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meta I love the fascination with the Fourier transform on this site even though I would venture most of us haven't thought of it since college if even exposed t

meta I love the fascination with the Fourier transform on this site even though I would venture most of us haven't thought of it since college if even exposed to it at all then. My hunch is that it's the first math concept many of us encountered that's not straightforward. Even integrating and taking derivatives is mostly procedural and intuitive. Plus it's so insanely cool when you understand the power of changing domains. I'm no expert, I'm a failed EE turned mediocre programmer, but I'm equally always in awe of it. Its history is so fascinating, especially how the FFT came up - I saw a great Veritasium video on it.

dustingetz 3y ago
afaict fourier theory is basically the heart of physics. What is energy? frequency! Why do things oscillate? Force fields and energy conservation.
ur-whale 3y ago
> I would venture most of us haven't thought of it since college Not sure what kind of engineering work you are doing, but I can vouch that your assessment is incorrect in general for any kind of engineering work, be it CS related or not. I've (n=1) had to think about the FT a very large number of times in my engineering career, be it for image processing, computer graphics, or any time there is some sort of time-based signal to deal with and understand. A bunch of colleagues working on radar tech, FT and related concepts are their daily bread. Anyone doing actual EE - same thing, it's always there lurking in the background Now sure, if what you do all day is react-type stuff, then yeah, maybe. Physicists - same thing, how can you possibly look at any kind of physical process and not at the very least think how the thing looks like in the frequency domain?
- bigmattystyles 3y ago
  I should say I'm also n=1 :-)
sudosysgen 3y ago
The DFT/FFR is actually very much useful and transformative to computer science. It is, along with Karatsuba's algorithm, the basis for a lot of the triumphs of computer science. Want to do polynomial interpolation? FFT. Want to do convolutions on large-ish images? FFT. Want to compress audio/images/video? FFT, or FFT-ish. Want to break RSA on a quantum computer? FFT also (well, QFT). Any algorithms class that left over the Fourier transform is, in my opinion, a small tragedy. That said, I personally think that integration is less straightforward than the Fourier transforms. It's the first task you're given that requires creativity, as there is no practical algorithm for it (sometimes, there isn't even really a way to do it). If you try to approach the Fourier transform as a piece of linear algebra, seeing it as an orthonormal transformation to periodic vectors/functions, it's a lot more intuitive.

dustingetz 3y ago

afaict fourier theory is basically the heart of physics. What is energy? frequency! Why do things oscillate? Force fields and energy conservation.

ur-whale 3y ago

> I would venture most of us haven't thought of it since college Not sure what kind of engineering work you are doing, but I can vouch that your assessment is incorrect in general for any kind of engineering work, be it CS related or not. I've (n=1) had to think about the FT a very large number of times in my engineering career, be it for image processing, computer graphics, or any time there is some sort of time-based signal to deal with and understand. A bunch of colleagues working on radar tech, FT and related concepts are their daily bread. Anyone doing actual EE - same thing, it's always there lurking in the background Now sure, if what you do all day is react-type stuff, then yeah, maybe. Physicists - same thing, how can you possibly look at any kind of physical process and not at the very least think how the thing looks like in the frequency domain?

bigmattystyles 3y ago
I should say I'm also n=1 :-)

sudosysgen 3y ago

The DFT/FFR is actually very much useful and transformative to computer science. It is, along with Karatsuba's algorithm, the basis for a lot of the triumphs of computer science. Want to do polynomial interpolation? FFT. Want to do convolutions on large-ish images? FFT. Want to compress audio/images/video? FFT, or FFT-ish. Want to break RSA on a quantum computer? FFT also (well, QFT). Any algorithms class that left over the Fourier transform is, in my opinion, a small tragedy. That said, I personally think that integration is less straightforward than the Fourier transforms. It's the first task you're given that requires creativity, as there is no practical algorithm for it (sometimes, there isn't even really a way to do it). If you try to approach the Fourier transform as a piece of linear algebra, seeing it as an orthonormal transformation to periodic vectors/functions, it's a lot more intuitive.