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A technique is introduced which uses the conventional polynomial representation of the antenna pattern produced by an equispaced linear array. Certain roots are displaced from the unit circle radially, to fill a portion of the pattern, which before this displayed lobes interspersed by deep nulls. The angular and radial positions of all the roots are simultaneously adjusted so that the amplitude of each ripple in the shaped region and the height of each sidelobe in the nonshaped region are individually controlled. Applications to a cosec2 ¿¿ ¿¿ cos ¿¿ pattern and to a flat-topped beam are presented. Experimental validation is also offered.