Statistical relationships among the first three formant frequencies in vowel segments in continuous speech

Statistical relationships among F1, F2 and F3 in vowel segments in continuous speech were investigated with 909 vowel samples from Japanese sentences uttered by 4 adult male speakers. Determined by minimizing the square errors from the measured F3, two separate planes corresponding to front and back vowels are situated in the F1F2F3 space to obtain the F3 values estimated from F1 and F2. Estimation errors are found to be comparable to difference limens in hearing. Also, uniform/nonuniform formant frequency scaling is discussed in terms of physical differences in the planes for individual speakers.