I always had a very vague "throws away data that's not perceived" idea of how MP3 works. With the background from this I was able to really understand the wikipedia page and found this great Ars article from 2007 to cement my understanding.
If I wanted to collect things like this to teach my kids, where do I look? How do we gather amazing resources like this in one spot?
I particularly love that it focuses on one topic and nails it.
SmarterEveryDay published a video on this topic few weeks back: https://www.youtube.com/watch?v=ds0cmAV-Yek
Interestingly if you're talking about discrete time fourier transforms (which is what we usually deal with in computers with jpegs, mp3s, etc), then you can perfectly represent a signal with say, 1024 samples using exactly 1024 sine waves without worrying about that effect. It's only in the continuous time variant that you have to worry about things like the Gibbs phenomenon (which you do run into once you start translating to real world output)
(arguably the whole point of a tutorial like this is to do it without the maths)
One idea that would be cool to see is a repeat of the video where the number of ‘harmonics’ is clipped.
Eg, show the video with only the first 5 circle components. Then the first 10, the first 15, and so on.
Will see the drawing approach the final image, and get the idea the low-freq harmonics do the bulk of the work but high-freq ones give the small details to make the hand a hand.