The Fourier Transform: What's Wrong with It?
29 points by teleforce 3 days ago | 13 comments
  • timonoko 3 days ago |
    Wrongness is that nobody bothered to explain what it means. Only 60 years later watching Youtube-video I learned that is was that simple. Mind blown.

    Could not find good video for EigenVectors and Nabla and all that shit. So incomprehension prevails.

    • tux3 2 days ago |
      If you couldn't find any good video, you may want to try books.

      There's more than enough texts on Linear Algebra that you should be able to find one that works for you, it is a very popular and widely taught topic.

      • galangalalgol 2 days ago |
        Different people learn in different ways, and luckily Gilbert Strang recorded all his lectures on mit open courseware before he passed. So now he can be the best linear algebra teacher in perpetuity.
        • coldtea 2 days ago |
          >Different people learn in different ways

          Not so sure, the idea of "learning styles" (visual learners, etc) has widely been debunked.

          • galangalalgol 2 days ago |
            Learning styles in the formal sense yes. But if you have dyslexia, a video will be better. And if you have auditory processing disorders or deafness you'll want closed captions.
          • jasode 2 days ago |
            The Learning Styles™ as in "visual vs auditory vs physical" is what the example articles from google searches have been about: https://www.google.com/search?q=learning+styles+debunked

            But that's not the same as different types of explanations or different illustrations/animations may finally unlock the key (that "aha" moment) for different people.

            E.g. many of us can instantly see trends and correlations in a illustrated graph rather than staring at a long list of numbers for hours. The so-called debunking of Learning Styles doesn't change why different re-arrangements of the same information can work better for comprehension or teaching.

            • carlmr 2 days ago |
              >E.g. many of us can instantly see trends and correlations in a illustrated graph rather than staring at a long list of numbers for hours.

              Some may even use this to suggest a correlation where there is none.

        • braincat31415 2 days ago |
          Dr.Strang is still alive, isn't he?
          • galangalalgol 2 days ago |
            He is! Cue the mark twain quote. Someone at work told me he had passed. Good news.
    • _aavaa_ 2 days ago |
      I believe this is a fairly intuitive explanation for Eigenvectors: https://www.3blue1brown.com/lessons/eigenvalues
    • danhau 2 days ago |
      What annoys me is that nobody seems to explain the FFT well. I would love to understand that algorithm, bit so far I haven‘t found resources that made it click for me.
      • AndrewOMartin 2 days ago |
        I saw this one a while ago.

        https://www.youtube.com/watch?v=nmgFG7PUHfo - The Remarkable Story Behind The Most Important Algorithm Of All Time

        In summary, FFT is just a "dynamic programming" version of Fourier Transforms, in that it's the same idea, just with avoiding repeating a lot of duplicated calculations.

  • sevensor 2 days ago |
    What's wrong with the Fourier Transform is that everybody and her pet rabbit can give you a half-baked explanation of Nyquist, but nobody understands windowing at all.