Pilot tone frequency doubling U.S. Broadcast FM stereo includes a $19\textrm{ kHz}$ pilot tone that needs to be frequency doubled to help demodulate the DSB stereo difference signal. 


How can this frequency doubling be done digitally?  
What signal paths need to be delay matched (etc.) to avoid phase errors causing loss of stereo separation?
You can multiply it (modulate it) with itself, which will give you a signal with double the frequency and a DC component which is trivial to remove.

The other way to do it would be to $h * |x(n)|$ with $h$ being a resonator (and $x$ your pilot tone). That is, having tracked the pilot tone, rectify it and then pass it through a very simple resonator at 38 kHz to get rid of harmonics. In this case, you will only have to phase match the filter's delay.