Uncertainty Propagation in (Gaussian) Convolution

Abstract Convolution of spectra, maps, or even higher dimensional data is often part of data reduction or analysis. Often a Gaussian kernel is used. When the convolved data are measurements, they are associated with uncertainties. This research notice derives how uncertainties propagate through the convolution. While the math is straightforward algebra, the results are not readily available. Here, the uncertainty propagation applied to regularly gridded data is provided. The calculation is done for uncorrelated data and correlated data.