Hello I am interested in smoothing out the sharp edges of a single rectangular wave centered at the origin. 

I am looking for a smooth function that looks almost exactly the same as the square wave except it is differentiable everywhere. 

I looked at Fourier Series but this creates a periodic function which I do not want. 
I want to create a rectangular wave of finite height and zero everywhere else. 

Ultimately, I want to plug this approximating function into NDSolve in attempt to get rid of "spiky" effects present in the solution of the wave equation. 

Thank You!