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I'm on my fourth year of Electrical Engineering, and the frequency spectrum has always been an abstract concept that I could never truly wrap my head around. Explaining it as a density of frequencies that, when inputed to sine functions, form a given function was a huge a-ha moment for me, thank you so much!
This video literally made me cry. I wish our current educational institutions taught math with the same beauty that you, Euclid, and other great thinkers were able to pull out of the logic of the numbers. Seriously great job!
I think this comment sums up why in 5, 10, 20 years, as the quality of free and inexpensive online education continues to improve, traditional brick-and-mortar education will lose its value significantly. If you can learn everything you would from obtaining a degree online at a fraction of the cost of attending a university, and more importantly can prove to employers that you know your stuff, how much will that degree be worth? From the employer's perspective it shouldn't matter as long as you can demonstrate your ability. Obviously there are exceptions (Doctors, for example), but AI, robotics and 3D printing could make short work of human doctors in our lifetimes - maybe we'll just train people with great bedside manners to supervise.
The moment I saw the sine wave in 3D my mind was blown it was like my brain had unlocked a level it didn't know existed, seriously huge props to yiu my dude you're genuinely making people passionate about math
For a sec I was fully expecting that the rest of the video from that point would be a count upwards to the end, with 0 discussion of the fourier transform lol
I've watched a few of these vids back to back now. I did my engineering apprenticeship back in '97 - '01. I could perform the math, answer the questions, but never really visualized what was occurring until now. A set of really great resources, showing what are beautifully simple ideas to grasp when taught in the right way.
HAHAHHAHA Aeronautical engineer here. Same for me. In my case i wasnt that fortunate, but its amazing to know were things come from. Gives you a whole nother level of understanding
I recently created a Patreon account for people who want to help support my channel. The link is on my RU-vid home page. Also, in case, you have not already seen them, I uploaded several other videos recently. As always, for each video that you like, you can help more people find it in their RU-vid search engine by clicking the like button, and writing a comment. Lots more videos are coming very soon. Thanks.
+Anders Feder, Patreon has the ability to accept payments through PayPal. As for donating per video, I wasn't sure whether to accept donations per video or per month, as both are options I could have selected in Patreon, but I decided on doing it per month as I thought that this would be less confusing to people. I am not sure I understand the last part of your sentence, but if you find that you can't create a Patreon account, please let me know. In any case, I really appreciate your interest in donating and in helping to support my videos.
Eugene Khutoryansky I meant to say that I am unlikely to go through the Patreon registration process, whereas I have already PayPal set up and ready to pay at the tap of a button.
This is the most beautiful thing I've ever seen on RU-vid, the only visual I've found thus far that truly captures the magic of sine functions. Thank you
Physics Videos by Eugene Khutoryansky You should be super proud of yourself for imparting knowledge in such a lucid way, that too as non profit service.
I just found your videos, and they are amazing. You take the most advanced concepts and visualize them in such understandable and intuitive ways... well, as intuitive as you can make these concepts to us humans. Every one of your videos I've watched so far has helped me connect things in a way I had not before.
hahaha I love how most of the engineers and people that use this kind of things are like "Damn. I thought i knew what i was doing but i actually had no idea."
What else can we say?... this is such a piece of art, taking into account the effort we had to have to abstract such math back in engineering college... great job!
This is genius....plus you managed to overlay the right kind of music that constructively interferes with learning. Good work, I love your videos, being a highly audio-visual learner.
@EugeneKhutoryansky really good :) I'm not sure why, but visualising a mathematical concept seems to come much less naturally than something abstract, which is a bit odd. It took me back to my apprenticeship, watching the oscilloscope as i plugged in / unplugged various modules, watching the waveform change, clipping, filters etc. I understood an 2 inputs give a certain output, but just couldn't visualise the process.
This is a work of art ! I am a big fan of simplicity and visualization. I think the biggest service to humanity is when you open someone's eyes in awe by simple explanation of a complex subject with brilliant visuals. You have done exactly that Dr.Khutoryansky. Please keep up the good work. May I ask which software did you use to produce these amazing 3D animations?:
As a student of electrical engineering I had to struggle visualizing Fourier series, but to visualize your beautiful representation was refreshing and spellbinding. Thank you. How easily all shapes of wave forms can be constructed from sine waves.
I am very fortunate to have these videos as I begin my engineering degree. I will always refer classmates who are struggling to understand concepts like the Fourier transform to this channel!
Seeing what's going on in equations (such as sums of sine waves) is the same as the difference between looking at a musical score, and hearing the music. The music is the point - the score, just a way of capturing change in a static form (as equations are, to what you show here). Thanks! You're a fantastic resource for anyone wanting to learn this stuff. Me, for instance!
Great analogy...yes, it's the difference between understanding the notation of something and understanding the thing itself at a deep level... I sometimes think the language of mathSSS obscures more than it reveals :D eg imagine trying to describe the colour red to a blind person. You can use the most complex language in the world but it wouldn't work. I think there needs to be some way of describing motion of things separate from language and maths, maybe. What that is I don't know, but it would be pretty handy!
Holy crap, theses videos are so good! that "ahh" moment mentioned below, I had the same thing, seeing the video from 00:00 to 00:40 Now I understand how cosin/sin wave functions relate to circular motion. simply amazing thank you
Thank you for helping me visualise mathematics.. I was searching for something like this since my childhood.. I knew maths is beautiful but was not able to visualise it.. This video made my day.. Heartfelt thanks to the creator of these videos.
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After watching this video I learned a ton. Even though I studied this in my four years of engineering I didn't realized this is what happening. THANKS a ton
Wow, this is the most relaxing thing I've seen on RU-vid! So beautifully made with the music in the background ! The ending is amazing, too :) You think you're searching a rather dry and boring topic on RU-vid and than you find art like this :-D
I would like to thank you so much for all these beautiful videos in your channel. Actually, these videos show how physics and science are beautiful and enjoyable not complicated and boring like what exists in books and theoretical resources.
I show my grade 7 son this video and give him a little bit explanation, he instantly know and master the Fourier things, polar system, vector concept and imagine number including Euler formula. This video just game changer.
I always enjoy the clever ways you explain concepts. In this one, I was expecting an explanation of how to perform Fourier decomposition and the FFT. I hope you'll consider that topic for a future video.
I'm making this comment in 2019, also, although I comprehend the language spoken I appreciate the narrator's explanations. Such a great post for those of us who want to learn more
It's so beautiful explaination. Many of my coworkers were some of the best engieers and scientists. But none of them could explain the Fourier Transformer in such simple and clarity manner of yours. Thank you. Most engineers know that complex wave forms were the sum of sine waves. But it's visually difficult for me to grasp the concept.
I only know the formula defining Fourier transform and Laplace transform and used them for analyzing linear systems. I loved how Laplace transform method simplified the way for solving linear 2nd order ODE which was commonly found in RLC circuits. Found their application also in Control Engineering both in conventional and modern methods using state space. But now, having been working as software developer for years, I forget many things about them, except the formulas. :)
The sphere and line model REALLY makes it make more sense to me than the typical circles connected at midpoints that you see in videos. It lets me see that its essentially adding a vector instead of just being random. I could have comd to thst intuition eventually but this helped a lot.
Beautiful. Really enjoyed it. I hope this will help young students want to pursue a deeper understanding of signal processing. The more general form of this idea introduces imaginary numbers (i.e., complex math) creating a very powerful tool. The Fourier transform is just one, among other types of transform, that allow us to manipulate the way we see mathematical functions. Just like logarithms allows us to do multiplication by adding and then transforming back to get the desired product, Fourier transforms allow us to study the characteristics of signals in time by looking at the signal in the frequency domain.
ProCactus imaginary numbers are numbers that not represent real things. You play with them all of the time in basic algebra, where the number doesn't correspond to any real thing. In the classical equasion y=mx^2+b. You only input numbers as you need to solve for various values of one type or another, but these numbers do not represent a real thing.
Mr. Eugene, your videos are extremely good. You have incorporated visual presentations using technology at a terrific degree. I entered college and studied electronics engineering on my 1st year. Now that I'm at 4th year, I seriously recommend your channel to the freshmen and future engineers.
Excelente Video, obrigado por ele, sou Estudante de Engenharia de Controle e Automação e este vídeo me ajudou bastante a entender o comportamento da frequencia no dominio do tempo.
This is one of the most beautiful videos I have seen! I cannot even imagine the minds of the scientists who discover these maths hundreds of years ago before modern technologies 🤯
beautiful - even the orchestral swells are perfectly timed to the revelations of the changes in perspective. You've given us all at the next evolution of learning maths
I really liked this video, especially the use of a multi-hinged arm to draw waveforms. It's very well done. I would, however, like to propose one correction. If a wave's amplitude were exactly zero, then its frequency must also be zero, because a wave with an amplitude of zero would be a flat line and not a wave. I think you intended to say, "infinitesimally small," instead of, "infinitely small." Real waves must have non-zero amplitudes and non-zero frequencies. Other than that one caveat, this video is great and I would recommend it to anyone who wants to see how waves stack on each other. Thanks for making these videos.
i thought the same about the sheet of paper example. The papers have a Volume, infinitesimally small however NOT 0. Nevertheless all theses videos are probably the best way to learn about advanced math and physic concepts.
THANK YOU!!!! I'm loving the more math heavy videos lately! You keep proving yourself as one of my favorite youtubers of all time! By the way, my family is from Odessa! Where in Russia are you from?
+the5chronicles, I was born in Kiev, but I moved to the United States when I was four years old. And thanks for the compliment on my videos. I am glad you like them.
That's the beauty of the visual approach .... you SEE the transform emerge by the simple shifts of perspective. The transform emerges from recognizing that a combination of sin waves of various frequency , amplitude and phase can be summed to emerge over sample time a particular output wave form ...this is exactly what the transform does...the video doesn't actually provide the equation but one should be able to see how the terms of it emerge from simple visual examination of this video...which is what makes it so awesome. If I'd had this video as a guide when I was learning the FT back in the mid 90's as an undergrad it would have cemented the mental imagery I was creating to try and understand it myself.
it is like "your are in the jungle and complain about trees which dont let you see the jungle!!!". This whole thing is fourier transform! You better have an idea about that then watch this wonderful video.
FYI,, fourier representation of any signal is a way in which signal can be represented as sum of orthogonal signals(complex exponential signals which is a sine wave by a simple formula) ....
I am an electrical engineer here in Brazil. Congratulations on this graphic animation where we can clearly see the result of the sum of the different harmonics of the Fourier series
