
... convolution, which is how we reconstruct a continuous scalar field from our discretely sampled data.We don't have time for details, but I'd like to note that the analytical derivative of a continously reconstructed signal is the result of convolving the same data, with the derivative of the filter.
I should also mention that its helpful for the filter to have some smoothing built into it, as these do, in order to help deal with real-world noisy data.