Described is an apparatus that includes a frequency source and a plurality of time domain direct digital synthesizers each having an input connected to an output of the frequency source and an output providing an output frequency signal. A particular time domain direct digital synthesizer includes a sigma-delta modulator that functions as a second order multi-stage noise shaping sigma-delta modulator. In one exemplary embodiment sigma-delta modulator outputs provide a unitary-weighted word used to switch certain unit capacitors that comprise part of a delay modulator to produce a time-varying delay having a time-averaged value that directly corresponds to a binary value appearing on a plurality of phase accumulator outputs.