Phase and amplitude disturbances in direct digital frequency synthesizers

The problem of the spurious phase and amplitude disturbances in direct digital frequency synthesizers (DDFS) at the digital-to-analog (DAC) output is discussed. Such a situation is met when a commercial synthesizer lacks the output filter (e.g., the whole set of the so-called Number-controlled oscillators) or is supplied, for some reasons, with a lower clock frequency. Authors of recent books on DDFS mention this phenomenon but lack to provide the explanation. The problem is dealt with in detail in this paper.