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A design procedure for the synthesis of non-uniformly spaced linear arrays is presented, which uses the Poisson sum expansion of the array factor introduced in the literature. By considering the nonzero phase term in the existent formula and using the appropriate line source pattern synthesis methods, a general design procedure is obtained to synthesize any type of pattern, such as sum, difference and shaped beams. This approach converts the nonlinear complex problem of pattern synthesis for non-uniformly spaced linear arrays to a simple problem, which makes it fast and easy to implement. Moreover, an extra optimization process is added to the synthesis procedure to improve final pattern and provide control on computed parameters.