Herzliche Dank Herr Professor!

Thanks Prof Kutz; I have really enjoyed your lecture series. A quick terminology comment: A "notch" filter is not a sharp-cutoff filter, but a band-stop filter, which may in fact be smooth.

in the coffee cup picture example, having the fft plot next to the picture may be doing a disservice to the explanation, or even using the red/yellow color to plot the points as there is no spatial (x,y) correspondance between the two two diagrams, the jpeg is really a linear array of values which after fft can be represented by the x,y log plot of the fft.