A simple method of multilayer filter synthesis is developed. The method is based on expanding the reflectance amplitude in a Fourier series and deducing the indices of refraction from the Fourier coefficients. The utility of the method is demonstrated by solving a general representative model for optical filters. The simplicity of the method is due to the fact that we deal directly with the reflectance amplitude. The method is applicable to cases of equal or unequal thickness films. To achieve a practicable design solution, the computed refractive indices are scaled and matched to a given set of available materials using the criterion that the error in the Fresnel amplitudes at each interface is a minimum, illustrative design examples are demonstrated.