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!
Fourier Visualizations
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Re: Fourier Visualizations
#12Earlier quoted context omitted.
> I am doubly upset at that teacher now. You shouldn't be. Wireless Technology is an advanced class for Electrical Engineering majors. Electrical Engineering majors would have gone through a class of Linear systems, where they would have learnt the intuition behind Fourier transforms as shown in OP's demo. I think the teacher might have done you a disservice by not mentioning the prerequisites, but thats the only thi…
> 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.
Re: Fourier Visualizations
#13Question: 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!
Re: Fourier Visualizations
#14Earlier 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.
In my case, I had few lecturers, who went completely bonkers, when they read anonymous questionaires, with the fact, that lectures were some blank copy paste of lecturer's notes -> blackboard -> students' notebooks. They could not admit that. I believe next year those lecturers were changed, though damage to our and older generations were done (badly delivered studies).
Re: Fourier Visualizations
#15Does it do anything? Not in Safari.
Re: Fourier Visualizations
#16In 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…
I have the exact same storry here. It was apparently evident to him, it's only years later when I wondered how MP3 compression worked that I connected WTF I learned at uni.
Never assume something is evident for everyone else.
Re: Fourier Visualizations
#17I 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 triangle inside a unit circle.
-Time dependent sinus function, sin(wt), can be represented using a uniform circular motion and y coordinate of position.
-Fourier says that you can represent (may be almost all) functions using sinus functions with proper frequencies and amplitudes. There is a way to find those coefficients using some mathematics: infinite or finite sums or integrals depending on application.
-Oh well, I have a wonderful idea, great analogy, listen: why not show Fourier transform/series using a circle on circle on circles, uniformly moving (constant speeds) particles and projections of their position to sideways as a function of time.
I don't think understanding its mathematical form is more complicated than understanding what a function is. It is already very simple, too much enforced simplification makes it complicated.
Re: Fourier Visualizations
#18Incidentally, this also shows why adding epicycles to your solar system model works.
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.
Re: Fourier Visualizations
#19In 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…
The way a teacher introduces the topic is extremely important. Shitty teachers perpetuate the myth that math is so hard. It's hard if the teacher either doesn't actually know what it is about, or has forgotten what it was like to be new to the topic.
I had similar classes in robotics (the lower-level kind: control theory, path planning, joint configurations, robot dynamics, inverse kinematics, stability), where we often had zero idea what was going on. The professor showed some slides dense with walls of text and badly typeset large equations, where we couldn't even keep track of what letter stood for what, the abstraction levels were mixed like spaghetti - sometimes talking about exact voltages, about mathematical tricks and shortcuts - but things weren't glued together with an overarching motivation.
So we learned stuff like Lyapunov-stability, the K-step ahead prediction, etc. but basically nobody had a clue what we were actually doing. And there was lots and lots of in-detail stuff.
This was in Hungary by the way. When I spent a semester in Germany and had a robotics course (slightly different focus), I thought it was so easy. There was a lot less material and we progressed much slower, but people actually followed what was happening. When you came out of a lecture, you could summarize in a few sentences what you've been doing. In my home university robotics class, we had no idea: we just saw a bunch of slides of incomprehensible math with no time to digest it.
When I see MIT lectures online, it also seems very "easy", in the sense that all the intuitions and motivations are laid out for you. I think this also has disadvantages. I can remember having many Heureka moments when disentangling the mess and finally putting puzzle pieces together, when learning from not so high-quality materials. I was proud about a lot of these "connections that I discovered", only to learn that some universities start with these high-level overviews and they don't count as exciting insight at elite universities, it's just part of the "boring, dry curriculum" as seen by students there.
Re: Fourier Visualizations
#20Earlier quoted context omitted.
> I am doubly upset at that teacher now. You shouldn't be. Wireless Technology is an advanced class for Electrical Engineering majors. Electrical Engineering majors would have gone through a class of Linear systems, where they would have learnt the intuition behind Fourier transforms as shown in OP's demo. I think the teacher might have done you a disservice by not mentioning the prerequisites, but thats the only thi…
> 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 in differential equations? If you didn't, that would have made the class double-tough.