I have an analog cable signal with a Yuan tv card. The picture quality is also terrible. Are you sure your cable signal is digital?? I think a tv tuner card will only use unencrypted or over the air digital. You may be getting an analog signal in or the digital signal may be downconverted to an analog signal with quite low resolution.
If you can get over the air digital, see what kind of picture you get from that. I get a really good picture from over the air digital, but can only tune in a very few stations. The cable signal is terrible, as I said earlier. I have tried various video cards and all kinds of adjustments, but cannot get a really good signal from the cable input.
Cable TV may have older analog Standard TV (not HD) signals for some channels, newer Digital TV (but still NOT HD) signals for some channels, some analog Pay TV channels, and some Digital HD channels, whether extra-cost or not. You really need to check with your cable company what channels and signal types they supply.
Many TV cards have the ability to accept three kinds of signals: analog Standard TV (still found on cable systems, but not OTA transmitters), new Digital TV signals in the Clear QAM format used only on cable TV, and new Digital TV signals in the ATSC format used only by OTA transmitters. Some don't have all these possibilities. Some have two TV input connectors, and can handle analog signals on only one of them, and digital signals only on the other. If you have one like that, you need a splitter in your cable to feed two signals separately into the two input connectors. Other tuner cards avoid this issue and deal with it all internally. You really need to read carefully the instructions for your particular card to figure out where to feed the cable in, and how to set it for the signals it provides.
Now, all that said, it is still possible that your cable signal is poor. On an analog channel, that will result in a picture with "snow" - random white or colored dots all over - or ghosts - double images. On a digital channel, weak signal results is random complete loss of signal - you either have decent picture or nothing. If your problem is simply fuzzy picture with no random colored spots, you probably have an analog signal at Standard TV quality, not HD. Or even digital - Digital TV is NOT automatically HD!