Single PWM input signal to H-Bridge DC/AC inverter
While not a direct answer to your question, you should look into the IRS2453. It is a self-oscillating full bridge driver with built in gate drive. You can set the switching frequency with just a resistor and cap. Pretty easy to use. Adjust frequency with a variable resistor or the like. 

Otherwise, if you want to use the RasPi, you can take a single GPIO and put that into a NOT gate and a buffer. The NOT output would go to one pair of FETs and the buffer to the other. I would suggest using gate drivers to speed up the turn on times in this case. This way requires 3 to 4 ICs instead of just 1.

I'd suggest the first option as the second will not have any dead time between switching and is therefore more likely to have shoot through issues. If "faster than 50 Hz" means 100Hz or something then you should be fine either way.

Just remember, if the voltage you're switching is higher than the voltage you're driving the top FETs with, you'll need a high side driver to actually get the top FETs to turn on. The IR2110/2113 does high and low side switching but you'll need 2 of them to do all 4 FETs.