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When clocked, the phase accumulator (PA) creates a [[modulo operation|modulo]]-2<sup>N</sup> [[sawtooth wave]]form which is then converted by the phase-to-amplitude converter (PAC) to a sampled sinusoid, where N is the number of bits carried in the phase accumulator. N sets the NCO frequency resolution and is normally much larger than the number of bits defining the memory space of the PAC [[look-up table]]. If the PAC capacity is 2<sup>M</sup>, the PA output word must be truncated to M bits as shown in Figure 1. However, the truncated bits can be used for interpolation. The truncation of the phase output word does not affect the frequency accuracy but produces a time-varying periodic phase error which is a primary source of spurious products. Another spurious product generation mechanism is finite word length effects of the PAC output (amplitude) word.<ref name="kroupa">Kroupa,Venceslav F.,''Direct Digital Frequency Synthesizers'', IEEE Press, 1999, ISBN 0-7803-3438-8</ref>
The frequency accuracy relative to the clock frequency is limited only by the precision of the arithmetic used to compute the phase.<ref name="kroupa"/> NCOs are phase- and frequency-agile, and can be trivially modified to produce a [[phase modulation|phase-modulated]] or [[frequency modulation|frequency-modulated]] output by summation at the appropriate node, or provide [[quadrature phase|quadrature]] outputs as shown in the figure.
==Phase accumulator==
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