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Sat, 09 Feb 2008

voyage of rediscovery

So it turns out that my discussion yesterday is (as you would expect) a well known one among those who build digital filters. There is even some terminology to go along with it.

The representation of numbers as plus or minus a fractional power of two is effectively canonical signed digit representation, and while my algorithm doesn't explicitly guarantee canonical results, it does so implicitly by minimizing the (log-wise) error in each step. It should be obvious that CSD is more efficient than two's complement at representing numbers, since digits are ternary (0,+,-) rather than binary.


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