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We calculate explicitly the radiation pattern for linear antenna with uniform distribution excited by a current pulse with exponential fronts. For a specific experimental form of non-symmetric exciting current pulse we demonstrate that our approximation is better for both the incident current pulse and the resulting energetic directivity than the approximation with the Gauss-like pulse. We study the dependence of the directivity from the signal shape and the length of antenna. In particular, we consider symmetric and step-like pulses