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In this investigation Woodward's synthesis problem for line-sources and infinite strip-sources with arbitrarily spaced sample points is discussed on the basis of the well-known sampling theorem of bandwidth limited functions. Herein is described a method of synthesis based on the migration of zeros of the integral function from which all possible solutions of the problem can be derived. Because of the nonuniqueness of the solution, a criterion is introduced, to derive a unique distribution function so that the integrated value of its squared magnitude is a minimum. It turns out that the solution under this criterion coincides with the one obtained by Woodward and Lawson. Examples are given to illustrate the different solutions obtainable for particular problems, and the significance of the least integrated squared magnitude criterion.