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Two-dimensional signals are usually represented for the purpose of digital processing as rectangularly sampled functions of two orthogonal independent variables. It has been previously noted that sampling a signal on a hexagonal grid can offer substantial savings in digital storage and computation. In this paper these two sampling schemes will be generalized, via a matrix description, to include arbitrarily sampled 2-D signals. Using this matrix description and a generalized discrete Fourier transform, a technique will be presented for interpolating a set of sample points from one sampling grid to an alternative one. Since the analog signal from which the original samples were obtained is frequently unavailable for resampling, the ability to easily convert from one sampling scheme to another can be important in the efficient processing of a particular signal.