Thank you for the clarification. It has helped tremendously! I'm a little unsure about how the autocorrolation is calculated. For the calculation of the autocorrolation with lag i, x(n)x(n-i) is looped and summed through from n = 0 to the length of the original signal. This summation is then divided by the length of the signal (I'm assuming this is what expected value means?). i is then increased from 1 to p (model order) to create an array of autocorrolations with different lags. Am I understanding this correctly?
Thanks again for all the help. Kind Regards, Robin On Sun, 2018-09-09 at 13:01 -0700, Timothy B. Terriberry wrote: > 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. _______________________________________________ flac-dev mailing list flac-dev@xiph.org http://lists.xiph.org/mailman/listinfo/flac-dev
