The Discrete Fourier Transform (DFT)

This video introduces the Discrete Fourier Transform (DFT), which is how to numerically compute the Fourier Transform on a computer. The DFT, along with its fast FFT implementation, is one of the most important algorithms of all time.

These lectures follow Chapter 2 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

This video was produced at the University of Washington

[Mutual_Information]

The amount of free, useful, precise information coming from this channel is remarkable and something to be grateful for. It legitimizes YouTube education.

[greensasque]

Can't say this for many videos, but my mind is now blown. 🤯
Finally after years the DFT makes sense.

[ahmedgaafar]

Steve, you really are the best professor on the planet period ....thank you so much for all these incredible high quality lectures.

[OrdnanceTV]

I have absolutely no clue what you're talking about but I love listening. Even without understanding it's very evident you're a talented and efficient teacher.

[wtfftwfml]

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.

[LydellAaron]

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.

[srikasip]

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!

[erikgottlieb]

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)

[funkflip]

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}.

[gloiremumbere]

I always struggle in order to understand deeply what Fourier transform really is, but now after watching your video I'm very confident in what's really is .Thanks a lot

[pranavpta]

Here it's mid night now, but you have opened my eyes !!! Lucky to find this lecture

[anantchopra]

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!

[MboeraKisaroKimambo]

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!

[nrdesign]

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!

[joakiti]

This is by far the best explanation I’ve ever seen. Thank you Steve, I hope to find reason to buy your book soon.

[zaramomadi]

When he said "thank you" in the end I wanted to take a huge mirror and send it right back at him

[AKASHSOVIS]

Omg, when I first learned DFT in class I was so confused, but I watched your video and now everything makes sense. Thank you so much. Please continue to make videos!

[iwdvrwt]

Thanks Steve for contributing on humanity. cheers!

[javadvahedi]

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

[sashacurcic]

This is very concise and organized and easy to understand. Thank you for posting it.