Discrete Fourier Transform - Simple Step by Step 

how is it possible that I have spent probably 40 hours trying to figure this out, dwelling in the dark and you answered everyone of my questions and uncertainties in 10 mins? You are my hero Simon Xu.

I waited 40 years for this! Thank you so much!

best video about this topic out there in youtube! I'm posting this after watching hours and hours of videos in 2023

5 years ago you‘ve made this video and since now nobody has explained it better than you did in just 10 min. Good job

Simon, I cannot stress enough how impressed I am by your explanations. They are very well thought out and presented. Pity that you haven't continued this channel. So easy to digest.

For me, you are the best one who explained the Fourier transform. After 7 years in the university, I understood the Fourier transform today. Thank you very much

Now is 2024, I find this is the most clear video talking about this topic. Thank you so much Simon!

You're a lifesaver, let the universe bless you kind sir. Thank you

Hands down this is the best explanation of Fourier. Wonderful!!

You made only a couple of tutorials ever, but boy, are these the best math tutorials I've ever seen on RU-vid... No frills, so clear! I'm so happy to have found these gems :D

you explain far better than all the textbooks i found about this topics. thank you man!

Nothing is better than a good example. Thank you so much!

By far the best explanation on RU-vid!

Honestly, thanks. The DSP teacher keeps pulling out random facts about a signal from the DFT plot and i'm like: "when did we talk about this in class?" You have just saved me hours of hair pulling frustration and for that I thank you.

Simply and concisely explained, saying all and only the necessary things to really grasp the concept. Best explanation on DFT ive ever seen!

This is the one video on RU-vid about Fourier Transform you need to watch, and I do constantly refer back to it. Thanks. I would really like to thumbs up this many times.

The best explanation on RU-vid channel I have ever seen in my life! Easily refreshed my knowledge about DFT. Thank you so much!!

Best video. Spent ages trying to figure it out but you are here with a short video clearly explaining it all. Much appreciated

Was able to program it in Excel, and from a constructed signal with three signals superimposed, was able to decompose them using your presentation.

Thanks for sharing! Best video about DFT.

Holy crap. Thank you. Why is it so hard for the rest of the world to explain this properly.

All the other explanations lacked a proper example. The best tutorial on this I have ever seen

Thank you! Your explanation is so clear and clean, while other videos on DFT usually take 1 hour only to make you confusing.

what a gem.. this answer everything, you really are the potray of Richard Feynman in describe of master at something

Best DFT video ever!

This is so much clearer than what is written in the books.

Finally someone who knows how to explain this stuff!

Best introduction on Fourier theory I have ever come across. Thank you times a million!

GOD!!!!!!!THE MOST MOST MOST AMAZING VIDEOS ABOUT FOURIER TRANSFORM I 'VE EVER SEEN!!!!!!!!!

3 years, 3 Years I have been trying to understand this fourier shit, and you explained it in 10 Minute

ENDLICH habe ich verstanden, wie die diskrete Fourier-Transformation funktioniert. In 10 Minuten. 10!!! Ich saß vorher stundenlang davor und habe es nur ungefähr verstanden. Herrlich erklärt und animiert. Du bist mein Held! Echt. Dankeschön! -Markus

simply easy understanding expression! very useful. I appreciate you. thank you so much from japanese dsPIC user.

Thank you so much for this, couldn't find anything else helpful online about DFT but this explains it perfectly!

I love the video. The explanation is so clear to unstand. I hate the lectures which nobody can understand.

The best clip about Fourier transformation so far. The example with sampling 1Hz sine wave is excellent.

I've been searching high and low for an ELI5 explanation that is visual enough for my pea brain to be able to turn this into code. Thank you!😍

Thank you very much, very useful! I have never seen it being explained more straighforward than this.

Thank you for making this nightmare way less frightening !! It's crazy how uni professors will never match your level of explanation.

I searched for a video that explains DFT this clear for like a week but failed to do so....just as a last attempt I atched this video and this made it clear........Thank you Simon Xu

Thank you for the explanation and the simple example. I am finally able to understand how the DFT works.

The Explanation is so good

Wow, excellent presentation. You made it simple to 'digest' and understand. Thanks!

This is the best and clearest explanation I have ever seen. Brilliant.

This is the best video I found on the subject so far... thank you! regards from a grad student from Brazil

Finally, a proper explanation.

Thank you very much!!! You explained it very crystal clear...I read a lot but I did not understand it like this. I made a mistake not seeing it even though it has been available for 6 years. Great work, hats off to you

Now that's a good explanation. If you understand this the other parts of the fourier transforms become easy

Yeah this is THE best explanation of Fourier Transform i have seen.Kudos.

Bro, what a nice explanation!!!. I hated the fourier series and transforms and DFTs but after watching your video, Now I have a picture in mind of what's going on and Now this has become my favourite topic. MAY GOD BLESS YOU A HAPPY LIFE.

Great video. You make me understand what is Fourier Transform for the first time.

amazing i spent so much time to get the concept and you simply explained everything in such a simple way

YES!!!!!!! THIS IS EXACTLY WHAT I NEED!!! 😌😌 thank you so much! i have been struggling so much.

You see, THATS HOW YOU DO THIS ! ! I wish my professor would watch this. Learning this would be SO much easier.

I usually dont comment in any video, but this one is just perfect! thank you so much!

its not just clear explained...the speaker is also very considerate, human

Greetings from germany.. You did a great job there.. I love how you explained it so easy. At the very beginning of DFT i was so confused and thougth "this is tto hard to be a question of my exam"... and now, after your video i would prefer to get one question of this .... great job! you made my day

Still the best after 8 years...

"If you can't explain it that simply, you don't understand it well enough."

This video amazingly describes all of my question marks. Simon, just thanks for the effort man

Very very lucid explanation. Wish I had it explained this way in engineering school.

Understanding complexity begins with understanding simplicity. Great example!

The most brilliant explanation I've come across related to DFT. Thank you so much :)

This is a very nice presentation, but not sure if the explanations for frequency resolution, why you drop < Nyquist, double, then average by 1/8 for the amplitude, etc. are quite correct. I think it's a lot clearer if you directly convert from Fourier Integral to the sum, where t->t_n=0,1/8 sec, ..., 7/8 sec., and F-> k Hz, dt->1/8 sec. These should give the correct results without the need to remember all the rules/explanations given here.

Probably the best explanation ive seen

purely amazed by the way you explain, reason it. thank you, sir.

Best explanation I've seen. The only one that made me understand the ecuation (not having much knowledge in calculus). Tnanks man.

Ahh someone with functional brain finally explain it nice job man.. People need to understand that if i looking for answers on youtube means i no nothing about the subject other idiots just start crashing coplex math till a point i forget the video title

OMG - its the first video I see on this topic that makes sense, Thank you soooo much

I enjoy maths that is explained using plots, clarifications on the terms used in formulas, and numerical examples.

I think I've just watched the greatest video about dft on RU-vid. Period! (no pun intended)

You make my life too essay... Thank-you very much... None of my teachers explain the actual consent... And thanks again...

You deserve all the praise you are getting. These videos are what I have been looking for, just like many other commenters. Thank you so much.

dear sir, my junior and i would like to thank you for getting us through highschool

"The Best Explanation of DFT in the Whole World"

Thank you for the best video about DFT.

That's comprehensive explanation!

Its one of the best explanation as I ever checked. But last part still a bit blur. With Neurist limit

Excellent video containing everythink one needs to know about dft at first sight. I didnt find this anywhere else!

absolutely amazing. this was much better that the lecture at university

This was the best explanation on DFT on RU-vid. Thank you.

Hands down the best video on DFTs... Thank you!!!

I'm a computer engineering major and this is super helpful and interesting! thanks!

Why do mathematicians like making things too complicated for nothing? This is the same concept that is unnecessary made sophisticated in the literature. Does it mean everything in the universe should be very simple when explained by someone who understands simplicity? I think every literature about DFT should refer to this video as an example. You need a nobel prize for this. Keep up the good work.

Holy, that was easier than I thought, thank you so much!

Best explanation of DFT i have ever seen.

The description was as promised, step by step. Thanks a lot!

Great explanation ! The example really puts everything together in a sensible manner !

holy shit i went through tens of videos trying to get this right. This one was the only true helpful video. Thank you so much.

Thank for your concise and clear explanation, Simon. It's pretty helpful.

Wowww...A difficult topic simplied in 10 mins...Please do more related content

Amazing video I feel like I'll get an A for my DSP class.

Wow! Possibly the best video on DFT on youtube. Thanks!

Just this one video was enough for me. Thank you.

thank you so much. really you get rid of far math knowledge so everybody can understand your explanations.

Superb explanation and example!

My god . that was a perfect example. thank you

Wonderful, clear explanation. Many thanks Simon.

Thank you so much ! Now I can sleep well today :)

Best ever illustration of FFT. Thanks a lot

thank you for giving me hope for my extended essay again xd