Convolution and the Fourier Series

How the Fourier Transform Works, Lecture 6 | Convolution and the Fourier Series

What is Convolution? What does it have to do with the Fourier Transform? Have you ever wondered what the Fourier Transform equation meant? Why is my mischievous little 2-year-old son hiding my slippers? I hope that by the end of this lecture, I will have explained the process of Convolution to you clearly enough that you'll understand how Fourier's revolutionary idea actually works... and yes, the slippers are really part of the explanation.

A transcript of this lecture can be downloaded from the following link:

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#learning #mathematics #math #convolution

Thanks for watching the video How the Fourier Transform Works, Lecture 6 | Convolution Signals and Systems

[vishnukartha]

I cant believe, how much work this guy put for making us understand the whole concept that easy. Hats off. 👍👍👍

[usmanzafar]

Yours is the most clearest explanation of Fourier Transforms that I found Online. I can say that Today I finally understood Fourier Transform. Thanks...

[martonkristofpalinkas]

Certainly a hidden gem, and yet the one that shines the brightest! Thank you, Mark, you are great!

[thefitnesstraits]

I am literally in tears .. of joy of course !! I am an analog design engineer this is a pure joy... after watching 100s of videos brought me here to understand the basis of Laplace transform.

[kdg]

Sir, Thank you for the brilliant six videos so far on the Fourier transform. The build up to this video was a great refresher for me, but the section here on convolution is a real eye opener to me as never understood it and thus how the FT comes about. I studied Chemical Engineering (1985 - 1988) with modules on Laplace transforms for use in Chemical Process Control. I never understood it intuitively. Now 28 years later, having a bit more time to re-visit this, I'm slowly joining up the pieces, (I have an average brain). Your work has been a tremendous help to me. I've not fully actualised the matter yet, but am getting there. I've got to get my "layers of mathematics" in the correct order & down on paper. I hope your efforts pay-off with your career, as your clearly a natural tutor and educator of difficult subject matter. Warm regards from UK.

[ZenoDiac]

Beautiful description of Fourier Series. Truely more students need to watch this.

[Amine-gzgq]

Fourier, Laplace and the mathematician who played a major role in the development of wavelets (Yves Meyer) are all French! I finally understood the Laplace transform only when I understood what "e" really is and the function e(growth rate * growth time) thanks to the book "Better Explained" by Kalid Azad and after watching a video by Zach Star (Youtube channel) where he talks about the Laplace transform. For a better visualization of the Fourier transform, I can recommend William cox (gallamine channel). Your video nailed it Mark even though I only watched a few minutes and I'm not exaggerating! I now know that the wavelet is another tool to analyze a function and you explained in one word and clearly what the Laplace transform is, congratulations! When I was a student I had classes on control theory and I wish I had this kind of content, I was so frustrated that I didn't have a clear view of "e" (which is just as important as pi), Fourier and Laplace transforms and how these mathematical tools relate to system controls (differential equations), now that I'm 32 I can finally say that I understand these abstract topics that have bothered and frustrated me for years. Educational systems suck (and Wikipedia too which I used to consult a lot when I was young and it didn't help me at all to see clearly), I think a lot of teachers don't understand these things clearly and the emphasis is not on explaining the origin of the topics taught and what exactly they are for and visualization but rather to use them stupidly (calculate integrals, etc...), if I don't understand the nature of the tool and I can't visualize it, I can't use it.

[littleKingSolomon]

Dear Prof. Mark Newman, you make learning so much fun. This fourier transform series is very enlightening and educative and yet very entertaining. Been on this somewhat hard-to-grasp concepts for about 3 hours and I still want more. Can't thank you enough.

[jpunditreviewsandtutorials]

I’ve been searching for a video like this for months. This video should have more views!

[maheswarapudixit]

This was the best explanation I could ever encounter to understand Fourier ! Thank you so much . We all indebted for this incredible and lucid explanation . Looking forward for much videos .

[JustinNinan]

Such beauty to Math! Such clarity in these videos and WHAT quality to these animations!!!
Thank you so much Mark Newman, THANK YOU, THANK YOU, THANK YOU! and if you ever stop making such videos, I will find you and I will twist your arm! Because, by doing so you will be depriving humanity from LOVING MATH! :D

[lazyboy]

Your guidance and patience have made learning this complex topic a joyful journey, knowing it's all thanks to your incredible teaching.

[hygenz]

Thanks for the lecture! Your explanation about fourier series and fourier transform is the very intuitive and comprehensive, especially your explanation about the fourier series formula.
Nicely done!

[curtpiazza]

This is wonderful! I'm beginning to understand this subject! Thanx! 😊

[ahmedgaafar]

enormous effort in each video, well done Mark.

[kishorsahu]

Your teaching style is amazing and simple

[acluster]

The whole presentation of the idea with visualization and animation is done to the perfection. You have figured out the art of story telling of the math. Hope you take up few more complex topic and make those videos to help generations of people for eons to come! Thank you.

[marcioaugusto]

Nice, very nice job. It's unique! Congratulations and a lot of thanks. You've inspired me, not only because I found the lessons that I'm looking for... but because you teached me how to teach. I believe that anyone can understand anything, but students have no motivation when they can't undestand a new concept at first look... this is because the teachers don't prepare his lessons, they have no empaty, they don't care about the different ways to explain the concepts... You are a good teacher of teachers! My best regards, from Brazil.

[gok_dogan]

19:00 💡
That is the key point of 👉
Difference of between the convolution and fourier.
What Joseph Fourier add with his famous formula.

[rauldurand]

This is amazing. How this lecture has no more views?