A low-power digital frequency synthesizer combining direct digital frequency synthesis techniques with serrodyne frequency translation principles to produce a wideband frequency response with high spectral purity. A conventional direct digital synthesizer is used to generate a high-resolution analog carrier signal from a low-speed digital clock signal. The carrier signal is phase modulated by a low-resolution signal generated from a high-speed digital clock signal. The modularity signal is a higher frequency signal than the carrier signal. The phase modulation is accomplished by exact decoded attenuators. The spectral purity of the resulting high-resolution output signal is unobtainable by conventional direct digital synthesizers, while providing significant power savings.