Ideal Lowpass Filter

For the ideal lowpass, the error bound is

$$\left\vert e_{qq}(t)\right\vert \leq 2^{-n_c} + a 2^{-(n_l+{n_\eta }+1)} + {\pi^2\over 8} 2^{-n_l}.$$

Let n_l=1+n_c/2 and require that the added error is at most ${1\over2}2^{-n_c}$. Then we arrive at the requirement

$${n_\eta }\geq {n_c\over2}.$$