A method and apparatus for reducing spurious output noise in digital frequency synthesizers that employ a sine amplitude converter (16) connected to a Digital-to-Analog converter (18) for generating an analog waveform from sine amplitude data. The method comprises the steps of adding random or pseudorandom numbers which are scaled to have a predetermined magnitude to the sine amplitude data and transferring a resulting addend to the Digital-to-Analog converter (18). The apparatus comprises a summation circuit (22) connected between an output of the sine function converter (18) and an input of the digital-to-analog converter and connected to a random or pseudorandom number generator (24) at a second input. A scale element (26) adjusts the pseudorandom number magnitude to provide numbers having values in the range +/- 1/2 times a minimum quantization step or at least significant bit of the Digital-to-Analog converter (18) resolution where n is greater than or equal to 1.