In the solution of fluid-structure interaction (FSI) problems, partitioned procedures are modular algorithms that involve separate fluid and structure solvers that interact in an iterative framework through the exchange of suitable transmission conditions at the FS interface. In this work we study, using Fourier analysis, the convergence of partitioned algorithms based on Robin transmission conditions. We derive, for different models of the fluid and the structure, a frequency-dependent reduction factor at each iteration of the partitioned algorithm, which is minimized by choosing optimal values of the coefficients in the Robin transmission conditions. Two-dimensional numerical results are also reported, which highlight the effectiveness of the optimization procedure.