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Given the phase coherence over non-blanked intervals, a simple and effective approach would be to additionally window the non-blank intervals with a matching window corresponding to the length of the time samples in between blanked intervals. Since the window only tapers the amplitude and does not modify the phase, there will be no issue with different window durations. This will significantly decrease if not eliminate the grating while provide phase coherent processing gain from interval to interval over all usable samples. The Kaiser window would be a good window choice for this application.