Discrete Fourier Transform - Simple Step by Step

Easy explanation of the Fourier transform and the Discrete Fourier transform, which takes any signal measured in time and extracts the frequencies in that signal.
This is a work in progress, let me know if anything doesn't make sense, and I will update the video to make that clearer. Thanks for watching!

[@haimijordaan1353]

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.

[@charliebolton5531]

I agree, somehow it was this video, after I already tried for 1 month to understand, this one might be the one that helped me finally get it!

[@g7k993]

without the 40h this video will sound alien to you.

[@cookingforbeginners4875]

This comment has 6x more likes than the video itself.

[@plekkchand]

How do you know that?@@g7k993

[@louisarquie6159]

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

[@Django1847]

You waited 40 years not for your wife and children but for Fourier Transform video. I respect it.

[@mafia12saleh]

HAHAHAHHAHAHHAHAHA

[@trung-tinvo-inh8806]

Thanks for your honesty, my first contact with Fourier Series was in 1985, just a few years short compared to yours :-)

[@sunsean3426]

That means you still haven't understand the process of Fourier Translation for so many years? I think it is the sadness for the educators and students. In China, I suppose most of the students in colleges even teachers don't understand the essence of Fourier Translation. When I studied in college I didn't realize this, I turn round and find this after so many years.

[@luisff7030]

After waited 14610 days it's finally release! and now as the people of this planet know the true behind the DFT, a new era will begin.

[@HamzaNajahOfficial]

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

[@juniorcyans2988]

That was how my professor did his job. He seems enjoy mystifying everything to confuse us, and his strategy works, because those silly kids believe he is super smart. What the hell?

[@urgay63]

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.

[@bhaiyyu]

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

[@satanaz]

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

[@vtcore]

Thanks for sharing! Best video about DFT.

[@louism.4980]

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

[@gloriajing7268]

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

[@davidcian4240]

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

[@MilanKarakas]

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

[@AmeltonGsairus]

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

[@SirSeaKing]

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

[@nikhilnagarkar7422]

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

[@guest9580]

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

[@helmutalexanderrubiowilson6835]

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

[@Copelion]

This is the one video on KZbin 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.

[@ballentinems2]

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.

[@daviderizzotti2724]

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

[@jackiezou4098]

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

[@pedrolins56]

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

[@ellieNC10]

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

[@StjepanBrbot]

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

[@mohamedabdalla6479]

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

[@pherchuz]

Was so hard to find someone that actually did this step by step, best video I've found on the subject!

[@shamsigamer4107]

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.

[@rvhp]

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

[@ronmaor5052]

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

[@sfaunl]

This was the best explanation on DFT on KZbin. Thank you.

[@shashidharmuniswamy2620]

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

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

[@willcheng1702]

Best DFT video ever!

[@nicolacasali8304]

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!😍

[@theedspage]

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

[@siruili7643]

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

[@Ureallydontknow]

By far the best explanation on KZbin!

[@saimanikanta7360]

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

[@GhanashyamSateesh]

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

[@cazaimi]

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

[@cookieuk1278]

Wonderful, clear explanation. Many thanks Simon.

[@alishaikali786]

Thanks for nice explanation, i waited for long time how the DFT related to continuous Fourier transform. The best video on DFT

[@tomschubert9725]

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

[@jacolansac]

Thanks man, really great video. Straight to the point, answering everything that needed to be answered

[@gerhardmalberg4966]

The Best explanation so far! Thank you.

[@exitmanwei7307]

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

[@user-ms8km7lh1l]

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

[@user-vl4vo2vz4f]

Finally someone who knows how to explain this stuff!

[@davidebotti8941]

Thank you very much. Simple, practical, clear, and implementable. Thank you!

[@takusanimasu]

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

[@johnlaurencechan3035]

The Explanation is so good

[@kaleevans1692]

About as an amazing explanation as I've ever seen. Great stuff man. Thank you👍🏾

[@jacobvandijk6525]

Understanding complexity begins with understanding simplicity. Great example!

[@zhenniqi136]

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

[@williamgillespie8462]

Thank you so much for this great explanation. I finally understand the DFT now! This helped me so much.

[@ivanverdugo2931]

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

[@channagirijagadish1201]

Excellent DFT Video. Thanks, Simon.

[@lightnblack1934]

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

[@ThierryPBeaulieu]

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

[@melvirpascual9428]

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

[@Sizifus]

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

[@Clerence3]

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

[@vegetablebake]

Wow. Brilliant explanation, appreciate all your hard work in making this video.

[@sarveshvazarkar6668]

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

[@unknown8088928]

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

[@mickshi279]

This video is just pure magic. Thanks for this amazing video.

[@engradilee]

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

[@anoop5611]

Awesome! Very nicely explained. Thanks! Please keep your videos coming!

[@evaldaszmitra7322]

Great video! Really cleared up my confusion about plotting complex numbers in frequency domain.

[@ebarcham]

Excellent presentation!! Good job!!

[@witoldsosnowski677]

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

[@faridawan3841]

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.

[@joho6051]

this is amazing. This has to be the best explanation video about this ever!

[@geekyfreak3597]

Very well explained and perfect structure. Thanks a lot!

[@kamalgurnani924]

Example made it much clear! thanks a lot Mr. Simon!

[@sukhosuh3890]

Thank you for this wonderful explanation. You're a genius!!

[@alpargur]

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

[@allaalzoy2010a]

thanks, that was really an astonishing explanation !

[@teyyaretey]

Thank you for the best video about DFT.

[@arturro1515]

Best explanation of DFT i have ever seen.

[@opcode66]

Thank you for this. Very clear and straightforward. I appreciate your work to make this video. Subscribed!

[@omartarek6658]

best video regarding that point have been searching for the entire day and that video solved it out . thank you

[@greywolf271]

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

[@azeiny]

Best ever illustration of FFT. Thanks a lot

[@cheymabahroun3824]

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

[@asdfasdf2267]

Thank you good sir, this video solves the missing link in the other 15 DFT videos i've watched.

[@user-hz9wr1ft7m]

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

[@ericxu7681]

Thank you very much!!This will help me a lot in understanding DFT in image processing!

[@zafarsustbd]

Short and very well explanation! Loved it! :)

[@inventorbrothers7053]

This was very helpful thanks. I spent hours trying to figure this stuff out on my own. Thanks

[@davidgoodwin16]

Great presentation and clearly explained - I was able to convert this to programming code, thanks.

[@ecdavek230]

Wonderful job .. concise, to the point, nicely worked example .. The whole package :)

[@daniellynch2047]

The animations are so helpful!

[@user-nt5qi2rm8y]

very good, very intuitive!

[@philipvankampen4381]

Thanks so much! Great explaination!

[@etools]

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

[@pworeo625]

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

[@marcelorofer]

Amazing work! Thank you so much!

[@Dudas314]

This is really clear and helpful, thanks for that!

[@Anisos]

Extremely good content. Thanks!

[@cherma11]

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