I have a 2003 Hitachi 56" t.v, and have a DVi-HDTV output in the back, will I be able to view HD programms?

I am getting a HDDVR reciever with Directv this month and will I be able to view HD programms with my t.v that has a dvi output only no a hdmi output ? also I have seen dvi to hdmi converter plugs will that work ?