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My clue is just to expand brackets and obtain coefficients of numerator and denominator of my transfer function. Am I right?

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  • $\begingroup$ Yes, you are right, only if your filter structure is a direct form. $\endgroup$ – Juancho Dec 23 '16 at 15:33
  • $\begingroup$ going from poles and zeros to Direct Form coefficients is easy. going in the other direction is a little harder because it involves factoring polynomials. $\endgroup$ – robert bristow-johnson Feb 24 '17 at 4:00
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This might look trivial, but with the pole-zero diagram alone one can get the transfer function with a scale (gain) ambiguity.

That is, all transfer functions $(Kb,a)$, where $K$ is a constant, have the same pole-zero representation. For this reason, we usually use pole-zero-gain terminology.

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