XKCD and Fourier
October 29, 2026 at 8:45 PM by Dr. Drang
If you’ve done Fourier series approximations of functions, you had three reactions to today’s XKCD comic:
First, of course, was a smile of recognition. Then came a “wait a minute” as you realized that the Gibbs phenomenon doesn’t get smaller as you add more terms to the Fourier expansion; it just concentrates itself at the corners:
That ringing never goes away. Here, for example, is the plot for
Finally, you realized that thinking like this ruins the joke.