The waveform generator includes a free-running ring oscillator, and algebra module, a switching module and an output module. The free-running ring oscillator includes a plurality of delay elements connected in a loop and a plurality of taps disposed between the delay elements, with each tap providing a uniquely phased, oscillating transition signal. The algebra module generates an output signal indicating a first rising edge of the arbitrary waveform in response to an input signal. The switching module includes a switch input port in electrical communication with the algebra data output port, a plurality of switch tap input ports in electrical communication with the free-running ring oscillator taps and switch output port. At the switch output port, the switch module provides a first transition signal selected from one of the plurality of free running ring oscillator taps in response to the signal indicative of a first rising edge received at the switch input port. The output module has at transition signal input port in electrical communication with the switch output port, a window input port in electrical communication with the algebra data output port and a waveform output port in electrical communication with the clock input port of the algebra module. The output module creates an arbitrary waveform at the waveform output port in response to the first transition signal received at the transmition signal input port of the output module and the signal of a first rising edge received at the window input port.