This note discusses some applications of convolution filter theory to gravity and magnetic maps. Sampling of the field is equivalent to a multiplication, and the corresponding convolution determines the sampling spectrum. If aliasing is acceptably small a specific filtering multiplication in the wavenumber domain corresponds to a convolution of a set of grid coefficients with gridded map values. The application of this theory to single-ring residuals, certain vertical derivatives, downward continuation, and low-pass filtering is discussed.

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