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We investigate the potential of using previewed wind speed measurements for damping wind turbine fore-aft tower oscillations. Using recent results on continuous-time H2 preview control, we develop a numerically efficient framework for the feedforward controller synthesis. One of the major benefits of the proposed framework is that it allows us to account for measurement distortion. This results in a controller that is tailored to the quality of the previewed data. A simple yet meaningful parametric model of the measurement distortion is proposed and used to analyze the effects of distortion characteristics on the achievable performance and on the required length of preview. We demonstrate the importance of accounting for the distortion in the controller synthesis and quantify the potential benefits of using previewed information by means of simulations based on real-world turbine data.