The FFT Algorithm - Simple Step by Step

I spent part of a semester in college learning this, back in the 1980's. It cost me ~$500 in 1985 $s. Now it's free on the Internet, and presented much more clearly. Thanks.

This is such an amazing straightforward explanation when combined with your video on the DFT. This was impenetrable to me when I got my engineering undergraduate. I was just grateful at the time I didn't have to fully understand it to use it. I hope at some point you consider teaching undergraduates. Even if you aren't an academic some of my best classes were taught by people from industry that wanted to make sure we got something useful.

By far the best explanation of exactly how the FFT algorithm works that I have been able to find on the net. I recreated your code in c#, and compared to some common FFT libraries - got the exact same results. Great work.

This is by far the best explanation of the FFT I had ever seen.

I've been trying to understand this algorithm for a long time, and this video made it click!

This is the greatest explanation of FFT ever! I hope that my knowledge and skills will allow me to pass my image processing test tomorrow😅

Thanks i literally transcribed the entire video into notes, very helpful

I have swept almost the entire YouTube offering on FFT and I agree that this is the most accessible and concrete treatment with the best presentation. I love fresh colour-coded method of teaching. Can you say what software you used to make this? Yes at 6:42 it is a tiny error in the 2nd term of F1 but it multiplies by zero and doesn't change the final answer. So the F1 equation should be: F1 = 0 + -1(0) + (-j)[1+(-1)(-1)] = -2j I believe the rest of the video is error-free. Great work! For an even better understanding I encourage viewers to split the summations one more time to have 8 summations, remembering that exp(x)*exp(y) = exp(x+y), and then it really becomes obvious how elegant Simon Xu's way of organizing terms really is. Then the pattern becomes obvious and you could technically split as many times as you want, confidently, to have 16 terms or 32 terms without having to do all the math but instead by following the pattern. Simon, "I'll be watching your career with much interest young man".... quote from Senator Palpatine :)

This is the best explanation of FFT on youtube. Thank you.

Awesome - great job describing this!

Finally... One of the hundreds who showed what should I do with the output of FFT. Till now this was implicit.

a lot better than many other videos out there.

I first used FFT as a R&D engineer in 1979. It took a microprocessor and a load of custom electronics. Recently did it on an Arduino. Awesome progress.

Instructors who may be reading: I absolutely hate it when you skip steps and make mistakes when I, the student, am trying to learn from following your "easy" explanation, step-by-step. It irks me so. You don't impress me; rather, you just frustrate and piss me, the student, off. I shouldn't have to find your mistakes; it's not my job to find your mistakes while twisting my brain in knots which shouldn't exist. You shouldn't be making mistakes. If you're making mistakes, then don't, in all your "brilliance," skip steps. (...seems a no-brainer to me.) But what's nice is I can finally say this to an instructor after so many years and not interrupt class to do it. :-)

@7:20 the phase-shift (exponential) index shall be doubled for F_2^o, and quadrupled for F_3^o.

your videos are beautiful! thank you so much!

You have great videos. You should continue making videos!!! Thank youu!

Thanks, Nice explanation!

very nice and straight forward explanation

O my god, you are brilliant!