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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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