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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?
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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.

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  • $\begingroup$ note the similarity between $x(t) \cdot x(t)$ and $x(t) \cdot \operatorname{sgn}\{ x(t) \}$ which is what $|x(t)|$ is. a resonator will deal with both. $\endgroup$ – robert bristow-johnson Sep 22 '16 at 19:44
  • $\begingroup$ Thanks @robertbristow-johnson, although, I am a bit puzzled. I like the trick with the sign anyway, I've always had $|.|$, in my mind as $\sqrt{.^2}$ but sign flipping is definitely faster. When you say "a resonator will deal with both" do you mean simply applying the sign and then filtering the square wave? The reason I distinguish between the two is because one produces a clean sinusoid while the other produces a fully rectified one and if you are going to use that for further demod then it better be as clean as possible. $\endgroup$ – A_A Sep 23 '16 at 8:34

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