The present invention provides a three position hydraulic piston assembly for a gear ratio change mechanism for a transmission exhibiting reduced gear shift noise. The apparatus includes a data processing unit for performing a pre-printing process of received printing data in single page units. A controller is configured to randomly select a basic wagering game outcome from a plurality of basic wagering game outcomes. A rotary part is rotatably journalled on the base. A pre-processor minimizes the effects of saturation limits for double sideband, truncated double sideband or single sideband processing to achieve superior output.