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.