Electronic – Amplify Square Wave with Simple Mofset Circuit

The circuit you're using is able to drive the cable very quickly to the low level, but only pulls up slowly to the high level because R1 limits the current available to charge up the capacitance of the cable. The maximum current you're going to be sourcing into your cable is about 3.3 mA.

One solution is, instead of buffering with the Q1/R1 combination, use a buffer/driver IC such as SN74LVC1G126. This can supply up to 32 mA current either sourcing or sinking. You'll have to work out from your cable length and capacitance per foot whether that will give you adequate edge speeds for your application.

user2943160's answer is essentially correct, but not perfect. As he states, there will be a glitch (runt pulse) produced when a pulse which will be swallowed comes along. In this case when the input goes high, the FF output persists high for the propagation delay of the FF, and this will produce a pulse. Likewise, the next pulse which comes along will be shortened by the FF propagation delay.

There are two ways to deal with this. Assuming the FF has a propagation delay of two inverters,

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will work, but it does have the possible drawback that it requires that the FF propagation delay be accurately known. If this is not the case, a more general approach is to operate the FF on the falling edge of the pulse.

^{simulate this circuit}