# How to obtain digital IIR filter coefficients for known z-plane zero-pole plot?

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

• Yes, you are right, only if your filter structure is a direct form. – Juancho Dec 23 '16 at 15:33
• 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. – robert bristow-johnson Feb 24 '17 at 4:00

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.