The Fast Fourier Transform (FFT) 

It is so crazy that Gauss discovered a lot of things in mathematics that took people hundreds of years to realize.

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

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.

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

Easily one of the best instructional videos on RU-vid, the clarity in your articulation of the concepts makes the otherwise murky subject so much more approachable. Can't applaud you enough for putting these videos togather. Cheers !

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

8 minutes for NOT describing the FFT

This format is simply the best.

the best series I came across recently

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

The best lecture series I've seen in RU-vid. Thanks a lot for everything.

Please Prof. Steve Brunton kindly we need video lectures on the wavelet transform , DWT , CWT , etc , thanks and best regards

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

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

No words to express my gratitude for this awesome content

Thanks from the lecture! from Japan

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.

Can't wait to watch the next video...i really love your work

Thanks you really rock and you’re a great story teller!!

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.

Amazing Prof Brunton.

Thank you so much for making this course publicly available professor! Your approach to teaching Fourier Analysis manages to provide a level of intuition on the subject that makes the equations themselves seem much less daunting. Also the anecdotes and stories you weave into this course are pretty much the icing on the cake.

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

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!

Your Videos are So awesome and wonderfully high quality!

Professor, please tell me how can I monetarily support you. The contents you created are beyond brilliant!

In addition to satellite TV, it is cool that the new digital Terrestrial TV broadcasting standard ATSC 3.0, which has just commenced in US also uses OFDM-based modulation and consequently requires FFT blocks on the receiver side and iFFT on the transmitter.

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

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

Steve ,you are the best .

how does he write backwards so well ???

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.

Obrigado, professor, por nos explicar o porque de usar o FFT (n x long) ao invés do DFT( n x n).

thank u for prompt reply. Be Well !

Thank you so much for explaining complex thing really Easy way! Can you do this for "Homomorphic Encryption" too??

beautiful video - very well explained

Great video! Thank you!

really high quality info, thnx.

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 🙃

very good

Where were you all my college life?

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

I think in the N Log N, the base is not 10 as mentioned here at 3:30. I think the base should be 2.

God bless you!

you are too brave keep going!!

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

awesome, thanks!

Sparsity and Compression is a private video... is a part of any membership plan?

Gauß was majorly underestimating his own work

Holy shit. Thank you. Thank you so much.

awesome

Do you plan to explain the algorithm and the math behind it? Trying to write this algorithm for a compute shader

T-Pain owes his career to FFT

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

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

Ok thank you :)

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

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.

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?

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

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?

the base of the log is 2 isn't it ?

Are ‘Private Vids’ available under your Membership Plan ?

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

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

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

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

what does PDE stand for???????

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

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

Hardware is the physics. Software is the math.

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

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?

That's logN base 2, not base 10. So for n=1000 we'd get logN = 10

idek what ur talking about but nice video!

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

Gauss was a freak

Left handed

fft batch

Don’t watch. He doesn’t explain the FFT.

bff2873

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

Please Prof. Steve Brunton kindly we need video lectures on the wavelet transform , DWT , CWT , etc , thanks and best regards