I would like to synchronize a pulse train signal with a sinusoidal voltage signal on an oscilloscope. The voltage signal cannot be delayed or otherwise manipulated. The two signals somehow need to be synchronized, but at the same time I need to be able to manually adjust the delay of the pulse train so that the rising edge is matched to some specific point in the voltage signal's cycle. Also, I need to be able to adjust the width of the pulse down to a few microseconds or less. Finally, I need three cases of operation: first, one pulse of the pulse train for every positive half-cycle of the voltage signal, second, one pulse of the pulse train for every negative half-cycle of the voltage signal, and third, one pulse of the pulse train for every positive and negative half-cycle of the voltage signal (two pulses per complete cycle or period).