As I understand it, analog signals are not the only problem. The signals will be digital, and they will not be broadcast on the current frequencies. That is to say, your TV will not work because the channels you can get ON THE AIR will no longer be used for public broadcasting. This does not affect you if you get cable, but it does affect those of us who chose not to pay for TV service. Right now, I get analog signals on the VHF and UHF frequencies my local stations use. In a year, those signals will stop.
Digital converters will allow televisions to receive digital signals through the air, and then convert them for use on conventional TVs. (I imagine this will be similar to the way a cable box works now.) The signals will NOT come in on the standard VHF/UHF stations we are used to, but with a converter that will not be an issue. Without a converter, your old TV will be useless except to play videos and DVDs on.
What WILL be an issue, however, is the difference between digital and analog signals. With analog signals, if you get a poor signal you get "snow" or other picture problems. That is annoying, but at least you still get to see the show. With digital signals, you will either get a perfect picture or none at all. If you have an unobstructed line of sight from the tower, your signal will be correct, otherwise, you will get no picture. Having seen a lot of technoglitches with the increasing use of digital technology, I suspect there will be a lot of video-audio sync problems and the like. But theoretically digital signals are an all-or-nothing proposition.