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Fourier Visualizations

bgrawi.com

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Re: Fourier Visualizations

#21

Post by kbenson »

eru wrote: post #12
kbenson wrote: post #10

Earlier quoted context omitted.

> I think the teacher might have done you a disservice by not mentioning the prerequisites, but thats the only thing you can be upset about. It was offered as a double elective for CS and CEE, which meant it was supposed to be accessible to both majors (if admittedly harder for CS majors). I can accept the class being hard, I can't accept the first three hours of class time being spent copying notes of his math notes…

Have you tried speaking up about it? Teachers don't have magic powers of mind reading.

Well, it was close to 15 years ago now, so read "I'm doubly mad" as "when something makes me remember it, I feel sense of loss, both for what I could have learned if the situation was different, and how I've felt about it and myself over the years regarding it."

I'm mad about it, but in the weird way multiple years can change that into into something that's not quite the same as the word usually implies.

Re: Fourier Visualizations

#22

Post by kbenson »

ci5er wrote: post #20
kbenson wrote: post #10

Earlier quoted context omitted.

> I think the teacher might have done you a disservice by not mentioning the prerequisites, but thats the only thing you can be upset about. It was offered as a double elective for CS and CEE, which meant it was supposed to be accessible to both majors (if admittedly harder for CS majors). I can accept the class being hard, I can't accept the first three hours of class time being spent copying notes of his math notes…

That's very sad - I'm sorry that happened to you. It makes me curious about one point. It sounds as if the class you took covered what my engineering program called "Communication Theory". We were expected to have two terms of differential equations and one each of linear algebra and statistics under our belts as prerequisites. (I think. This was a long time ago...) Were you missing, at least, having at strong basis…

I had plenty of differential equations, but I never took linear algebra. I'm fairly certain it was introduced in one of the semesters of calculus, but IIRC there was a separate linear equations class offered. I never took statistics, but it always seemed like it was one of the more practical and useful math classes.

To be clear, my problem wasn't that there was a lot of math. My problem was that there was no context, and what we were copying off the board could easily have been copied from a book or pamphlet. I'm not sure what the practical reason is to spend multiple classes deriving one version of the FFT from another with zero context.

Re: Fourier Visualizations

#23

Post by ddv »

kbenson wrote: post #6

In college, I took a CS elective that was shared with the electrical engineering major. It was taught by a PHD student, and was 90 minutes twice a week. I believe it was something along the lines of wireless technology. The first day, the teacher walked in, wrote an equation (FFT) on the board, and spent the next 90 minutes manipulating it into different forms (from his in-hand notes), with no explanation of what or…

Along the same lines, I thought this article is really good at building some intuition about the Fourier transform:

http://betterexplained.com/articles/an-interactive-guide-to-...

Re: Fourier Visualizations

#24

Post by diger44 »

Hi, I am the creator of this visualization. I didn't know that it was posted last night, but I can answer any questions you have now. I've added a "Tips/things to try" modal to it. I don't know how many of you tried the audio portion of the visualization, but it's a cool and more unique part of the demo!

The github link is here: https://github.com/bgrawi/Fourier-Visualizations

Re: Fourier Visualizations

#25

Post by diger44 »

tempodox wrote: post #15

Does it do anything? Not in Safari.

Creator here, sorry about that! It's because Safari does not fully support WebAudio yet, and I can't really test it to see what's causing the issue. Use chrome for now to see the whole thing work.

Re: Fourier Visualizations

#26

Post by diger44 »

bbtn wrote: post #17

I don't know if this kind of visualizing Fourier transform is helpful to anyone doing/will do work using this idea, but it is not useful to me, and I don't think it is useful to anyone, apart from being somewhat interesting representation, in a way an illusion. Here is how I see this: -Sinus (and cosinus etc) is defined using a right triangle, unit length hypotenuse simplifies things, so they are shown on a right tri…

Hi, creator here,

I appreciate your feedback, my eventual goal of this site is to expand to concepts like directly using FFTs with arbitrary waves where your suggestion might be constructive, as yes circles on circles does make it seem more complicated than it is. One of the goals of this specific visualization was to demonstrate how fourier series relate to oscillators and sound, in which case a circle representing a frequency or set of tones added together made more sense.

For reference, I did not personally come up with this particular style of representing Fourier Series, I based it on this: https://commons.wikimedia.org/wiki/File:Fourier_series_squar... which is used on the main Wikipedia page about Fourier Series themselves.

Re: Fourier Visualizations

#28

Post by dolguldur »

alisey wrote: post #13
dolguldur wrote: post #11

Question: I came across some super-nice interactive textbook-style website which gently introduced the Fourier transform with many intuitive and interactive graphics. It was top-notch modern, with dynamic SVGs and looked excellent. This was about 6 months ago and I can't find the page anymore and I forgot to bookmark it. If this rings a bell, please share the link! Thanks!

https://jackschaedler.github.io/circles-sines-signals/

Awesome, that's exactly what I was looking for. Thanks!

Re: Fourier Visualizations

#30

Post by qubex »

bonoboTP wrote: post #18
qubex wrote: post #3

Earlier quoted context omitted.

I keep mentioning that the apparently surprising fact that geocentric models of the solar system allowed successful prediction of celestial events is due to the (accidental) approximation afforded by low-degree Fourier transformations, up to and including excessively-awed mumbling about what the Antikythera Mechanism implies about ancient greeks' knowledge of heliocentrism and gravitation.

Aside from approximating the elliptical orbits as circular, there is no further approximation in the epicycle geocentric model. It really is like that, it's not some low-degree approximation. Again, aside from the circularity instead of the ellipses.

You are correct. Thanks for pointing that out.
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