trade off edge sharpness with edge translation effects in the next step 110 the sample values f k u03b4t are convolved with the kernel values h t u2212 k u03b4t according to the finite convolution sum at t t the process continues at step 112 where the result of the convolution sum g t is output the process will continue until the final sample value has been calculated the following paragraphs provide a more detailed explanation of the kernel according to the preferred embodiment interpolation with a continuous kernel effectively gives a continuous function g t that is an approximation of f t and is given by the finite convolution sum the kernels are by definition of finite support and symmetrical about s 0 the kernel of the preferred embodiment is a modified cubic kernel and can be shown to be an interpolating kernel where the interpolated function passes through the sample points of the original function as h 0 1 while h k u03b4t 0 for k u2260 0 which ensure that g k u03b4t f k u03b4t from equation 4 any sample of g t can be calculated using the continuous kernel h t and a finite number of original sample points f k u03b4t adjacent to the sample being interpolated for example the conventional cubic kernel defined by equation 1 requires the four adjacent sample points while the modified cubic kernel defined by equation 3 requires only two the modified cubic kernel is what.