Formant (source code)
= Formant
{title2=$F_1,F_2,\ldots$}
{wiki}
A <formant> is a resonant spectral feature associated with the filtering of speech by the <vocal tract>. Its centre <frequency> and bandwidth describe different aspects of the feature; the first few formants are conventionally labeled $F_1,F_2,\ldots$. <Praat> represents estimated formant structure as time-sampled centre <frequencies> and bandwidths.<Formant Analysis in the Praat Manual by Paul Boersma>[Formant object reference: frame and formant attributes]{ref}
A simple physical model treats the <vocal tract> as a uniform tube, closed at one end and open at the other. Under those ideal boundary conditions its resonance <frequencies> are
$$
f_n=\frac{(2n-1)c}{4L},\qquad n=1,2,\ldots,
$$
where $c$ is the <speed of sound> and $L$ the tube length. For $L=0.17\,\mathrm{m}$ and $c=340\,\mathrm{m\,s^{-1}}$, the first three model resonances are 500, 1500 and 2500 <hertz>. A real <vocal tract> has a varying cross-section, losses and moving articulators, so this illustrates the mechanism rather than predicting every <vowel>.
These resonances are distinct from the <fundamental frequency> of <vocal fold> vibration. The <source-filter model> separates the repeating excitation from the filter's <spectral envelope>, explaining how a speaker can change vowel quality without making the same change in <pitch>.
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