Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

The impossibility of perfect audio stretching

Audience:

Tags: audiosignal-processing

This article explores the question of how to stretch audio waves without distorting their frequencies. It focuses on an example audio signal of two interfering sine waves, and aims to show that there is no single “perfect” way to stretch an audio signal: some form of distortion is inevitable. It briefly introduces/motivates modern audio stretching algorithms towards the end.



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6.35 Overall score*
17 Rank
9 Votes
8 Comments

Comments

7

I loved the idea, but it’s hard to read with how little text is shown on screen at once.

I would also suggest permuting the text: before getting into the formulas for sine waves, just (i) explain a little what the axes do, and let the user play with them to see for themselves (maybe start by constraining which dimension the dots can move) (ii) then doing your spiel on the problems with certain naive forms of time stretching (iii) then give the formulas.

5.8

I enjoyed the content and discussion surrounding the problem and the interactive visualizer was nice. It would be slightly better if moving the frequencies did not require a replay, but instead continuously updated. There’s also some sort of auto scrolling on the website that makes it slightly difficult to scroll.

6.4

Don’t like the layout. Too much empty/wasted space, hard to read the text. Put the interactive lower, so that the text can take more room, and keep the text fully black (not faded) to the bottom. Or put the interactive to one side, and the text in its own column.

4.9

Clear introduction to the challenges of stretching audio.

6

Really hard to read with the diagram covvering up more than half of the space.

7.5

Neatly done. My only gripe/nitpick is that the sticky scrolling makes it the text harder to read (since the text gets clipped by the wave diagram).

5

I’m giving a lot of points off here because the quality of the explanation doesn’t matter if you can’t read it. I’m on Firefox macOS and the audio box takes up almost 70% of my screen. The text doesn’t like to scroll past the headings, and it very often overflows since as mentioned the audio box is so large.

That being said, I was able to (eventually) read it by zooming way out, and here is some feedback on the actual content.

  • The audio box is actually very helpful to the explanation and definitely needs to be there, although as mentioned I would make it significantly smaller
  • The explanation itself is clear and I learned a lot of things I hadn’t known before (audio stretching is a lie?!)
6.4

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