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At one time, everyone thought that 28.8K and 33.6K would be the end of the line. To get higher speeds, you'd need radically different modems that wouldn't work over standard phone lines.
The advent of 56K modems has changed all that. You can now have a faster connection using your existing phone lines and new modems that work just like your old modem, only faster.
The nature of 56K technology is a little different than existing analog modems. In particular, it depends on a half-digital connection to achieve its higher speeds. Read more about it in "How it works" and find out one of the major consequences of this design in "Cons: Only one A/D conversion allowed."