[flac-dev] Confusion about linear prediction within flac

[Robin Patrick Decker]

Hi,

I'm researching lossless compression for a highschool mathematics
research essay and am fairly confused about how the linear prediction
coefficients are solved for within flac.

As far as I understand, Levinson Durbin Recursion is used to solve for
these coefficients, however, what I don't understand is what the
toeplitz matrix is composed of. I found sources using samples from
within the time series to construct a linear system: 
http://practicalcryptography.com/miscellaneous/machine-learning/linear-prediction-tutorial/

However, talkbox, a scikit for signal proccessing (
https://github.com/cournape/talkbox/tree/master/scikits/talkbox/linpred
), first autocorrolates the signal using discrete inverse Fourier
transforms which then passes it to the levinson durbin algorithm.

I would really appriciate an explanation or information on a good
resource to learn more about how the prediction coefficients are solved
for.

Once the lpc coefficients have been solved, as far as I understand you
must also store part of original signal with length equal to the
prediction order since you need the previous samples to predict the
next sample of which only the residual is known. For the next values
the  residual is used to retrieve the original value which is fed into
the predction model to further reconstruct the time series. Is this
correct?

Kind Regards,
Robin Decker