Hi
A good old analog TV set will not do much of anything with a single line of video. About the most simple is the old NTSC waveform that is essentially two frames that interleave. You get a full frame every 1/30 second. The signal can be looked at a number of ways and you get a different bandwidth each way. Just to move things on, let's say it's a 4.5 MHz bandwidth That gets you to something more than 9 mega samples per second. It would take a generator that will do a 100K sample run to do that.
Now, since it's an analog signal, you would need a very good lowpass filter between the generator and the TV. A more realistic setup would be about 20 mega samples per second and a somewhat easier to build filter. At that point you have a 200K sample generator. If you want to do it with the generator here on the desk and not play with a filter, you need to run a few mega samples through it. Oddly enough that's a bit more than this one will do.
Consider that none of this is actually synthesizing the waveform. All you are doing is playing back a digitized video signal. The only way you set it up is to do creative software to produce the file. You then just us the generator as a fast ADC to play your file. A $30 video card is a much easier solution.
Bob