Vary the length of square waveform
The most steightforward decision is to use this spike to trigger interrupt in Arduino. The interrupt procedure starts one of the counters and sets 1 at one of the pins. After N milliseconds by counter or by inner timer the Arduino outputs 0 to the same pin, so you will have needed length of the positive pulse. This will work while pulse length will be less then time between successive spikes. Do not forget to make standard spike amplitude enough to start interrupt, but not too big not to damage Arduino. Of course you can work without interrupts, just testing the input in main cycle, but it will be less presise. You will need a decision, how to conveniently control the pulse length by some tool. It can be infrared pult or some other tool and you must see the set time value, so you will need to use some indicator. May be LCD  1602 keypad shield will be enough for this.