# Translations:Prediction-error filters/7/en

Thus, ${\displaystyle FB=B-Z^{\alpha }T}$, so ${\displaystyle F=1-Z^{\alpha }TA}$. Because ${\displaystyle TA=K}$, we see that the Z-transform of the prediction-error operator is given by ${\displaystyle F\left(Z\right)=1-Z^{\alpha }K\left(Z\right)}$, which gives ${\displaystyle f={\delta }_{0}-{\delta }_{\alpha }*k.}$.