  We describe an analytical method for computing the orbital parameters of a
planet from the periodogram of a radial velocity signal. The method is very
efficient and provides a good approximation of the orbital parameters. The
accuracy is mainly limited by the accuracy of the computation of the Fourier
decomposition of the signal which is sensitive to sampling and noise. Our
method is complementary with more accurate (and more expensive in computer
time) numerical algorithms (e.g. Levenberg-Marquardt, Markov chain Monte Carlo,
genetic algorithms). Indeed, the analytical approximation can be used as an
initial condition to accelerate the convergence of these numerical methods. Our
method can be applied iteratively to search for multiple planets in the same
system.
