Source is the square generator. This signal go through the high pass filter. When you pass a square wave through this filter type you get two tiny pulses on the other side (derivation of input). One positive and one negative.
This pulses attack a NPN and PNP circuit, so you can get two positive pulses.
Now this pulses trigger a 555 that conform the output pulse.
At this time you have double frequency.
You can control duty cicle output changing 555 capacitor.
Violet: input f (t)
Green: derived input
Orange: conformed signal
Red: output 2f (t)