A question on eliminating ringing on a pulse
The ringing is because the inductor and capacitor are acting as an underdamped resonant circuit. You can add more damping by placing a resistor in parallel with them both or a resistor in series with the inductor or capacitor. If you increase the value of series resistor (or decrease the parallel resistor) the ringing should start to subside but, you will never get a perfect rectangluar wave coming out when ringing is minimized.