Well Known Closed-Form Solutions

$$\begin{array}{c} \mbox{Order}\\ \begin{array}{\vert\vert r\vert\vert c\vert c\vert c\vert c\vert} \hline \hline & 1 & N & \mbox{Large $N$} & \infty \\ \hline \hline \mbox{FIR} & \mbox{Linear} & \mbox{Lagrange} & \mbox{Windowed Sinc} & \\ \hline \mbox{IIR} & \mbox{Allpass}_1 & \mbox{Thiran} & & \mbox{Sinc} \\ \hline \end{array}\end{array}$$