The Fast Fourier Transform (FFT)

Concepts simplified to the very core. Thank you for the lecture series!

Karl Friedrich Gauss must have been, no doubt, one of the smartest men who ever walked the earth. Absolute genius.

Amazing explanation! But what I couldn't wrap my head around is how can he write backwards so casually ?!

T-Pain owes his career to FFT

please help me with this, why for a 10 sec audio, n=4.4x 1000000. what basically 'n' is?

I thought the complexity of FFT was n*log2(n) not with a base of 10?

awesome

Gauß was majorly underestimating his own work

So this is just an introduction of FFT? Well I was hoping for learning the details and implementation.

Dear Prof. Brunton, is FFT mostly used for simple domains problems? (FEM, FVM, Meshless, etc)

awesome video and explanation.... how the heck are you writing backwards??

It is so crazy that Steve wrote every notes from the back, which means every characters and graphs he is writing should be flipped along y axis by 180 degrees

Hardware is the physics. Software is the math.

Steve ,you are the best .

Wow did this just make me understand scaling the dow Jones day trading ? Very useful information! I wish this guy was my personal teacher!

I just recently read a paper that it's actually faster to just compute the DFT if you're using GPU acceleration, since matrix multiplication is inherently more parallel despite vendors actually providing their own optimized FFT libraries. The performance benefit of DFT is even greater the larger the input compared to the optimized FFT library.

The paper is:
Davuluru, Venkata Salini Priyamvada; Hettiarachchi, Don Lahiru Nirmal; Balster, Eric (2022): Performance Analysis of DFT and FFT Algorithms on Modern GPUs. TechRxiv.

Wow! This is an awesome explanation! Down to earth, straight forward, excellent! BTW - you are quickly, and legibly writing backwards like some kind of Leonardo DaVinci !! What the heck! Incredible!

Great video! Thank you!

Isn't it O(n(n+1))?

No words to express my gratitude for this awesome content

Thank you so much for these very clear explanations! They are really helpful

An important point I missed in the video is the Kronecker property for the multivariate case. This enables the use of many 1-dimensional operations instead of one N-dimensional operation. Also called "vec-trick" on tensorproduct elements.

Are we not going to talk about how well this guy writes backwards? 🖊

Did he really write mirrored on glass better than I write normal on paper?

I never understand how you do your videos. How the heck do you write in the air, and how you this invisible board trick. Please explain

So he's left handed, can you figure out how I figured it out?

did my man just casually write on the board backwards for us to see it in the correct orientation? Because that's impressive

God bless you!

I wish I could be your student in my uni life 😭 you explained what I need to grasp

Fantastic! What system did u use to produce the lecture?

a) What is this FFT image called in general? (b) What kind of information can you obtain from the FFT image? (c) Is this same as an electron diffraction pattern?

This content is amazing, thank you so much for posting this. I knew how to compute a fourier transform of on a defined function but was incredibly confused how computers did it on the sample data they create from analog signals. I had no idea you could do it to discrete data.

Gauss was a freak

bkchodi krke chala gayam bataya toh nahi ki compute kaise krte h

Very well produced - thank you Steve for this excellent lecture ! FFT is truly what drives the World today... and into the future - with endless applications, in the physical sciences astro, aviation, and medical world.

Ông này viết ngược luôn ghê vch :)) respect!

FFT, how about that FHT (Fast Handwriting Transform)??? Can you reveal that algorithm?

When we say O(nlog(n)) isn't the log base 2? so in the case where n = 1000, log(n) ~= 10 not 3?

awesome, thanks!

I was wondering who invented FFT so I went to wikipedia, letting the video continue to play while I tuned it out to read. When I tuned back into the video, you were just finishing explaining exactly that. Oops 🙃

I was just watching this but I kept being distracted and impressed by the fact that you are writing backwards. :O

Thank you so much, I am so excited to learn when I watch your videos!

If you can right in reverse, you can explain the Fourier transform.

you are too brave keep going!!

8 minutes for NOT describing the FFT

This is what online lectures should be like. Thank you very much Dr. Brunton for sharing these lectures. I can't emphasise enough how amazingly done these are.

if I plot the spectral where the X axis is time, do I have to IFFT first? thank you

I was watching a video of a kid drinking a bottle of Gatorade through a toilet paper roll straw. How did I end up here?