Filtered compact realization of a band coefficient

The derivative filter is needed for the weighted infrared topology. The parameter $T$ is an exact time-slice choice, not a packet time-window approximation.

Choose $t_2-t_1>2T$. The construction for $u=v$ at $t_1$ and $u=\mathrm{i}v$ at $t_2$ gives strictly ordered compact source profiles. Set $g_1=\lambda ,g_2=\mu$.