[flac-dev] Confusion about linear prediction within flac
Timothy B. Terriberry
tterribe at xiph.org
Sun Sep 9 20:01:41 UTC 2018
Robin Patrick Decker wrote:
> I would really appriciate an explanation or information on a good
> resource to learn more about how the prediction coefficients are solved
> for.
The Wikipedia page on this subject is not terrible:
https://en.wikipedia.org/wiki/Linear_prediction
The very high-level answer is that if want to choose your coefficients
to minimize the mean squared error of the prediction, then you get a
least-squares problem where the matrix you're inverting is just the
auto-correlation matrix of your signal (the Yule-Walker equations). The
discrete Fourier transform is just a computationally efficient means of
computing the auto-correlation, at least if your order is sufficiently high.
> 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?
Yes.
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