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is it possible to guess the stability of a filter with given coefficients a and b? I know that the right way would be to calculate the pole positions and check if they are in the unit circle but I think I read that there also is another method.

Cheers

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  • $\begingroup$ What research have you done so far? The non-recursive coefficients (what you call b) do not affect stability (except for the case of a zero-pole cancellation). $\endgroup$ – Juancho Feb 10 '16 at 18:36
  • $\begingroup$ I've read that it's sufficient to check if the sum of the recursive coefficients stay bellow 1. Sadly, I have no clue where I read this and as far as I know, that's just not a legit way to check stability. However, I might overlook something as most scientific source in the web overcomplicate everything.... So you don't know of such a method either? $\endgroup$ – ruhig brauner Feb 10 '16 at 20:14
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In the general case there is no simple way to determine the stability of a discrete-time system (unless it is FIR, in which case it is always stable). In order to check stability you don't necessarily need to compute the poles of the transfer function, but you can use the Jury stability criterion, which does not explicitly compute the poles, because the latter is generally a numerically ill-conditioned problem.

For a second-order system the denominator coefficients have to be inside the stability triangle, which can be checked very easily.

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  • $\begingroup$ Ok, so what I've read might have been a special case for BiQuad filters. :) Thanks for the response, very helpful! $\endgroup$ – ruhig brauner Feb 10 '16 at 20:59

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