Abstract
It has long been known that there is no unique analytic solution to the inverse problem in speech. However, for any problem with multiple solutions, a unique solution can still be obtained by optimizing some function on the set of possible solutions. Several investigators have done just that for the speech problem. In this work, we return to the analytic approach to ask two questions. First, despite the fact that the spectral frequencies do not uniquely specify the area function, what about articulation do they specify and what additional information is necessary for unique specification? Second, if such information were available, what is the form of the function that specifies the area function given all the necessary spectral information? Based on theorems from network synthesis it is known that the zeros or formant amplitudes can provide the extra information. Assuming that the poles and zeros of the driving point impedance are given (sidestepping the difficulty of obtaining these parameters from a speech signal), a functional relation is presented that uniquely specifies articulatory information given acoustic information. The relation between this method and pole-residue methods will also be discussed. [Work supported by NIH Grant DC-02717.]
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