3blue1brownBasics of Fourier Analysis | The Linear Algebra behind sound
What is sound? How can we represent it mathematically & in a computer? And how can we manipulate sound by changing its frequency content using Fourier analysis?
This videos gives an introduction into the linear algebra behind the Fourier theorem and motivates the underlying math by building a simple low-pass filter in Python (SageMath) to cut off high frequencies of a square wave signal.
We will discuss it in a continuous setting first (including the orthogonal decomposition theorem), then motivate the discrete setting (DFT) by analogy. This video is explicitly *not* about the Fast Fourier Transform (FFT).
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Comments
5
Interesting but quite a basic application of FFTs and filters...
6.9
It is a very nice video and the style looks really cool, however, the topic introduced has been covered many times. I still do think video is great, if it were about a topic i did not know about, i would love it.
4.6
The Video is great if you already are familiar with Fourier Analysis but if you have never heard of it, I fear that all the mathematical expressions will be very confusing. For example right at the start where the waves were added up, it would be better in my opinion not to show the complicated looking sum of the mathematical expressions and instead just graphs of sin waves with different frequencies on top of each other.
6.9
I really liked this new perspective on the Fourier Analysis. The video went into great depth and gave very deep insight into the Fourier Transform as an actual transform in the sense of algebra.
Especially mentionable is the difference to common approaches of the Fourier series (as eg in 3b1b), making the video score high on the scale of novelty.
The style of animations is well done, highlighting that Manim was not used (at least it didn't look like it)- a merit in my opinion, making a difference to other entries (Not that Manim was bad, but a development of own style needs to be respected).
Where I unfortunately couldn't grade the video as high was in the section "clarity". Oftentimes, we had a lot of text to read on the screen, which was hard to follow without pausing. On one hand, this allowed for mathematical strictness, on the other hand, full sentences might not always be the best choice. More visualisations could have helped to clarify this further (admittedly, this might be difficult to realize here).
I gave the video a well deserved overall rating of "better than most", because i really liked this interpretation of Fourier Analysis and felt like Ive learned something new today.
Thanks a lot to the author for their entry to SOME and I'd be looking forward to see another video of them in next years SOME!
7.1
Really high quality, only note would be that there is a lot of information in a 20 minute youtube video so requires some motivation to take it all in
4.8
How did you get from integrating a complex series to a series of sin? at 10:50? https://youtu.be/SB_8kS_kBMI?feature=shared&t=649
I guess the coefficients must cancel somehow. The square wave shown is odd, so a sin series works. I just forget how the exponentials combine to make sin without an extra i.
Maybe I would rate this as good quantity and could use more quality.
3.4
to vectoriel space oriented => heavy comments.
for me no interest.
6.7
You did a great job! I use this example in my Linear Algebra classes. My only recommendation is that a lot of what you do requires knowledge beyond LA (complex analysis, generalized inner-products to functions , etc) so my challenge is to try to approach the content with as little mathematical overhead as possible so that it is accessible to more people. You could completely skip the fourier analysis and jump right into DFT, and just use sines and cosine curves (not e^{2*pi*i*n/N}). That would make a lot more sense for an LA class.
9
Excellent motivation and explanation of a complicated and fascinating area of maths