Why A DDS builds its output by stepping a phase accumulator and looking up sample values that a DAC converts to analog. Because the phase word is truncated and the DAC output is sampled and quantized, the errors are periodic rather than random, so they fold back into the passband as discrete, repeatable spurs (aliases and phase-truncation lines). That is why DDS specs are dominated by a spurious-free dynamic range (SFDR) number rather than a noise floor figure.
Watch out Broadband noise is the usual limitation of analog PLL synthesizers and amplifier stages; DDS phase noise is actually very low, and its problem is the sharp discrete spurs instead.
DDS = Discrete Digital Spurs. Sampling and truncation errors repeat, so they land on specific frequencies, not spread as noise.