What information is contained in the lookup table of a direct digital synthesizer (DDS)?
Why A DDS works by stepping a phase accumulator at the clock rate; the accumulator's output is a phase angle, and the lookup table (usually a ROM holding one cycle of a sine wave) converts each phase value into the corresponding amplitude sample. Those amplitude numbers go to a DAC, which reconstructs the waveform, and a low-pass filter smooths the steps. So the table is simply a stored map of phase angle to waveform amplitude.
Watch out The choices about phase relationships describe a phase-locked loop, where a phase detector compares a reference with a VCO; a DDS has no such feedback loop, and its phase information lives in the accumulator, not the table.
DDS chain: phase accumulator makes the angle, lookup table supplies the amplitude, DAC makes the wave.