The glorious Fourier Transform. Finally. Thanks 3Blue1Brown!

[Zucca]

After picking up my jaw on the floor here we go. Kind of pissed off that it took me almost 15 years to finally understand the Fourier Transform in this simple way...

Outstanding, pure math porno stuff....

[janoc]

That's a pretty good explanation, in fact! Excellent video tip, thanks! 

[rbm]

I'm with you, zucca!  I love 3Blue1Brown videos alot.  I watched his Calculus video series and, like you, was amazed how little I had understood about calculus for 20 years, all of which suddenly became crystal clear in a couple hours watching this series.  The same revelation occured for me with this video about Fourier Series.

[kony]

Only thing I lacked on this visual explanation is the remark about the sinc convolution of specral peaks due to finite rectangular sampling window, but it got called "almost-FT", so fair enough.

[Zucca]

sinc convolution of specral peaks due to finite rectangular sampling window

  that´s why if the time span increase you see the peak assuming more the dirac impulse shape in the f domain. You see it very well in the video.

[janoc]

Coincidentally, not so long time ago I was studying some DSP basics and Fourier transform was part of it. I think I have understood fairly well how it works and how do you calculate it using convolution, but this video really made the things "click".

In the textbooks nobody bothers with explaining the basic stuff like how did they figure out that sum/integral formula. The explanations usually put the formula down as a fact and then fiddle around with it trying to explain how to use it but rarely provide any sort of intuition about what it really represents. Which kinda sucks and makes the understanding a lot more difficult.

[rx8pilot]

I watched it yesterday.... excellent presentation. Excellent channel.

The guy focuses on understanding concepts as opposed to memorization.

Short and misplld from my mobile......

[ataradov]

Have not watched this one yet, but on topic of FT, there is a series on a mechanical machine that does direct and inverse transforms.

Here is the first video in the series:

[Bud]

I do not share everyone's excitement about the video. I do not find it useful. Good luck thinking about center of gravity next time you work on your DSP routine or editing audio.

[kony]

Sure, just follow the textbook provided recipie without any intuitive understanding of what the transform is or does. It gets the job done. Sometimes.

The point of those videos is not to provide straight forward practical solving algo for subset of problems, but rather aid to gain intuitive undestanding of the operating principle, which is IMHO way more usefull if it locks into your knolwedge framework. Once you have this intuitive overview of what it is and does, you can easily handle the formal notation and accept the implications it has. Note I am not saying it should fit into such framework without validation of correctness and hunting for corner cases on which it falls apart. But it is still orders of magnitude more usefull initial point than reading dry and even dryer formal proof, or listening to egoistic estrade by mostly clueless proffesor which above all enjoys his pureness of formal expression, nothing else allowed. (Yes, I know good math teachers do exist, but they are super rare).

I have met plenty of A+ students passing each exam first try with ease, and it was very entertaining to see how they were failing to apply their supposed knowledge about the topics on similar, but not exactly matching problems to those they prepared for during the mesmorisation. Photographic memory and wee bit of logical thinking can get you very far here.

I recommend reading A Mathematician’s Lament by Paul Lockhart - the issue he conveys covers the entire span of our educational system from elementary to universities.

[ataradov]

I do not share everyone's excitement about the video. I do not find it useful. Good luck thinking about center of gravity next time you work on your DSP routine or editing audio.

After watching the video, I agree. It took quite a bit of effort to process, even knowing how FT actually works. I can't imagine this being helpful to people that know nothing about it.

Nice visuals though.

I feel like just writing down the first few terms and messing with coefficients in Matlab will give better understanding of the subject.

[@rt]

Bravo! I did a video animation square wave approximation... It was nice, but just got my ass kicked

[Zucca]

Some EE don't like math...

[janoc]

I do not share everyone's excitement about the video. I do not find it useful. Good luck thinking about center of gravity next time you work on your DSP routine or editing audio.

Center of gravity is nothing else but an average ... And it is actually explained in the video too. 

And if you know how the transform is calculated, you will fairly quickly realize that it isn't anything else but a convolution. However, the geometric intuition is easier to comprehend than understanding when does convolution give you a maximum peak.