In John Coleman's (2003) paper "Discovering the acoustic correlates of contrast", he mentions using "15 autoregressive filter coefficients (a1 - a15)" as an acoustic variable in measuring the correlates of a contrast. My advisor told me these are LPC coefficients, but I am a little confused as to exactly what that means.

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A waveform can be described as a sequence of integers. A speech waveform comes from running a source sound (the glottal wave, a kind of buzzing sound) through the "transfer function", which embodies vocal tract resonances. LPC coefficients (14 would be normal: twice the number of expected formants, plus 2 – this is the "order" of the model) come from estimating an "LPC model", which is an equation that allows you to predict the value of the waveform at a point, based on preceding waveform values. Suppose you have 2 coefficients a(1) and a(2), and waveform samples y(1) and y(2), then the value of y(3) should be a(1)*y(1) + a(2)*y(2). The coefficients are the weight assigned to a particular previous sample, so y(15)=a(1)*y(1)+a(2)*y(2)...a(14)*y(14).

  • Thank you! I think this makes sense to me. A follow up question: What do these coefficients correlate to, acoustically? In other words, how are they useful in acoustic measurement?
    – Lisa
    Mar 5, 2018 at 15:53
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    Essentially they are about formants, but they aren't formant measures themselves. The "transfer function" is the pattern of formants in a waveform, and the coefficients are. As far as I know, it's useless to say e.g. "We compared a(2) in vowel set A vs B and found...", so you have to do something fancier to extract meaningful information.
    – user6726
    Mar 5, 2018 at 16:15

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