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The optimization of the transmitted signal time-frequency structure is the very important part of the radar system design from the point of view of the radar system effectiveness. In this meaning the radar ambiguity function is the basic tool used for the radar system features testing. The synthesis procedure of the signal with simultaneous amplitude and phase manipulation is presented in the paper. The procedure is based on the Zak transform that is connected with the radar ambiguity function. The Legendre polynomials were applied in the procedure mentioned above. The results of the simulation tests are presented as examples of the consideration main effects.

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