Translations:Causality and stability of digital systems/32/en

The right-hand expression is the factored form of the transfer function. The $a_{i}^{-1}$ are its poles and the $b_{i}^{-1}$ are its zeros. For simplicity of presentation, we will assume that $p>q$, so that $H\left(Z\right)$ is a proper fraction in Z. In addition, we will suppose that all the poles $a_{1}^{-1}$, $a_{2}^{-1}$,..., $a_{p}^{-1}$ are simple ones. We now write $H\left(Z\right)$ as the sum of partial fractions