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Yes and if you run the numbers for a couple dBm out and spread across a 6 MHz ATSC signal, compared to the actual stations (depending where you live, I guess) you'll have a range of perhaps feet. Maybe tens of feet.

Shannon's law is not to be denied! (And what decade did it rename from "Shannons Law" to "Shannon–Hartley theorem" anyway?)

No.

And you don't need to be an jerk and interfere with broadcasts. It's an antisocial activity frowned on by 99.99 percent of the public and hardware hackers. There's plenty of good science that can be done in all aspects of RF experimentation for a small investment of time and little money.

To give the GP the benefit of the doubt, there are plenty of low-power FM transmitter dongles that people use legitimately to play audio over low-cost FM radios.

If you're having difficulty assessing the feasibility of something like this, you're going to have all kinds of trouble actually implementing your "diabolical" scheme.