The full spectrum inversion (FSI) technique allows for effective retrieval of profiles of bending angle and optical depth. These profiles are directly derived from a Fourier transform of a measured radio occulation (RO) signal. Though the entire signal is used in the FSI Fourier transform, only some fraction of the signal contributes significantly to each pair of bending angle and optical depth, whereas noise and disturbances throughout the signal contribute to the errors for all pairs of bending angle and optical depth. The impact from noise and other disturbances may be reduced if window functions are applied in the computation of individual Fourier components. In this study, it is demonstrated how window functions can be applied to the FSI technique. In the approach described here, the window functions are applied in the frequency domain, and it is demonstrated that this technique can be applied in an iterative way to further reduce the impact of noise and disturbances. To assess the merits of using window functions, we apply the windowed FSI to simulated cross-link signals. The results from the simulations show that application of window functions in the FSI technique results in some noise reduction for both white noise and a spike in the signal, whereas iterative use of the window functions was found to significantly reduce the errors from these noise sources, as compared to standard FSI retrieval. It was also found that in terms of relative errors, retrieved derivatives of optical depth are far more sensitive to signal disturbances than retrieved bending angles.