In an RF source, a digital waveform synthesizer comprises a computational module to synchronously determine a desired periodic function, f(θ), within a first bandwidth portion, to which computational result there is combined an injected digital noise increment in an adjustable range of bounded amplitude, specifically selected to average over discontinuities of the DAC transfer characteristic. The combination is effected after passing the injected noise increment through a programmable digital filter forming a composite tuning word having a total bandwidth at a selected Nyquist zone and thence passing the composite tuning word through a truncation component to a DAC. The programmable digital filter is constructed to displace the spectral distribution of the injected noise increment to a portion of the total bandwidth remote from the first bandwidth portion.