Tabulated Alternative (Order $N$ )

Design a digital filter (FIR or IIR) that approximates

$$H_\Delta \left(e^{j\omega T}\right)= e^{-j\omega \Delta T},\quad \Delta = \hbox{Desired delay in samples}$$

optimally in some sense, with coefficients tabulated over a range of $\Delta$ samples (and interpolated on lookup).