No, yes and no.
First, there are two types of converter boxes. The term
DTV tends to imply that you're referring to the over-the-air digital television converter boxes. They convert
ATSC/
8VSB (the transmission format used by local broadcast channels, to transmit their signals through the air) into something your analog television can use. However, since you're posting in the cable/satellite forum, and talking about Cox, I suspect you're concerned about cable television service. Digital cable is transmitted by a more efficient modulation format, QAM, instead of the less efficient
ATSC/
8VSB. (Over-the-air broadcasters would not have been able to transmit using QAM, because the more efficient format is also more subject to damage from over-the-air interference.) There are converter boxes that convert QAM for use by your old analog television, but generally they're mostly available for rental from cable companies, since there really isn't a big market for them being sold to customers directly. I remember seeing one for sale a few years ago, at $180, but more recently I haven't been able to find one for sale, legitimately.
Okay, but I said, "No, yes
and no." The first "no" was in reference to the fact that most of the time when we talk about
DTV converter boxes we're referring to the
ATSC/
8VSB converter boxes, which will
not help you with Cox. The "yes" was in reference to the fact that there are QAM converter boxes. So we're left with the second "no": Even if you did have one of these QAM tuner boxes, many (but not all) cable service providers encrypt many (but not all) expanded basic channels, and a customer-owned QAM tuner, without a CableCARD port for you to put a rented CableCARD into, would not be able to tune in the encrypted channels.