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.
Book Website: databookuw.com
Book PDF: databookuw.com/databook.pdf
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/Data-Driven-Sc...
Brunton Website: eigensteve.com
This video was produced at the University of Washington

[@andrewgibson7797]

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

[@MathStringInputOutpu]

Who is this guy, why can he write in mirror like nobody's business?

[@nullspace209]

There is a LOT to be said about the commutative property of the integrals. But I am sure simple minded physicists don't mind.

[@Seanovis]

Kuh-sey might be the worst variable

[@someoneunknow1285]

Is he writing backwards?

[@erickgomez7775]

"My red integral" I guess Steve might be color blind, or I am color blind

[@br-rk5th]

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.

[@invinity3982]

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

[@sebastianrada4107]

"That is a little bit convoluted" hahahaha

[@mogomotsiseiphemo1681]

I am not convinced!

[@kummer45]

Subscribed. Took me one second to reason why.

[@karthickpn450]

Steve, Big fan of your lectures.

[@user-oq4kh6wp8k]

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.

[@AbhayaParthy]

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

[@quantabot1165]

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

[@erickappel4120]

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

[@abcd1111223]

Thank u for ur clear explanation!

[@leiyplane2011]

Fantastic representation!

[@thesila2000]

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

[@SDen-mp4yc]

Great video! Thanks.