Several designs of infrared absorption based gas detector use a Fabry-Perot Interferometer (FPI) to modulate the incident light. In these systems, generally the FPI's fringes are matched with very well defined rotational absorption lines of a target molecule such as CO2, CO, N2O, CH4, etc. In order to obtain modulation the cavity length of the FPI is scanned over one half of the reference wavelength. In this work, we present a simple analytical method based on the Fourier Transform that describes the performance of these systems. Using this method the optimal reflectivity and optical spacing of the FPI can be determined. Furthermore, the modulated signal generated by the system as a function of the cavity length scan can be calculated by applying the inverse Fourier Transform. Finally, this method describes the underlying reasons why for some filters the background amplitude is severe, and gives guidance on the choice of optimised filters. Our method evaluates the optimal FPI parameters and the modulated signal much faster than the direct numerical computation which is used currently. Simulation results for different molecules in combination with diverse filters shapes are presented, with a comparison to directly computed results.