Formant-frequency estimation by linear transformation of the LPC-cepstrum
David J. Broad, Frantz Clermont · The Journal of the Acoustical Society of America · 1988
Correlations near 0.98 between vowel formant frequencies and linear combinations of 1/3-octave-band spectrum levels reported by Pols et al. [“Perceptual and physical space of vowel sounds,” J. Acoust. Soc. Am. 46, 458–467 (1969)] suggest that the formants might be estimated by linear transformation of either a low-resolution log spectrum or of the first M cepstral coefficients ci, which are linear functions of a log spectrum. Applying this idea with M = 14 to four speakers results in pooled intraspeaker prediction errors of 41, 126, and 134 Hz for F1, F2, and F3, respectively. These become 52, 164, and 218 Hz when regressions on data from three speakers are used to measure formants from a fourth. The method is therefore not very accurate, but it is robust in that large errors from misidentified peaks are rare. A study of single-resonance waveforms explains why the method works: The ci are roughly cosines in the resonance frequency F, with i half-cycles over the analysis bandwidth; these ci (F) form a basis set for approximating the function Fesl = Freal.