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We demonstrate experimental post-compensation of ultra-wideband (UWB) antenna dispersion at a receiver front-end by using programmable microwave photonic phase filtering. After the received RF signal is modulated onto an optical carrier, we utilize a hyperfine resolution optical pulse shaper to apply the conjugate of its spectral phase in the optical domain. After optical-to-electronic conversion, this yields an electrical waveform, which is compressed to bandwidth-limited duration. Further we use this technique in two schemes: a radar configuration in which we resolve two close echoes from different paths, which initially interfere and mask each other due to the dispersed response of the antenna link, and a spread-time UWB transmission configuration in which we retrieve and compress a distorted signal received in line-of-sight. To our knowledge, this is the first experimental demonstration of dispersion post-compensation of UWB RF waveforms to approach the ultimate bandwidth-limited resolution, as well as identification of such signals by matched filtering and compression. Our technique is programmable and offers potential to enhance performance in UWB radar and communications.