Notes on DDS (Direct Digital Synthesis)

Direct Digital Synthesis is a technique that generates signals with exceptional resolution and reasonable levels of distortion.

As the attached picture shows, from 20,000 feet, the operation of a DDS system is deceptively simple. The contents of a counter (phase accumulator) are feed to a look-up table that sends information to a DAC. The table maps a phase value to a sinusoidal output. As the table moves from one location to the next the phase difference is always the same.  

In this model, if the counter has 2n states and the Table has 2n entries, the resultant DAC output will repeat every 2n clock pulses- setting an output frequency to Fout = Fin/2n. Notice that if the accumulator increases its step size from 1 to 2, the output will be loaded with the value from every other Table location. The phase/step doubles so the frequency doubles – the update rate stays constant, the phase change per pulse doubles, the frequency doubles, and the number of pulses/cycle halves.

Not only does changing the step size change the output frequency, it immediately changes the phase of the output.