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Using a modified Chebyshev pattern function with some control parameters, the Zolotarev difference patterns are synthesized by two proposed approaches. One approach consists in forming the pattern function expressed as the multiplication of the modified Chebyshev polynomial with an arctangent function; the other applies an interpolation technique to control the side lobe levels. The control parameters are given in the expressions of the SLL (Sidelobe Level) and array element number. Under the Fourier relation, the sampling theorem and the FFT algorithm are used to obtain the Zolotarev difference patterns with equal or unequal sidelobe levels. The synthesis examples show the simplicity of these two techniques and the capability to control the pattern' s sidelobe levels.

Using perturbation technique, the linear relation between the array pattern and its parameter (current, spacing) perturbation can be established. In a simple and fast way, the formulas to determine parameter perturbations by FFT (Fast Fourier Transform) algorithms are developed and presented in this paper. These formulas can be generically applied in the array synthesis to approach the specified pattern or to improve the pattern performance. Applying them on the synthesis of pencil beam patterns, for which the lower sidelobe levels and/or narrower main beam width are desired, it is shown that the sidelobe reduction can be easily achieved, meanwhile keeping a desired narrow beam width.

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