Two different types of stationary Fourier transform spectrometer, one of them based on a triangular interferometer and the second one based on a Savart-plate interferometer, were built and tested. The theoretical background that underlies the operation of fixed optics spectrometers is given as well as a description of the mathematical routines used for the reconstruction of the spectrum from the interferograms produced by a particular light source. Finally, the spectra of various light sources were measured and the performance limits and accuracy of the two instruments were established.