Several designs of infrared sensors use a Fabry-Perot interferometer (FPI) to modulate the incident light. In this work we analyze the particular case where the FPI fringes are matched with very well defined rovibrational absorption lines of a target molecule such as CO(2), CO, N(2)O, or CH(4). In this kind of sensor, modulation is induced by scanning the FPI cavity length over one half of the reference wavelength. Here we present an analytical method based on the Fourier transform, which simplifies the procedure to determine the sensor response. Furthermore, this method provides a simple solution to finding the optimal FPI cavity length and mirror reflectivity. It is shown that FPI mirrors with surprisingly low reflectivity (<50%) are generally the optimum choice for target gases at atmospheric pressure. Finally, experimental measurements and simulation results are presented.