The Fourier Transform and Convolution Integrals

This video describes how the Fourier Transform maps the convolution integral of two functions to the product of their respective Fourier Transforms.

These lectures follow Chapter 2 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

This video was produced at the University of Washington

[kummer]

Subscribed. Took me one second to reason why.

This man describes all the details in an exhaustive manner. This is exactly what many students are searching for. I can't imagine Lebesgue Integration at this level of detail. Even thinking about makes me cry of happiness. . There are many Doctors like him doing an outstanding job.

And this was recommended as a random

[invinity]

your in-depth explanation of complex concepts is phenomenal. thank you

[andrewgibson]

Hahaha. "Rather convoluted expression." I see what you did there.

[vivekvaghela]

Finally someone explained mathematically everything.

[趙嘉俊]

I'm really appreciate this video that professor made.It's helps me understanding this concept and helps me to accomplish my assignment, sorry for my bad english, thank you.

[erickappel]

By far the best math lecturor i've ever experienced!

[supervince]

Holy moly I've never found math so satisfying

[br-rkth]

Also, something else that I think needs to be addressed is the way that EVERYONE describes the difference between correlation and convolution. In the time domain, one of the functions is time reversed for convolution. But, and this is a big BUT, in the frequency domain it is when we are performing a cross-correlation that one of the DFTs is conjugated (equivalent to time reversal in the time domain). It took me a long time to sort this inherent ambiguity out. This ambiguity needs to be recognized. To assume that everyone realizes this is a big mistake.

[udishsharma]

That's gorgeous man. Simple and nice

[AbhayaParthy]

Great video! Thanks Steve. I've learnt so much from your lectures.

[quantabot]

Its a liiitle bit convoluted . Smooth explanation, I havent done convolution integrals yet but i understood this

[ahmetenesbozcal]

Great series on FT's and FS's but It would be awesome to include dirac delta function in this lecture series

[delendaanouar]

Great one, i want to thank you for your work. And i have also a request : can you make for us some videos about the following topics: Fast fourrier transforme (FFT) and the integrator operation. Thank you in advance.

[taquilo]

I love this. I’m giving a crash course of DFT to my younger colleague, where I’m fuzzy on some theorem derivations.

[alfonsoortizavila]

6:22, it is called Fubini's theorem :)

[thesila]

i love u just survived my breakdown thank you seriously thank you

[pritamroy]

@SteveBrunton Hallow, professor Steve. A wonderful vide series with precise and definite explanation. First of all, thank you and your team. Now coming to my question and that is why do we need convolution ? We had function multiplication operation before but even then why we had to invent Convolution, what's the advantage and purpose of convolution ?

[СерёжаСметанкин]

На часах 2 часа ночи, но я не могу оторваться. Круто!

[p_square]

At approx. 5:37, you said that you are going to multiply e^-i(omega)y with e^i(omega)x and you took i(omega) common for both the terms. But I think that you can't take -ve and +ve positive common because they are opposite. Or, what I think is that when you took i(omega) common, your final expression came out to be e^i(omega)(x - y) so you are correct. Please correct me If I am wrong

[sayanjitb]

Thank you so much for this embellished presentation. I got a doubt, what is the diffusion kernel, anyway?