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I am having some difficulties understanding LPC and speech processing in general. The professor asked us to provide an heuristic way to select the order of LPC? For example if I wanted to model 3 formants what would be the order I should use? I understand the order of prediction is the number of coefficient used in the estimation of the signal $s(n)$: $$\hat{s}(n)=\sum_{k=0}^p a_ks(n-k)$$

I am also open to any resources for a beginner in automatic speech recognition.

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Usually you use 2 complex conjugate poles for each spectral peak. By other words, the order of the LPC model should be the double of the spectral peaks you want.

If you have 3 formants then you should use, at least, a 6th order LPC model.

You can try this yourself: record some vowels and then try (for each vowel) to use matlab or python to plot an LPC based spectrum. Change the order of the model to see if it can mimic the original spectrum.

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