The present paper presents results from a wave energy conversion that is based on a direct drive linear generator. The linear generator is placed on the seabed and connected to a buoy via a rope. Thereby, the natural wave motion is transferred to the translator by the buoy motion. When using direct drive generators, voltage and current output will have varying frequency and varying amplitude and the power must be converted before a grid connection. The electrical system is therefore an important part to study in the complete conversion system from wave energy to grid connected power. This paper will bring up the first steps in the conversion: rectification and filtration of the power. Both simulation studies and offshore experiments have been made. The results indicate that this kind of system works in a satisfactory way and a smooth DC power can be achieved with one linear generator.