A waveform generator for generating a smooth version of an original waveform which contains abrupt transitions, includes a phase accumulator incremented at successive sampling times to produce an output representative of the phase of the original waveform, a phase scaler arranged to convert the residual contents of the accumulator following a transition from phase to time, computing means responsive to the time to calculate a number of samples along a smooth transition, each offset by that time from the sampling times, and a sequencer to replace the otherwise abrupt transition with the sequence of samples from the computed smooth transition.