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An iterative optimization technique, based on the method of parallel tangents coupled with an efficient line searching technique, is proposed for the design of two-dimensional linear-phase FIR digital filters. The performance index for the optimization procedure is shown to be convex and hence this technique will always converge towards the global minimum. An important feature is that the design time increases slowly as the number of filter coefficients increases. To illustrate the technique several circular low-pass filters were designed. These filters compare favorably with filters designed using the minimax technique that was developed by Harris. The technique can also be used for the design of one-dimensional and multidimensional linear-phase FIR digital filters.