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.

1 Answer 1


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
  • 1
    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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.