With the exception of CRT models, all HDTVs (and digital TVs in general) are fixed pixel displays. The fixed Resolution of a Fixed Pixel Display is known as its Native Resolution. This applies to DLP, LCD, and plasma TVs.
All incoming signals must be upsampled or downsampled into the display's Native Resolution, so a 1920x1080 (1080p or 1080i) video Frame would have to be downsampled for display on a 720p (1280x720 Native Resolution) fixed pixel HDTV. Likewise 720p or standard definition video will have to be upsampled to the Native Resolution of 1920x1080 for viewing on a 1080i or 1080p fixed pixel HDTV.