We obtain the form of the gravitational waves emitted by eccentric binary systems, including general relativistic periastron advance effects. Using the method of stationary phase, we find the Fourier transform of the amplitude. The Fourier analysis is based on an approximation of the waveform consisting of a linear superposition of five harmonics of the orbital frequency, valid up to medium eccentricities (e≃0.33). We show that it is not necessary to change the detector parameters in a light-recycling design to achieve the optimum signal-to-noise ratio for the different harmonics. We also find that, for eccentric orbits, the observation time window can be enlarged by a factor of 10 in some cases.