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Awesome reverse engineering project. Next up: reverse engineer a NN's solution to Fourier Transform!

• mananaysiempre 4y ago
  The Fourier transform is also linear, so the same solution should work. No clue if an NN would find it though.
  • perihelions 4y ago
    What's an analog implementation of a Fourier transform look like? It sounds interesting!
    • bradrn 4y ago
      It looks like Albert Michelson's Harmonic Analyzer: see https://engineerguy.com/fourier/ https://engineerguy.com/fourier/ (and don’t miss the accompanying video series! It’s pretty cool.)
    • mananaysiempre 4y ago
      Depends on what kind of “analog” you want. In an NN context, given that you already have “transform with a matrix” as a primitive, probably something very much like sticking a https://en.wikipedia.org/wiki/DFT_matrix https://en.wikipedia.org/wiki/DFT_matrix somewhere. (You are already extremely familliar with the 2-input DFT, for example: it’s the (x, y) ↦ (x+y, x−y) map.) If you want a physical implementation of a Fourier transform, it gets a little more fun. A sibling comment already mentioned one possibility. Another is that far-field (i.e. long-distance; “Fraunhofer”) diffraction of coherent light on a semi-transparent planar screen gives you the Fourier transform of the transmissivity (i.e. transparency) of that screen[1]. That’s extremely neat and covers all textbook examples of diffraction (e.g. a finite-width slit gives a sinc for the usual reasons), but probably impractical to mention in an introductory course because the derivation is to get a gnarly general formula then apply the far-field approximation to it. A related application is any time the “reciprocal lattice” is mentioned in solid-state physics; e.g. in X-ray crystallography, what you see on the CRT screen in the simplest case once the X-rays have passed through the sample is the (continuous) Fourier transform of (a bunch of Dirac deltas stuck at each center of) its crystal lattice[2], and that’s because it’s basically the same thing as the Fraunhofer diffraction in the previous paragraph. Of course, the mammalian inner ear is also a spectral analyzer[3]. [1] https://en.wikipedia.org/wiki/Fourier_optics#The_far_field_approximation https://en.wikipedia.org/wiki/Fourier_optics#The_far_field_a... [2] https://en.wikipedia.org/wiki/Laue_equations https://en.wikipedia.org/wiki/Laue_equations [3] https://en.wikipedia.org/wiki/Basilar_membrane#Frequency_dispersion https://en.wikipedia.org/wiki/Basilar_membrane#Frequency_dis...
      • bradrn 4y ago
        > Another is that far-field (i.e. long-distance; “Fraunhofer”) diffraction of coherent light on a semi-transparent planar screen gives you the Fourier transform of the transmissivity (i.e. transparency) of that screen Ooh, yes, I’d forgotten that! And I’ve actually done this experiment myself — it works impressively well when you set it up right. I even recall being able to create filters (low-pass, high-pass etc.) simply by blocking the appropriate part of the light beam and reconstituting the final image using another lens. Should have mentioned it in my comment…
    • ilyt 4y ago
      A prism and CCD sensor. Probably bit more fuckery to get phase info out of that tho.