William E. Sabin wrote:
The signal on the cable goes to a phase-locked-loop in the TV rcvr. This
keeps the TV picture synchronized.

I won't say it doesn't happen, but I'd be surprised if your cable
operator is transmitting a 14.318 (or 3.579) signal down the cable.
(that doesn't mean they don't have a leak that needs fixing!)

Roughly 15,700 times a second, a brief burst (about 8-11 cycles) of a
3.579MHz reference signal modulates the TV RF carrier. This burst is
used to synchronize the color circuits. Left-to-right and top-to-bottom
scanning is synchronized with other pulses that modulate the same carrier.

So, for example, on a channel 2 station (RF carrier at 55.25MHz), the
synchronizing burst would create a sideband at 55.25 + 3.58 = 58.83MHz.
(it would also create a lower sideband around 52MHz but a filter in
the transmitter lops off most of the lower sideband, around 54.25MHz.)
No 3.58 signal is transmitted.

That's how an over-the-air station would work. But cable differs only
in that the output of the transmitter is connected to a combiner and
then to the cable to your house.

(and, of course, the transmitter is a LOT less powerful!)
--
Doug Smith W9WI
Pleasant View (Nashville), TN EM66
http://www.w9wi.com