The frequency response data of a generalized system is used to design fixed-structure controllers for the H2 and H∞ synthesis problem. The minimization of the two and infinity norm of the transfer function between the exogenous inputs and performance outputs is approximated by a convex optimization problem involving Linear Matrix Inequalities (LMIs). A very general controller parametrization is used for continuous and discrete-time controllers with matrix transfer function or state-space representation. Numerical results indicate that the proposed data-driven method gives equivalent performance to model-based approaches when a parametric model is available.