Filter-band images obtained by integrating the signal of the HSIM output cubes in the spectral bands (Hβ+MgI region) of the IzJ-grating (0.82−0.93 μm (left) and 1.17−1.33 μm (centre)) and the H + K-grating (1.55−1.75 μm (right)) when considering a QSO of L_[OIII] ∼ 10⁴² erg s⁻¹ at the nucleus of the lenticular host (i.e. NGC 809) at redshifts 0.76 (left), 1.50 (middle), and 2.30 (right). Host luminosities are scaled to 10¹² L_v, ⊙ (top), 10¹¹ L_v, ⊙ (middle) and 10¹⁰ L_v, ⊙ (bottom). Intensity is in logarithmic scale and normalised to the peak of the brightest case (top left panel). Contours correspond to the average S/N in the rest-frame 5050−5250 Å corresponding to a stellar continuum region including the MgI features (brown contours are S/Ns of 0.06, 0.1, 0.3, and 0.6; S/Ns values of 2, 5, 9, 14, and 20 are drawn as blue contours; the purple contour indicates an S/Ns of 1).