A new approach to periodogram analyses.

We present a method for Fourier analyzing quasi-periodic light and radial velocity variations. The scheme gives a particularly clear interpretation to the periodogram, reduces the alias problem, allows detection of very weak components, has potential for greater precision in frequency measurement, and is a shorter computation than the usual method. Our development points out the possibility of error in evaluating the zero-frequency component by the usual method. We derive, under appropriate assumptions, a rigorous evaluation of the phase of each component. Subject headings: pulsation - variable stars