Altera NCO MegaCore Function - Manual (Page 20)

Table 3-1: Derivation of Output Values
Position in Unit
Circle
Range for Phase x sin(x) cos(x)
1 0 <= x < π/4 sin(x) cos(x)
2 π/4 <= x < π/2 cos(π/4x) sin(π/2-x)
3 π/2 <= x < 3π/4 cos(x-π/2) -sin(x-π/2)
4 3π/4 <= x < π sin(π-x) -cos(π-x)
5 π <= x < 5π/4 -sin(x-π) -cos(x-π)
6 5π/4 <= x < 3π/2 -cos(3π/2-x) -sin(3π/2-x)
7 3π/2 <= x < 7π/4 -cos(x-3π/2) sin(x-3π/2)
8 7π/4 <= x < 2π -sin(2π-x) cos(2π-x)
A small ROM implementation is more likely to have periodic value repetition, so the resulting waveform's
SFDR is lower than that of the large ROM architecture. However, you can often mitigate this reduction in
SFDR by using phase dithering.
Figure 3-2: Derivation of output Values
Related Information
Phase Dithering on page 3-6
CORDIC Architecture
The CORDIC algorithm, which can calculate trigonometric functions such as sine and cosine, provides a
high-performance solution for very-high precision oscillators in systems where internal memory is at a
premium.
The CORDIC algorithm is based on the concept of complex phasor rotation by multiplication of the
phase angle by successively smaller constants. In digital hardware, the multiplication is by powers of two
UG-NCO
2014.12.15
CORDIC Architecture 3-3
NCO IP Core Functional Description Altera Corporation
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