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We experimentally demonstrate an all-optical all-fiberized scheme that can eliminate linear perturbations in the time domain. The technique relies on performing optical Fourier transforms on distorted signals to move their distortions from the time to the frequency domain. A near-complete transformation is obtained by using cross-phase modulation with parabolic pulses as a time lens. Mitigation of second- and third-order dispersed pulses is demonstrated as well as good transform behaviour.