Abstract We analyze light transmission both through a 1D waveguide that has a regular array of atoms inside, and through a stack of equally-spaced partially reflecting mirrors. We view the atoms and mirrors as linear filters. As such, they have two inputs, light coming in from both sides, and two outputs, light going out to both sides. The example systems formally have the individual filters chained so that inputs and outputs of successive filters are cross-coupled, whereupon the filters act cooperatively. Such an arrangement may form a band-stop filter with sharp edges and a deep minimum of transmission.