An animated introduction to the Fourier Transform [video]
1–10 of 33 posts
Re: An animated introduction to the Fourier Transform [video]
#2I think it's much easier and more direct to visualize the time-domain as superposition of helical components and the transform as an exploration of what happens when you twist the "cylinder" with varying "intensities". You avoid the vague center-of-mass spike depicted here and start from the get-go with the terms of the transform.
Re: An animated introduction to the Fourier Transform [video]
#3I’ll just leave this here
http://tomlr.free.fr/Math%E9matiques/Math%20Complete/Analysi...
Mathematics of the discrete Fourier Transform by Julius O. Smith. (O stands for Orange I hope)
Re: An animated introduction to the Fourier Transform [video]
#4Source code of the video: https://github.com/3b1b/manim/blob/master/active_projects/fo...
Re: An animated introduction to the Fourier Transform [video]
#5I think it's much easier and more direct to visualize the time-domain as superposition of helical components and the transform as an exploration of what happens when you twist the "cylinder" with varying "intensities". You avoid the vague center-of-mass spike depicted here and start from the get-go with the terms of the transform.
Perhaps you can explain what you mean by “exploration of what happens” and “terms of the transformation”? That’s pretty vague as a description of a visualization.
Maybe you’re talking about a visualizing a discrete Fourier transform?
Re: An animated introduction to the Fourier Transform [video]
#63blue1brown’s videos are excellent. They build intuition in a calm and friendly way with an appropriate amount of useful animation. This is how we make mathematics accessible.
I’m currently considering moving back into academia and there are a lot of topics in my field that I know students often struggle with that would be greatly helped by some simple animations. Fortunately I’m pretty competent with blender and I relish the idea of developing something worthwhile.
Re: An animated introduction to the Fourier Transform [video]
#7I think it's much easier and more direct to visualize the time-domain as superposition of helical components and the transform as an exploration of what happens when you twist the "cylinder" with varying "intensities". You avoid the vague center-of-mass spike depicted here and start from the get-go with the terms of the transform.
Perhaps you can explain what you mean by “exploration of what happens” and “terms of the transformation”? That’s pretty vague as a description of a visualization. Maybe you’re talking about a visualizing a discrete Fourier transform?
Yep, it's vague, sorry, I'll need to try my hand at a video.
Re: An animated introduction to the Fourier Transform [video]
#8This one is related and (I think) quite good:
Re: An animated introduction to the Fourier Transform [video]
#9He touches on it - but I’d love to see an intuitive explanation of why the response of each frequency to the input function is linearly independent. i.e the fact that Fourier transform of the sum is equal to the sum of the Fourier transforms. This is “why it works” - it’s what makes the frequency space an orthonormal basis - but it’s never been intuitively obvious to
me. Otherwise, there would be more than one way of decomposing a function into a superposition. e.g. what would be useful is to give an example of a set of functions which are not linearly independent.
Re: An animated introduction to the Fourier Transform [video]
#10I’ll just leave this here http://tomlr.free.fr/Math%E9matiques/Math%20Complete/Analysi... Mathematics of the discrete Fourier Transform by Julius O. Smith. (O stands for Orange I hope)
Poking around the web turns up https://amzn.com/097456074X/ https://ccrma.stanford.edu/~jos/pubs.html