Analyse the "Gibbs Phenomenon" from Image Data

Slightly related to my previous post regarding the ringing artifact in compressed images, I have a question regarding the Gibb's Phenomenon, and am wondering if anyone has any experience with it. I would like to show that compressed images exhibit artifacts of this phenomenon (overshoot/undershoot). Wikipedia ( http://en.wikipedia.org/wiki/Gibbs_phenomenon#Description) says that the Gibbs Phenomenon would force the fourier series to "exceed the height π/4 of the square wave by approx. 9%". - Can anybody tell me how can I model this from image data?

Ideally, it would be great to show the sine wave extracted from the image against an ideal (square) sine wave...