0095—4470/98/030207#24 $30.00/0  1998 Academic Press Journal of Phonetics (1998) 26, 223—260 Article ID: jp980076 Parameterization of vocal tract area functions by empirical orthogonal modes Brad H. Story National Center for Voice and Speech, WJ Gould Research Center, Denver Center for the Performing Arts, 1245 Champa St, Denver CO 80204, USA Ingo R. Titze National Center for Voice and Speech, WJ Gould Research Center, Denver Center for the Performing Arts, Denver USA and Dept. Speech Pathology and Audiology, University of Iowa, USA Received 8 September 1997, revised 30 March 1998, accepted 22 April 1998 A set of ten vowel area functions, based on MRI measurements, has been parameterized by an ‘‘empirical orthogonal mode decomposition’’ which accurately represents each area function as the sum of the mean area function and proportional amounts of a series of orthogonal basis functions. The mean area function was found to possess a formant structure similar to that of a uniform tube (i.e., nearly equally spaced formants) suggesting that empirical orthogonal modes are perturbations on the mean ( & neutral) vowel shape much like past vocal tract analyses have considered perturbations on a uniform tube. The acoustic characteristics of the two most significant empirical orthogonal modes were examined, showing that both modes tend to increase the first formant as the modal amplitude coefficients are both increased from negative to positive values. However, the second formant was found to decrease in frequency for increasing values of the first modal coefficient and to increase for increasing values of the second mode coefficient. Next, a mapping between F1-F2 formant pairs and vocal tract area functions is proposed which is largely one-to-one but was initially limited by a constant vocal tract length. A possible method to include variable vocal tract length and higher ordered orthogonal modes in the mapping is given. The mode-to-formant mapping suggested the possibility of an inverse mapping to determine physiologically realistic area functions from a speech waveform and a simple example is presented. Finally, empirical orthogonal modes for a collection of ten vowels and eight consonants were derived and showed many similarities to those for the vowel-only case.  1998 Academic Press 1. Introduction Models of the vocal tract have long been used to transform articulatory parameters, such as the positions of the tongue, lips and velum, to an area function; i.e., the cross-sectional area of the vocal tract as a function of the distance from the glottis. These models have typically been defined with reference to the midsagittal plane, which is a convenient refer- ence because of the large body of x-ray films of speech production that are available for