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This paper describes a new method for estimating the vocal tract area function directly from the acoustic speech waveform. Dynamic changes of the area functions and formants in voiced speech sounds are obtainable. The filtering processes of the inverse filter model and an acoustic tube model of speech are analyzed and they are shown to be identical, with the reflection coefficients in the acoustic tube model as a common factor, thus making possible the extraction of the reflection coefficients by the inverse filter processing of the speech signal. The discrete area function can easily be obtained from the set of reflection coefficients. Analysis examples for vowels, diphthongs, and consonants in vowel-consonant-vowel utterances are given.