ABSTRACT
The paper discusses some questions about Fourier transforms, how they enter into quantitative spectrum analysis, and how they can be applied to learn more about stars. Physical processes that are better analyzed in terms of Fourier transforms rather than line profiles, and vice versa, are identified; advantages of Fourier analysis are enumerated; and the analysis technique is outlined. The use of Fourier transforms is demonstrated by summarizing typical applications to stellar rotation, macro- and microturbulence, stellar magnetic fields, and velocity distributions in globular clusters and galaxies. Observational techniques that should be employed to obtain the best results from a Fourier analysis are considered along with some basic limitations of the Fourier approach.