analog - Best circuit to get an array of signals with the same frequency and edge-synchronizable to a reference but individually controllable duty-cycles?

I am looking to build a circuit to control five different FET drivers individually. The input signal would be a single shot from a function generator, which should produce five output signals, with the same frequency and phase but the duty cycles need to be individually controllable. Basically, I am trying to replace five function generators (synchronized to the same clock) with one single function generator and a circuit board due to limited resources. The outputs need to have only two levels i.e pulse wave

EDIT: Olin's suggestion (using a MCU) or a FPGA seem to be the best options but any analog alternatives are much appreciated. Thanks :)