Driving high and low inputs of a MOSFET driver with a single PWM signal
The reason why the drivers have two signals for the high-side and low-side MOSFETS (or other power switches) is because usually you want to first switch both sides OFF for a short period of time and then to switch the needed MOSFET ON.

Usually, the switching OFF is slower than switching ON. This way if you switch the input signals in the same time, there will be short period when both transistors will be open and the power source will be shorted.

In result, the power switches will dissipate big amount of power/heat and the efficiency of the circuit will be very low (well, or both switches will be burnt).

For low power schematics, where the switching goes faster and the resistance of the switches is higher, such "shortcuts" are not dangerous, but for high power (above several watts) such behavior is not acceptable.

So, you need to form two pulses, where the positive edge of every pulse will be little delayer in order to provide a gap, where both signals are 0.