> I have a PhD in machine learning

Do not take that badly, but have you learned actual statistics and the mathematics behind them? Or like the few ML people I've met, do you just use and tweak models?

The part you quoted is extremely clear to me, even without actual pictures: it just means the approximation you use departs from the actual function, tell you where and why.

I can infer there will be an artifact, and how I could try to minimize it.

> Sometimes Gibbs phenomenon leads to an artefact (called Gibbs artefact) that we see in our images of the heart when we are doing a certain sequence called stress perfusion cardiac MRI.

You describe where and when it happens in practice, not why it exists in theory.

Different needs for different people!