Synchronous demodulation (SD) is the signal recovery method of choice when the input envelope signal is modulated by either a pure sine wave or a square wave. SD is less efficient for pulsed periodic signals with a low duty factor. For the latter signals, we introduce data processing that applies gating on a part of the signal period to achieve optimum conditions for recovering the pulse amplitude by quadrature SD. The proposed method is evaluated for signal-to-noise performance against Boxcar-type gated integrators in simulated data, as well as data acquired from physical measurements, in the presence of and Gaussian noise. It is shown that by combining the gating and SD principles, our suggested gated SD outperforms other routine signal processing methods under typical noise conditions.