XKCD and Fourier

And now it’s all this I just said what I said and it was wrong Or was taken wrong Previous post XKCD and Fourier October 29, 2026 at 8:45 PM by Dr. Drang

现在这一切就是我刚才所说的，我说了我所说的，但那是错的，或者被误解了。上一篇博文：XKCD 与傅里叶，2026 年 10 月 29 日晚上 8:45，作者：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.

如果你做过函数的傅里叶级数近似，你对今天的 XKCD 漫画会有三种反应：首先，当然是会心一笑。接着你会“等一下”，因为你意识到吉布斯现象并不会随着你在傅里叶展开中增加项数而减小；它只是集中在拐角处：那种振铃效应永远不会消失。

Here, for example, is the plot for ∑k=1,3,5,…994kπsin⁡(kπx) Finally, you realized that thinking like this ruins the joke.

例如，这里是 ∑k=1,3,5,…994kπsin⁡(kπx) 的绘图。最后，你意识到这样思考会破坏笑话的趣味性。

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