ArTeMiS is a sub-millimetre camera to be operated, on the Atacama Pathfinder Experiment Telescope (APEX). The ultimate goal is to observe simultaneously in three atmospheric spectral windows in the region of 200, 350 and 450 microns. We present the filtering scheme, which includes the cryostat window, thermal rejection elements, band separation and spectral isolation, which has been adopted for this instrument. This was achieved using a combination of scattering, Yoshinaga filters, organic dyes and Ulrich type embedded metallic mesh devices. Design of the quasi-optical mesh components has been developed by modelling with an in-house developed code. For the band separating dichroics, which are used with an incidence angle of 35 deg, further modelling has been performed with HFSS (Ansoft). Spectral characterization of the components for the 350 and 450 bands have been performed with a Martin-Puplett Polarizing Fourier Transform Spectrometer. While for the first commissioning and observation campaign, one spectral band only was operational (350 microns), we report on the design of the 200, 350 and 450 micron bands.