Fourier series

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Im intending to do some code in matlab to show an application of the Fourier series, I was thinking of the synthesis equation, or to show the Fourier spectrum of an image ( this is the transform, not the series I know).
But is like tha cat says, this is trite, so, isnt any other thing to be a bit more "eye candy"?
I try to show it to a linear algebra group.