square wave with Gibbs phenomenon

I'm trying to create a square wave that accounts for the Gibbs phenomenon (the overshoot that occurs when a square wave changes direction). Specifically, I want to add overshoot at just the leading edge of a rise or fall.

Square waves are easy - manually or via function 'square'. I can also do the Gibbs phenomenon separately as an abbreviated summation of the Fourier Series. Where I'm stuck is combining the two. Maybe its simple, but I can't quite get it.

I'm not really asking for code (but I'll take it!), just a pointer in the right direction...

For more on Gibbs phenomenon:

Thanks!