The Fast Fourier Transform Algorithm

Visitng your lectures for my Bachelor's Thesis Project! I think there are very few teachers who are as coherent as you!

8th November, 2023. 1:15 AM

I also recommend reading "Numerical Recipes" in C or Fortran, it explains this algorithm from a computer scientist's perspective.

The DFT matrix has to be calculated anyway right? So this FFT is just used to speed up the multiplication of the input vector with the DFT matrix?

This is really an engineering video. It doesn't use or show why something is true in theory, but just shows how it works, not WHY it works

Sir u missed 6...😂😂

wait, does this lecturer write everything in reverse?

The only thing I can't wrap my head around is how he is writing everything backwards.

that's what i needed. However i would prefer to hear you talking about what you do than the music. Still very comprensibile btw

Great!!!!

Awesome video. Thank you

Why Transform not found.. I dont understan english language

ARE YOU WRITING IN REVERSE!? THAT'S AMAZING!

Amazing!

0,2,4,6; not 8

Steve, I've just paraphrased (and sourced) this video in my final report for my MSc project.

“The FFT is based on the fundamental observation that the DFT matrix has so much symmetry that if the even and odd indices are reordered, one can massively simplify the calculation by taking advantage of redundancies and cutting the DFT computation in half, recursively”.

Hello professor,

I am recently writing my thesis in experimental aerodynamics area and watching your videos to learn the signal processing techniques. Your videos are the most beneficial academic videos I have ever watched. But I have to cite the information on the videos. How should I do that?

Thanks in advance, respects.

thanks you.... you helped me a lot. your work is appreciated

Amazing Lectures! Thank you very much!

I have a question:
In terms of threading and parallelization (like with OpenMP or CUDA) do you think the FFT is better?
I'm just thinking; because it seems that even DFT has a higher order of computation FFT seems to have a longer span/critical path of computation.. meaning more bottlenecks/parallelization inhibitors?

Simply Wow!!
I truly enjoyed watching this entire video and its like, u made me get inspired.
Thank you for this awesome lecture.

first time in my life I have seen the clear working of FFT. WoW..........Awesome

I can confidently say that this is a great channel. I liked every video. Many Thanks.

This factorization was never taught to us

forgot about 6

Hate to say it, but my signal processing class is nothing like this. My professor only goes over the math parts and nothing more. He doesn't even mention how any of it is used to process signals. So thank you for actually putting the SIGNAL in SIGNAL PROCESSING.

The 6th element of the vector is very sad 😢

It's legendary!

How are you writing backwards??

Thank you so much Steve. Cleared the concept. :)

Fantastic overview! Sorry if this is a dumb question–but what do the "diagonal" matrices contain?

I recommend your channel to my friends when they asked me to explain how FFT works. Great channel!!!!! Keep up the good work professor!!!

COMPLETELY USELESS! Here's a video on the FFT algorithm but I'm not actually going to show you the algorithm because you're not going to code it up

I'm trying to get an intuitive understanding of FFT algorithm...can we say it's a play on the exponent by repeated squaring algorithm. It basically optimized by reducing repeated calculation of Wn^k. Or from another angle it is dynamic programming where the common building blocks Wn^k

Amazing.

It's interesting the FFT has too many dimensions for each dot product to be orthogonal. Obviously at each frequency the 2 dot products (sine and cosine) are orthogonal. The Hadamard transform is a much simpler case.

Bro you make some very good videos but I gotta be honest your swallowing tick thing gives me anxiety to the point I wanna punch the screen every time you do it.
Also maybe some examples, even with tiny matrices would have helped me a lot as that way I could just look at the screen to get it instead of going back like 5 times to re-hear what you said until I do.
Hopefully you can appreciate my dumb observations, thank you!

Very good content

did anyone else realize how well this guy can write backwards?

Sir, your explanations are excellent.

Although a bit too convoluted at some points.

Amazing explanation sir

Hi, so [ F 0; 0 F] is nothing but diagonal entries of the fk-even and fk-odd coefficient after bitwise shuffling.

Thank you for sharing, Steve Brunton. This is great lecture!

Thanks for the great lecture. Just one very minor thing. At 04.52 you said 1012 by 1012 matrix, I think it will be 1024 by 1024.

How are you writing like that?

very clear, thank you