Detect button/signal on for a certain time period
If the signal were passed through an RC low pass filter you would get a step response like this: -



You could set a voltage threshold at about 63% of full charge and use an op-amp as a comparator to produce a delayed output that went low to high after 1 second.

However, if the signal fell back to zero before exceeding the 63% level you would need to reset the capacitor charge to zero. This can be done with a diode across the resistor: -



The diode rapidly discharges the capacitor so that the charging RC time constant is reset for the next positive going input. There are more sophisticated methods that involve an inverter driving a MOSFET that discharges the capacitor but how far do you need to go?

You could also latch the event using a D type flip flop but again, how far do you need to go?