Only off-air HD is true HD. Cable and sat providers are sending you MPEG2 or MPEG4, over-compressed and low-res. I assume you refer to the local Fox channel, not FX, right? If so, can you get it off-air?
The problem with your local HD channel could be in the uplink that the cable company receives, or in the compression that they apply after that, or both.
In any case, it's not likely to improve. Local channels from the satellite providers are no better, quality often suffers.