A method, apparatus, and program product enable ticket holders, e. The DSP apparatus can include a DSP module configured to perform a DSP algorithm on digital signal samples of the signals. The first arithmetic circuitry, which may comprise a carry-propagate adder, processes the first portions of the input operands to generate at least a temporary sum and a carry output. Determining a weighting value for the pixels of the second digital image data which corresponds to a weighting of a image value of the pixel in the ratio of the image value of the pixel to image values of surrounding pixels. An axial direction of rotation of each roll is transverse to the rotational axis of the input shaft.