The amount of free, useful, precise information coming from this channel is remarkable and something to be grateful for. It legitimizes KZbin education.
@gabrielnicolosi87066 ай бұрын
It is not "free". Most likely, Professor Brunton has these lectures as one of the deliverables of many of his NSF grants. Thus, this is paid by the US taxpayer. :)
@greensasque3 жыл бұрын
Can't say this for many videos, but my mind is now blown. 🤯 Finally after years the DFT makes sense.
@Eigensteve3 жыл бұрын
Awesome!
@ahmedgaafar53694 жыл бұрын
Steve, you really are the best professor on the planet period ....thank you so much for all these incredible high quality lectures.
@gmoney68293 жыл бұрын
I’m glad I have this guy as my uncle
@funkflip4 жыл бұрын
The video is very nice. Thank you! Just a small remark: The indexing of f and f hat in the matrix vector multiplication is wrong. Should count up to f_{n-1} not f_{n}.
@Eigensteve4 жыл бұрын
Good catch, you are definitely right!
@VarunAgrawal114 жыл бұрын
@@Eigensteve Or conversely, shouldn't you simply make the summation from 0 to n? Since for f_0 to f_n you now have n+1 sample points, and x is an n+1 size vector. By making your summation to j=0:n, it is summing over n+1 points which is the standard notation used in approximation theory.
@eric_welch3 жыл бұрын
@@iiillililililillil8759 you can change summation range if you pull out the j = 0 term and add it in front of your sum :) similar to how it is done in series solutions for certain differential equations
@masoudsakha93312 жыл бұрын
Thanks for great lecture. However, I think the last element of vectors must be F_n-1 instead of F_n.
@LydellAaron4 жыл бұрын
I like your insight that this should actually be called the Discrete Fourier SERIES. Thank you for your way of relating the matrix to the computation. Your perspective help me see how the matrix is related to the tensor and quantum mechanics.
@srikasip3 жыл бұрын
Oh my goodness! Stumbled onto video 1 in this playlist this evening. and I can't stop. Steve, you're amazing. I actually finally feel like I understand what a fourier series is and why it works. can't wait to get to the end. This is easily the best set of lecture on this topic i've ever experienced. HUGE thanks!
@srikasip3 жыл бұрын
Also, are you writing on a window? ......backwards?!
@wtfftwfml98 Жыл бұрын
I have to give you credit for giving the absolute best educational videos I have ever seen. The screen is awesome, the audio is great, you explain thoroughly and clearly, you write clearly, your voice is not annoying and everything makes sense. Thank you mr sir Steve.
@javadvahedi62784 жыл бұрын
Dear Steve I really enjoy your teaching format and also your wonderful explanation. Just one suggestion, It would be great if you could have at least one practical lecture at the end of each series of lectures, e.g for Fourier series transformation lecture designing one lecture which shows a real problem is great and enhance the level of understanding. Stay motivated and Many thanks for your consideration
@Eigensteve4 жыл бұрын
Great suggestion. Let me think about how to do that.
@zaramomadi55693 жыл бұрын
When he said "thank you" in the end I wanted to take a huge mirror and send it right back at him
@erikgottlieb9362 Жыл бұрын
Mr. Brunton. Thank you for clear, concise, organized presentation of DFT. Appreciative of how much time and effort such a presentation / explanation takes to create and deliver. Appreciative of the format you use and precision in getting explanation correct. Explanation of terms and where terms originate has always been helpful in your presentations. Going through the whole DFT, FFT series again to refresh my thinking on the topics. Thanks again. (Erik Gottlieb)
@anantchopra16634 жыл бұрын
Excellent video! The video was conceptually very clear and to the point. You are an amazing teacher, Prof Brunton! I loved your control systems videos too!
@user-iw1dv3rw4t4 жыл бұрын
Thanks Steve for contributing on humanity. cheers!
@joakiti3 жыл бұрын
This is by far the best explanation I’ve ever seen. Thank you Steve, I hope to find reason to buy your book soon.
@nitinshukla67514 жыл бұрын
Your ability to explain something this abstract in such a simple manner is simply astounding. However i was more impressed by your mirror writing skills. hats off sir..very very good video.. Subscribing to you.
@vitormateusmartini39462 жыл бұрын
he does not write backwards... it's a lightboard
@mariogutierrezdiaz33662 жыл бұрын
Hi Professor Brunton, Just wanted to let you know I took your AMATH 301 course at UW in 2012. It really kicked my butt but learned so much. I still use the RK4 for work once in a while. You and Prof. Kutz were both outstanding. Wish you both well!
@Eigensteve2 жыл бұрын
That is so nice to hear! Really glad it has been useful since then... that must have been my first class too!
@sashacurcic17194 жыл бұрын
This is very concise and organized and easy to understand. Thank you for posting it.
@ozzyfromspace2 жыл бұрын
One of my friends posed me an interpolation problem and I instinctively decided to try a DFT. I used some for loops and got the job done, but I never thought that you could build a matrix using fundamental frequencies. That's clean. Then when it came time to using the algorithm, I realized that it was super slow! Granted, it was an interpolation on some 2D data, but still. My laptop couldn't handle an interpolation over fairly small grids (at 35x35, I was waiting seconds for an answer), which blew my mind. But on further inspection, a for loop (or matrix multiplication) is like O(n^2) but likely all the way to O(n^3) after naive implementation details, so it makes sense. What I'm trying to say is, I can see why you think so highly of the FFT, and I'm super excited to learn how it works, and maybe even implement it myself 🙌🏽. You rock, prof!
@JoelRosenfeld3 жыл бұрын
Heya! I really enjoy the pacing of your lectures. It's also nice for me to get a quick recap of some signal processing before assembling my own lectures. It is also helping me fill in the gaps of knowledge I have around data science, where my training is in Functional Analysis and Operator Theory. This past fall I dug through the literature for my Tomography class looking for a direct connection between the Fourier transform and the DFT. Mostly this is because in Tomography you talk so much about the Fourier transform proper, that abandoning it for what you called a Discrete Fourier series seemed unnatural. There is indeed a route from the Fourier transform to DFT, where you start by considering Fourier transforms over the Schwartz space, then Fourier transforms over Tempered Distributions. Once you have the Poisson summation formula you can take the Fourier transform of a periodic function, which you view as a regular tempered distribution, and split it up over intervals using its period. The Fourier integral would never converge in the truest sense against a periodic function, but it does converge as a series of tempered distributions in the topology of the dual of the Schwartz space. Hunter and Nachtergaele's textbook Applied Analysis (not to be confused with Lanczos' text of the same name) has much of the required details. They give their book away for free online: www.math.ucdavis.edu/~hunter/book/pdfbook.html
@ZetaCarinae4 жыл бұрын
The last time I tried to give a similar lecture I messed up the indexing much more than this, it was a little comforting to see you do it too. It made me wonder if it was worth it to count from 0 always when teaching linear algebra (probably not).
@Eigensteve4 жыл бұрын
Thanks for the feedback... yeah, I know that when I make mistakes in class, it actually resonates with some of the students. I hope some of that comes through here.
@joeylitalien13554 жыл бұрын
Hey Steve, your videos are great. I love the format and the clarity of the exposition, keep up the good work.
@Eigensteve4 жыл бұрын
Thanks!
@julesclarke61404 жыл бұрын
I agree, it's both clear and enjoyable, you sir are a life savior. Merci !
@nrdesign19913 жыл бұрын
I *finally* understand it. Memorizing it for exams is not good enough for me, i want to *get* it. Now I do, and see all the great applications for it. Filtering out specific frequencies, isolating specific frequencies, or the same with a broad spectrum of frequencies will be extremely easy with it. Either just calculate a few values individually, or just take/throw away a chunk of the resulting vector. Great videos!
@_noname_60342 жыл бұрын
yo how tf u writing like that
@MboeraKisaroKimambo10 ай бұрын
It took me 5min and 55sec to discover that you're writing correctly, I was wondering why are you writing the inverse way! Thank you for the great presentation!
@soorkie3 жыл бұрын
Thank you. This video really helped me. Thank you for keeping this open and free for everyone.
@miguelaugustovergara41853 жыл бұрын
Please never stop uploading useful content like this, nice teaching method!
@duameer68322 жыл бұрын
You made me feel that I can understand something too!! I’m so glad to understand this. Love and prayers!
@johnnyhsieh020810 ай бұрын
Big appreciate Prof. Steven Brunton.
@ziggly0018 Жыл бұрын
Some videos ago I was concerned at the implications of this being called the DFT, as it not repeating would be problematic for me, and from my understanding of others' implementations, it is supposed to repeat, so I was happy to hear you clear up the easy to make mistake that this was an actual transform and not a series. Things make sense again now. It's still weird that its mislabeled though.
@olayomateoreynaud99562 жыл бұрын
At 0:30 you already solved the question that brought me here. Thank you!
@michaelpadilla141 Жыл бұрын
A nice way to think about the mathematical sums, which Prof. Brunton doesn't explicitly mention, is that each of the n+1 rows in the matrix as a vector that functions as a basis function, together which span the space of all n+1 element vectors. Hence all you're doing is taking the inner (dot) product of the original signal with each of those n+1 basis functions (the vectors), i.e. projecting the orignal signal against each of those basic functions to see how much of it is along each of those (vector space) directions.
@muhammadsohaib6814 жыл бұрын
Dear Professor Thank You so much for your nice explanation!!! 💓
@Kay-ip9fy2 жыл бұрын
This is one of thewonderful lessons I've got, thank you so much for your enthusiastic!
@Martin-lv1xw2 жыл бұрын
Damn STEVE...YOU SAVED MY DAY...THANK YOU SO MUCH FOR SUCH A COOL PRESENTATION.
@manuelaayo4199 Жыл бұрын
Thank you so much for this series of videos. Just a small suggestion; to be consistent, it seems that the vector should have points from f_0 to f_(n-1)
@YYchen7132 жыл бұрын
I think I'm just going to watch all your videos for my machine learning course this semester instead of my professor's lecture which was so painful and frustrating....
@SreenikethanI4 жыл бұрын
Absolutely fantastic video, sir! Thank you very much!
@LL-ue3ek2 жыл бұрын
Thank you for the presentation with clarity and intuition. I have a question, @ 9:14 you mentioned something about the fundamental frequency wn. If we are given a piece of signal like you drew, how do we decide what frequencies to look for in that signal? and hence how do we decide what fundamental frequency we can set wn to be? In other words, how do we know if we should look for frequency content from 10 - 20 hz instead of 100-110hz?
@maksymkloka7819 Жыл бұрын
Great video. One of the better ones. I wish you explained the exact meaning of the coefficient in the exponent though ... e.g. I never really understood the relationship between sample frequency and number of data points (N). Seems like they will always be the same.
@augusto2884 ай бұрын
the matrix for the Fourier coefficients and the f function samples should also go up to n-1 and . If someone was confused about it.
@mz1rek3 жыл бұрын
At 10:49 corrected the matrix size to be n but then the vector size became n+1; needs another correction but I'm still watching! Edit: I saw the same catch in the comments below, but I think the solutions given weren't the best: My solution is as follows: n should be kept the same as it is the number of samples, also the summation should go until n-1 to give n points and nxn matrix size, but the summation formula should contain f_{j+1} keeping everything else the same. This way you don't even need the x_{0} data point. Still liked the video a lot...
@Jonas.verhaegen8 ай бұрын
I'm just here because I wanted to make an audio visualizer as an add-on for my gui exercise in c++. Guess I underestimated it.
@JamesB-yh2xx Жыл бұрын
Amazing video. Very clear and well presented
@christiaanleroux40164 жыл бұрын
As far as I understand, when we take the inverse discrete fourier transform, we end up with the function values at x_0, x_1, x_2, ..., x_n, but how would you determine what the values of x_0, x_1, ... ,x_n are? I need to know this for my masters thesis please help me if you can.
@mikefredd33902 жыл бұрын
I got some insights. Thank you. The FFT next.
@alireza983254 жыл бұрын
You are a good human.
@McSwey2 жыл бұрын
There's a minor issue after reindexing, the last index should be n-1 not n. But it's not that important, great video as always!
@euyin774 жыл бұрын
I think the summation should go from 0 to n because you have n + 1 rows in the pink column vector and n columns in the yellow matrix.
@recomoto3 жыл бұрын
Or there should have been n-1 measurements
@devaniljaquesdesouza30243 жыл бұрын
Observe that there are n+1 values of f so the sum must go from 0 to n, isn´t it?
@orionpritchard11172 жыл бұрын
More impressive than the math is that Steve is writing mirror-imaged. Leonardo DaVinci would be proud.
@FFLounge Жыл бұрын
one thing i don't really understand is why there is a "j" in the exponential e^{2\pi1k/n}. Aren't e^{2\pi1k/n} sort of like the basis vectors we are projecting onto? Why do we need to raise each of those to the j's?
@rhysparker69983 жыл бұрын
Great description thanks, FFT was a nice bonus.
@eju13163 жыл бұрын
Always leaning a lot from your lecture! Appreciate it, sir.
@ephimp31899 күн бұрын
How is something like this recorded? is he writing on transparent glass or mirror? how is the background removed?
@harsh_hybrid_thenx4 жыл бұрын
One thing i want to point out i suspect the DFT matrix is a symmetric one ..... Is it ?
@Eigensteve4 жыл бұрын
Yes
@lokranjanp35206 ай бұрын
To understand how important the FFT algorithm is, it helps nations know when other countries are performing underground nuclear tests from anywhere in the world. hope that helps :)
@BloodHuntress994 жыл бұрын
COME ON DUDE LETSGO LETS MAKE ME SMART!!!! i have an exam in the morning it's currently 2 AM and I'm cramminggggggggggg
@BloodHuntress994 жыл бұрын
on a side note... how did you write backwards? or was the video flipped?
@BloodHuntress994 жыл бұрын
or did you actually write backwards.....?
@rafidbendimerad Жыл бұрын
Thank you so much for this video. I think that our data vector should be :[f_0, f_1, f_2, . . ., f_{n-1}] instead of [f_0, f_1, f_2, . . ., f_n].
@AbhishekMazumdar-h6o6 ай бұрын
Thanks for the amazing video... however kudos for being able to write mirrored!!
@ehabnasr69252 жыл бұрын
What would be the 2-d version of the DFT system? will the vectors be matrices and the DFT matrix be a 3d tensor?
@shlimon7667 Жыл бұрын
are you drawing everything mirrored? That's impressive if so
@alexeyl224 жыл бұрын
Awesome! I’m curious if it is too much to expand matrix form for a 2D function, i.e. 3D matrix.
@Eigensteve4 жыл бұрын
This is coming up soon when we look at the DFT/FFT for 2D images.
@Saens4064 жыл бұрын
I dont understand how you can have information about the presence of a certain frequence. How come there are discrete frequence?
@masoudsakha93312 жыл бұрын
If I am not wrong we collect the sample of data from x(t) in time domain so the elements of the second vector (red one) are not the signal frequencies and just the amplitude of our signal in time t?
@sealedwings67883 жыл бұрын
Does Mr. Brunton have a more conceptual video on why that fundamental frequency is defined, why we sample it with harmonics proportional to it etc.? Thanks
@ishtiakhasan83972 жыл бұрын
great way to explain. huge respect
@ryannoe863 жыл бұрын
Insightful… also, how in the world did you write backwards on that glass and make it look so good??
@CigdemO279 Жыл бұрын
i thought maybe its mirrored
@AG-cx1ug Жыл бұрын
At 14:55 shouldn't the last value be wn ^ (n(n-1)) instead of wn ^ ((n-1)^2) Since the value is at the fnth value row wise and jnth value coloumn wise?
@mbisavunma662 Жыл бұрын
Dear Prof. Steve. I think there are n+1 data points (starting from "0" to "n"), but you have calculated the frequencies for (f1,f2, f3, .., fn) total "n" points. I think that one point is missing? Is something wrong?
@alt-f46663 жыл бұрын
In DFT, you can tell there's a linear system of equations (whose dimensions are n*inf) that's being solved through inner products, by eliminating all terms except 1 on each equation, since the complex basis vectors are orthogonal to each other. Thats pretty straightforward and intuitive. However, when f is continuous, Fourier treats it the exact same way, which seems wrong, since the e^(iωx) and e^(i(ω+dω)x) vectors arent orthogonal to each other anymore, so even if we use inner product, there will still exist some non-zero 'remainders' on each equation which we cant get rid of. Also, any F.T. of a function f in the [-inf,+inf] domain is problematic, since the inner product of any pair of 2 basis vectors diverges. Do we assume then, that we extend our domain to [-inf,+inf] in such a way that the I.P. remains 0? Unfortunately, noone explains those.
@yingxia804810 ай бұрын
Only one minor thing, if change the index from 1 to 0, f range in the equation is from f0 to fn-1, not fn.
@MinhVu-fo6hd4 жыл бұрын
Professor, I have a question. Since I often notice that a lot of fhat are zeros, can we use a different number of basis (preferably less) than n?
@tondann4 жыл бұрын
Wait wait wait, are you writing all that backwards on a glass pane, so that we see it correctly written?
@samarendra1093 жыл бұрын
no, the video is just mirror reversed. (See his hair. It's mirror reversed)
@AlbertoM4A13 жыл бұрын
@@samarendra109 I had to pause the video to look in the comments to see if he was writing backwards, It was driving me crazy, small obsessive compulsive attack XD
@bowenzhang44713 жыл бұрын
I've been thinking about how he did that for an hour but still can't get it.
@JoelRosenfeld3 жыл бұрын
He is writing on a piece of glass and he flips the video after. He is a lefty, which you can see in his early unflipped videos. His part is also the other way.
@rugvedkatole86473 жыл бұрын
Its a tech invented by a prof from northwestern university, heard about it while doing a course from northwestern
@tomasenrique Жыл бұрын
These videos are amazing! Thanks much!
@ismailsarwar7334 жыл бұрын
Hi Professor, just out of curiosity I am asking this. Are you writing backward on the other side of the mirror or what? 🤔 Nevertheless, Greats videos.
@garyrandomvids20984 жыл бұрын
I'm thinking the same thing. If it is mirrored then Professor is left-handed and writing to the right, then nothing is wrong here. If not then it is very hard to do. So I think it is mirrored. Very good video, clear explanation, 4k image quality really helps me to focus. Thank you very much, professor!
@gaylordsimon33134 жыл бұрын
I believe it's the same technique as professor Matt Anderson uses on his physics videos. He explains this method on the video: "Learning Glass - What is he writing on?" link: kzbin.info/www/bejne/eYirfqeJg7Crj6M
@UmutKaradabann Жыл бұрын
Hello, I did not understand the sizes of the matrices. I think the bottom element should've been fn-1 on the first and last vector. Can you please explain why it goes to fn?
@anujsaini02712 жыл бұрын
How you are writing in reverse direction???
@Foxie-12 жыл бұрын
3:44 - It's a really interesting idea to perform the car diagnosis like this! But what stage goes after the FFT one, is it a neural network or something else?
@monster2842 жыл бұрын
Thank you Steve! I am still not 100% on how we get from the Fourier series coefficients to the DFT coefficients (f-hat_k). If someone could explain that or share a relevant resource, I would greatly appreciate it.
@miklosbence38522 жыл бұрын
Hi, great video. Question: you say you multiply the vector with the matrix, but to make dimesions match, shouldn't you multiply the matrix with the vector ?
@p.z.8355 Жыл бұрын
so how do I do a complex matrix multiplication on the computer f.e using c++ ? just store sin & cos for every entry or is there a better way ?
@resu23814 жыл бұрын
Great video! I have one question. Why do we have multiple images of our signal in time domain after performing DFT?
@Eigensteve4 жыл бұрын
I'm not quite sure I understand your question. If you are asking why the DFT/FFT has multiple "mirror" copies, this is because the DFT/FFT is complex-valued, and so there is redundancy in going from "n" real valued data points to "n" complex valued Fourier coefficients.
@resu23814 жыл бұрын
@@Eigensteve So that is why after DFT our signal is periodic? Or it is because we have discret spectrum.
@Eigensteve4 жыл бұрын
@@resu2381 Yeah, the DFT is assuming we have periodic data, so you can't build a DFT model that isn't periodic.
@resu23814 жыл бұрын
@@Eigensteve Thank you!
@ronitwilson65603 жыл бұрын
made a lot of things clear, thank you
@area51xi7 ай бұрын
Why does the number of frequencies have to equal the number of samples.
@garekbushnell34542 жыл бұрын
This is excellent, thank you very much. A question - does it matter if the spacing between your independent variable samples isn't even/periodic? If it does, how do you approach that scenario?
@mks6760 Жыл бұрын
In any kind of complex maths explanation, I value preciseness the most. This guy has a good visualization but should have been prepared better if he is interested to make the video helpful.
@pawechosta38352 жыл бұрын
it's really complicated. When we use Binary Algebra, we can get s formula of a function almost immediately. This is a formula for the first 16 primary numbers: y (n) = 5 a3 a2 a1 a0 +5 a3 a2 a1+ 5 a3 a2 a0 + 9 a3 a2 + 1 a3 a1 a0 + 5 a3 a1 + 5 a3 a0 + 21 a3 + + 1 a2 a1 a0 + 3 a2 a1 + 1 a2 a0 + 9 a2 + 1 a1 a0 + 3 a1+ 1 a0 + 2
@harsendevsisodia224 жыл бұрын
How did you write it??? I mean it seems you are standing behind a clean glass, that means you must have to write everything from right to left,sort of a mirror image of a normal writing............that's so cool, I really wanna know if that's how you did it??? (Also yeah I'm supposed to concentrating on DFT instead of the mirror image writing, but that's me,I can't help it...)
@JohnVKaravitis4 жыл бұрын
It's called a "lightboard." They are writing normally on glass, and recording the person writing. You have a choice: Capture the work in a mirror, and video the mirror, so everything looks normal writing, OR, record as they write through the glass, and then put the video into Microsoft Movie Maker and "FLIP HORIZONTAL." The glass is low-iron glass, so no reflections, there are LEDs at the top and the bottom of the glass. The light gets trapped in the glass, and, as they write on the glass, the marker ink makes a path whereby the light can escape. Also, black backdrops behind the writer and the camera. Easy once you know the trick behind the magic.
@harsendevsisodia224 жыл бұрын
@@JohnVKaravitis OOOHHHH Thanks brother, I thought he must have trained his brain to write in reverse, which would have been pretty impressive, but this was cool too , thanks
@Tyokok Жыл бұрын
Hi Steve, at 13:07, if your increase your sample data to 2n, then your DFT matrix first row will be 2n of 1s, and f0_hat will be doubled, is that right? Thank you!
@purethanwarat37562 жыл бұрын
Thank you very much!! This video is amazing!!
@nami15402 жыл бұрын
When i try to discretize f_hat from the continuous Fourier transform, I can't figure out how dx disappears. Shouldn't some delta x be part of the f_hat function?
@maomaohuang1752 жыл бұрын
great lecture
@LydellAaron4 жыл бұрын
How would an efficient DFT look, if I have a series of n-coefficients λ0, λ1, λ2, λ3, ..., λn which are prime numbers (2, 3, 5, 7, ..., P(n)) times a factor (f0, f1, f2, f3, ..., fn). And each factor is a positive integer, including zero?
@altuber99_athlete3 жыл бұрын
Is there a difference between the Discrete Fourier Transform and the Discrete-Time Fourier Series? They seem the same thing, including their formulas. Even at the beginning of the video you said the DFT should be called a FS.
@zz97583 жыл бұрын
Great professor! Thank you!
@mehdiheshmati12583 жыл бұрын
Are the vector dimensions correct, shouldn't the coefficients be indexed from 0 to n-1?
@simondemarque28263 жыл бұрын
if you don't know the fundamental frequency, how do you proceed, ? step-wise ??
@moniquevanveen19603 жыл бұрын
How you remove sonic waves from antenna and wirreless media and data, from outside your home?
@patrickdaly78762 жыл бұрын
sorry, I just could not concentrate on the DTFT while trying to figure out how the hell youre doing the writing, right hand, from right to left, is there a mirror involved (i cant see how) or did you really learn to write the other way ?!, thanks!