The technique of Fourier analysis is reviewed and the equivalence and relative advantages of convolution filtering in the space domain and multiplication filtering in the frequency domain are demonstrated with actual field examples. We discuss the design of ideal filters in terms of the relationships between the main lobe and the side lobes. Cut-and-try methods appear to favor the hanning window or the hamming window, since these windows minimize the Gibbs phenomenon associated with the downward continuation or high-pass filtering operation. New sets of coefficients for convolution filtering, based upon Fourier transform theory and the sampling theory, are derived.

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