Recently, Fourier spectroscopy has been discussed as a promising project to introduce into undergraduate physics laboratories. Such a project can have great educational value if the student who conducts the experiment and takes the data can conduct and observe every step of the analysis procedure as well. Fast Fourier analysis computer programs, although they provide great speed and flexibility, prevent the student from participating in the analysis of the experimental data and therefore make little contribution to the student’s understanding of the Fourier integral theorem. This paper presents a simple method of analysis whereby the student experimenter can integrate, point by point, any interferogram to obtain its Fourier transform. The manual technique requires no special equipment and is based on relationships that most undergraduate physics students can derive from the Fourier integral equations.