The Discrete Fourier Transform (DFT)

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Publicado 2020-03-28
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.

Book Website: databookuw.com/
Book PDF: databookuw.com/databook.pdf

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

Amazon: www.amazon.com/Data-Driven-Science-Engineering-Lea…

Brunton Website: eigensteve.com

This video was produced at the University of Washington

Todos los comentarios (21)
  • 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.
  • @ahmedgaafar5369
    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.
  • @zaramomadi5569
    When he said "thank you" in the end I wanted to take a huge mirror and send it right back at him
  • @wtfftwfml98
    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.
  • @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!
  • @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.
  • 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)
  • @anantchopra1663
    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!
  • @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.
  • @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}.
  • @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!
  • @sashacurcic1719
    This is very concise and organized and easy to understand. Thank you for posting it.
  • @doneel.5338
    Thank you for the explanation focused on the implementation of DFT. Fourier series makes much more sense to me in general as well! Now I will attempt to code it :)
  • @WahranRai
    You must also replace indice n by n-1 if you start with f0....f_n-1 etc...
  • @pranav2pta
    Here it's mid night now, but you have opened my eyes !!! Lucky to find this lecture
  • @masoudsakha9331
    Thanks for great lecture. However, I think the last element of vectors must be F_n-1 instead of F_n.