneme in any spoken language there corresponds one or several sequences of vocal tract shapes. With the development of digital signal-processing concepts, these shapes can be efficiently modeled. In Chapter 10 we showed how simple acoustic tubes could be digitally modeled. In this chapter, these ideas are extended to more complicated acoustic tube structures that relate to spoken sounds.
11.2 ACOUSTIC TUBE MODELS OF ENGLISH PHONEMES
Fant first traced area functions from the X-ray data. An example is shown in Fig. 11.1 for the vowel /i/ as in /bid/.
On the left is the tracing and on the right we see the area of the tube as a function of the distance from the glottis. This area function is quantized as a concatenation of cylindrical tubes. This string of tubes can now be approximated by analog T networks  or digital waveguides . Straightforward mathematical derivations for a practical system (four or more tubes) become difficult. Computer ...