To derive speech wave data from area function specifications and the reverse, to predict the area function from the speech wave, are fundamental problems of acoustic theory of speech production. Deviations from ideal resonator theory in terms of vocal tract boundary conditions and source filter interactions are discussed. Perturbation theory is related to special problems of male-female vocal tract scaling. Shortcomings of the inverse transforms are discussed. Merits of lossy transmission line theory over standard linear prediction procedures are emphasized. The use of bandwidths for removing ambiguities is illustrated in simple models. A limited amount of bandwidth data supplementing formant frequency data and model related vocal tract constraints appears to be optimal.