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The measurement of an antenna in a reverberant or semi-anechoic chamber, or even in an anechoic chamber with non-ideal absorbing material, will include the effects of multipath propagation, which will be evident in a distorted radiation pattern. In those situations, an improvement of the measurement can be achieved through removal or compensation of the undesired contributions. A simple technique to eliminate those contributions, based on the well-known Fourier transform algorithm, is used in this paper. It starts from measurements of the system's response in the frequency domain, followed by Fourier transformation of data to the time domain, detection and gating of undesired echoes in the time domain, back to the frequency domain, and retrieval of the antenna radiation pattern at the frequency of interest. The method is evaluated under different measurement conditions.