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An Interactive Introduction to Fourier Transforms

by a1k0n on 1/11/19, 12:30 AM with 22 comments

• by agurk on 1/11/19, 1:16 PM

  This is great as it doesn't just explain the basics, it also shows how they are used in MP3 and JPEG files.

  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[0] article from 2007 to cement my understanding.

  [0] https://arstechnica.com/features/2007/10/the-audiofile-under...

• by Waterluvian on 1/11/19, 1:16 PM

  This is incredible.

  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.

• by SlowRobotAhead on 1/11/19, 6:29 AM

  Wow. This is by far, hands down, the best way I have ever seen this explained. Just excellently done.

• by unao on 1/11/19, 6:38 AM

  Very impressive end enlightening indeed.

  SmarterEveryDay published a video on this topic few weeks back: https://www.youtube.com/watch?v=ds0cmAV-Yek

• by sbergjohansen on 1/11/19, 10:50 AM

  At the time of writing the Gibbs phenomenon -- the overshoot occurring at discontinuities of a square wave, which does not go away no matter how many harmonics are included (see https://en.wikipedia.org/wiki/Gibbs_phenomenon) -- is not correctly represented in these visualisations, implying that important aspects of the underlying maths are obscured. In my opinion this limits the didactic value of an otherwise impressive presentation.

• by jamesbrownjr on 1/11/19, 10:55 AM

  Slightly unrelated, here's a beautiful mathematical approach to the discrete fourier transform with evaluating a polynomial at the nth root of unity in the complex numbers:

  https://ocw.mit.edu/courses/electrical-engineering-and-compu...

• by jeffwass on 1/11/19, 4:59 PM

  Very cool.

  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.

• by travisgriggs on 1/11/19, 3:53 PM

  This is really cool. I especially like the rotating circles visualization. Another video that helped me finally "get" Fouriers is the 3Blue1Brown video:

  https://www.youtube.com/watch?v=spUNpyF58BY

• by ryandvm on 1/11/19, 1:40 PM

  Really fantastic work. Best interactive write-up I've seen of a technical topic in a long time.

• by jacobolus on 1/11/19, 9:12 AM

  In the animation at the top, should use a different color for the circles vs. the hand/pen.

• by whytaka on 1/11/19, 1:53 PM

  That was the most impressive opening demonstration. My eyes popped out of my skull.

• by FrankDixon on 1/11/19, 10:23 AM

  Beautiful! How long did it take to make this blog post?

• by zero_kool on 1/11/19, 4:50 PM

  Amazing work! Thank you :)

• by fdsak on 1/11/19, 10:48 AM

  Epic ...thanks