I want to measure the phase angle between two 100 MHz waveforms. One way to do that is to phase shift one of them 90 degrees and mix those two with the other, and lowpass the I and Q products. The filtered I and Q voltages plot a circle as a function of the phase difference, and the angle is the arctan of those two voltages.
If I do all that inside an FPGA (except the analog filters) I'd use a digital phase shifter, and XOR gates as the mixers, and the mediocre internal XADC to digitize the voltages. Simple!
The voltage plot of filtered I and Q vs angle becomes a diamond instead of a circle. We need a new function to convert to angle, and I modestly suggested "larktan." One of my FPGA guys can figure out how to do that.
I just thought that looked cool.