Thanks everyone for the helpful questions. I was actually hoping to make a permanent connection between the Arduino and coax cable, but of course the BNC plug connection should be detachable.
Regarding the frequency involved, unfortunately all I know is that the signal we're trying to send to the BNC/coax-accepting device is 30 Hz (alternating high/low TTL signal at every frame of a 30 fps video). So if I'm thinking about this correctly, I need to program my Arduino to send the information at a frequency that is significantly higher than 30 Hz, if I'm going to detect a 30 Hz signal with some precision? I suppose I also need to see what frequency the device that I'm sending the information to can accept...