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The sequence of directions is completely defined in
Equation 1.12
and Equation 1.14:
|
(1.17) |
be the general term of the iterative system determined by Equation
1.10 and 1.11, where and are
polynomials in the variables d.
Setting the initial vector to
we get:
Now define a new initial Vector
:
From Equation 1.21 it follows that the gain inherent in
the CORDIC algorithm is a constant for a constant number of iterations
and independent of the initial values if coordinate . Consequently, multiplication can be performed by initializing the
rotation with the control parameter amplitude. This eliminates
the need for an additional multiplier and reduces the design
complexity enormously.
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Norbert Lindlbauer
2000-01-19