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I am currently trying to implement an iterative block-wise algorithm in which AR coefficients are computed for each block. There is a issue with my code where values get too large, and I was wondering how linear prediction handles stability issues. For an onset block for example, the coefficients for a low order IIR-filter may result in an unstable filter, at least from my intuition.

My question is:

  • Is the linear prediction method able to produce instable sets of autoregressive filter coefficients?

I realize this might be a stupid question, and I feel like I missed something. Please note that I would like to hear about linear prediction, I am not asking for someone to fix my code problem (yet).

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Ok, I found out from a book that linear prediction always results in minimum phase filters, which implies stability.

This can be shown using the mean-squared error (MSE) criterion which is to be minimized in the autocorrelation method. The proof is done by contradiction; if an all-pole filter had a single pole outside of the unit circle, the derivative of the MSE in regards to the pole radius is always greater than zero. In terms of the MSE, this implies the pole position is not optimal, so it cannot be a result from linear prediction (under ideal conditions, I assume).

The actual proof can be found here.

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