[Radio Wrangler]

Jeremy has it right.

If the output of a DDS's DAC was a series of theoretically perfect impulses, it would give a flat output across the frequency range (filters allowing!) but that would be very difficult to arrange.

Instead, the output is a series of steps and the voltage is held for the time between steps. this is called a 'Zero-order hold' and is the cause of the (sine(x))/x roll-off which also includes a series of periodic notches. The same function also crops up in the frequency response of tape heads due to the the thickness of their gap.

Outside the theoretical world, practical people ran into trouble with DAC glitches on every clock edge because multiple bits changed at once and they did not all have equal settling times, so the steps occurred with disproportionate twangs which made a right muck of the plans for controlling the output spectrum. In the 1980s, Sony DACs were the ones to have for low glitch energy. DDS chips were coming on the market with digital outputs only.. add you own DAC.

David