Uniqueness of articulations determined from acoustic data

What is the minimum set of acoustic data that determines a unique shape of the vocal tract? This depends in part on the degree of accuracy with which the vocal tract shape is to be specified (the number of points on the surface of the vocal tract that are determined), in part on the kind of acoustic data (whether both frequencies and bandwidths of the formants are known), and in part on the constraints that are imposed on the possible shapes of the vocal tract, so that only potentially observable shapes are considered. We assume that the degree of accuracy required involves specifying 18 points along the vocal tract, and that the articulatory constraints are those that have been observed in non‐nasalized vowels. We then show the extent to which we can determine the shape of the vocal tract, given only two or three formant frequencies and no bandwidth information.