Impact of the spectral resolution on the PDFs of the transmission function T as a function of input wavelength shift Δλ_e. We show the PDF of T over all emitters and LOS at z = 3, similarly to Fig. 2. In blue we show the mean for a given Δλ_e, while in green we show the median. We show the transmission at different spectral resolutions R ∈ {600 000,60 000,6000,1800} (solid, dashed, dotted, dash-dotted). Resolutions below 600 000 are computed as convolution with a Gaussian of FWHM λ_FWHM that sets the spectral resolution as R = λ_c/λ_FWHM. The shaded regions enclose the central 68% of all individual transmission curves. The darkest (lightest) shade corresponds to the lowest (highest) spectral resolution. As the resolution increases the median increases and the shaded region widens. At our fiducial resolution of ∼60 000 these statistics have converged.