You need a microcontroller to drive the h bridge with pwm.......
The h bridge is designed to provide a digital output where it gets switched fully on or off. This mode of operation reduces losses across the semiconductors which would cause them to overheat or otherwise require a reduction in the overall power handling capability of the bridge.
For this reason you cannot apply an analog drive signal (sine or triangle) and expect to see an analog output,instead due to the switching action of the h-bridge you will get a square wave output.
To shape the ouput squarewave into a sinewave you use coils and capacitors to control the instant on/ off voltage of the square wave. This can also be done with the use of a transformer as the coil.
Further smoothing can also be achieved by using Pulse Width Modulation (PWM) of the drive signal applied to the H bridge. This rapidly switches the h bridge on and off so as to control average output voltage . PWM controls the rise and fall of the voltage for either the positive or negative half of the cycle. Directional control of the h bridge determines which half of the cycle is being output. Again the pwm pulses output from the h bridge are smoothe with coils and capacitors and or a transformer.
This technique is calls direct digital synthesis DDS
Here is an arduino tutorial
http://interface.khm.de/index.php/lab/experiments/arduino-dds-sinewave-generator/