Demonstrations of electromagnetic eavesdropping attacks on digital video-interface cables usually first amplitude-demodulate the received signal, then resample the result into pixel-aligned raster images, and finally average consecutive video frames obtained this way. This non-coherent process discards useful phase information. Software-defined radio receivers allow us to coherently demodulate and average such signals, using a linear process that preserves phase information. We describe techniques for performing phase-coherent resampling and periodic averaging of compromising emanations from HDMI video cables and demonstrate how the preserved phase information enables better discrimination of on-screen colours.