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> I tried to do it with a cap but somehow the comparator starts to violently oscillate when I assemble the circuit.It should not. May be you place capacitor in wrong place? Please, provide us a schematic.
You need a resistor connected between the capacitor and the comparator input, weakly pulling this circuit node to some well defined voltage within the valid input range of the chip and draining bias current of the input pin away from there.Look up "highpass RC filter".
Bias should be at least 0.5V (or more). Now your input pulse generates negative voltage on comparator pin.
> where does this 0.5V come fromIt's your input pulse amplitude (from OP)
Note that signals much greater than 3.0 V will result increasedinput currents and may cause the device to operate more slowly.
> however, the same effect of the input signal getting distorted as in the 'biased' version.Check the voltage on comparator input pin. It should not exceed 3.0V
Stupid question: do you have 100nF between the comparator's VCC and GND pins?