22 pages ; International audience ; A theoretical model of the influence of detection bandwidth properties on observed line shapes in laser absorption spectroscopy is described. The model predicts artificial frequency shifts, extra broadenings and line asymmetries which must be taken into account in order to obtain accurate central frequencies and other spectroscopic parameters. This reveals sources of systematic effects most probably underestimated so far potentially affecting spectroscopic measurements. This may impact many fields of research, from atmospheric and interstellar physics to precision spectroscopic measurements devoted to metrological applications, tests of quantum electrodynamics or other fundamental laws of nature. Our theoretical model is validated by linear absorption experiments performed on H2O and NH3 molecular lines recorded by precision laser spectroscopy in two distinct spectral regions, near- and mid-infrared. Possible means of recovering original line shape parameters or experimental conditions under which the detection bandwidth has a negligible impact, given a targeted accuracy, are proposed. Particular emphasis is put on the detection bandwidth adjustments required to use such high-quality molecular spectra for a spectroscopic determination of the Boltzmann constant at the 1 ppm level of accuracy.