The Fourier Transform and Convolution Integrals
Вставка
- Опубліковано 9 лют 2025
- This video describes how the Fourier Transform maps the convolution integral of two functions to the product of their respective Fourier Transforms.
Book Website: databookuw.com
Book PDF: databookuw.com/...
These lectures follow Chapter 2 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: www.amazon.com...
Brunton Website: eigensteve.com
This video was produced at the University of Washington
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
your in-depth explanation of complex concepts is phenomenal. thank you
He does a pretty good job with real concepts too
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 video.....
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.
Steve, Big fan of your lectures.
By far the best math lecturor i've ever experienced!
Holy moly I've never found math so satisfying
Hahaha. "Rather convoluted expression." I see what you did there.
Its a liiitle bit convoluted . Smooth explanation, I havent done convolution integrals yet but i understood this
That's gorgeous man. Simple and nice
Great video! Thanks Steve. I've learnt so much from your lectures.
Finally someone explained mathematically everything.
I love this. I’m giving a crash course of DFT to my younger colleague, where I’m fuzzy on some theorem derivations.
Is he still alive? Did you loose hair? Is still with Jenny or she separated him when she discovered some Fourier Convolutions on this desk?
(Just some humor).
i love u just survived my breakdown thank you seriously thank you
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.
Thank u for ur clear explanation!
Great series on FT's and FS's but It would be awesome to include dirac delta function in this lecture series
Great video! Thanks.
На часах 2 часа ночи, но я не могу оторваться. Круто!
6:22, it is called Fubini's theorem :)
Awesome, thanks!
saved my life! Thanks
Fantastic representation!
you saved my homework
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.
Thanks -- Yep, the FFT is coming soon!
4:41 "This is where it gets a little bit convoluted". Hah, quite topical!
@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 ?
Excellent
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
yes, you are absolutely wrong and seem a bit confused. by algebraic property of exponential, one can add their exponents [e^a * e^b = e^(a+b) ; a,b belongs to R or C]
@@sayanjitb I also thought the same but I got a bit confused and got the answer wrong. Thanks for correcting me
Thank you so much for this embellished presentation. I got a doubt, what is the diffusion kernel, anyway?
Amazing, thanks a lot!
Great vid
At 4:37
Steve- This is where it gets a little bit convoluted...
My poor self- I thought convolutions were the topic from the start 😥
Massively simplify this "convoluted" expression :D
Where does one use this property in physical applications?
There is a LOT to be said about the commutative property of the integrals. But I am sure simple minded physicists don't mind.
love this
With convolution in the time domain, we have to time reverse one of the functions before we do the convolution. When we do the convolution in the frequency domain(multiplication in frequency domain) do we have to time reverse one of the functions before we take its fourier transform? If not, why not?
No, because the time reversing appears naturally in the inverse transform.
"That is a little bit convoluted" hahahaha
Wait, this guy is writing upside down? Pretty useful video btw
It is not intuitively obvious to me that the in the formula for convolution ( sum over k (f(t)*g(t-k) ) that g(t-k) implies that it is time reversed. That is not obvious. What part of the formula for convolution (in the time domain) implies that one of the functions is reversed in time?
The aesthetics in this video are crazy good but a bit unsettling lol
I only want to be taught by a floating head and arms on a black background in 4K from now on.
K-see
Bless you
K-see
Bless you again
Yes, this is it ))
Is he writing backwards?
"My red integral" I guess Steve might be color blind, or I am color blind
I thought it was 1/sqrt(2pi)?
That’s what my professor taught us
I like your videos but this is definitely not a rigorous mathematical setting for the problem.
Engineers would like it but mathematicians will doubt alot of assumptions you already did in the proof.
I am not convinced!
Kuh-sey might be the worst variable
Who is this guy, why can he write in mirror like nobody's business?