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We report, with an unequivocal time-domain measurement, that an appropriately chosen undulator taper can compensate for an electron beam longitudinal energy-chirp in a free-electron laser amplifier, leading to the generation of single-spike radiation close to the Fourier limit. The measurements were taken using the frequency-resolved optical gating technique by employing an advanced transient-grating diagnostic geometry. The reconstructed longitudinal radiation characteristics are compared in detail to prediction from time-dependent three-dimensional simulations.