Will analog televisions be obsolete?

No. Set-top boxes which convert digital signals to analog signals are available now and will continue to be available at lower prices to consumers as the transition progresses. However, to enjoy the full benefits of Digital TV, including superior sound and clarity, you must own a Digital TV set. An analog television, with the addition of a set-top box, will still allow viewers to enjoy all of the programming they have always enjoyed.

Source:  http://www.dtv.gov