If a Fourier Transform can be computed from something in which Quantum Bits are implemented by some underlying physical system, then is there anything self-existing in Nature which could be used to (or does in actuality) implement a Fourier Transform?
Now, I don't know the answer to that.
Something not occuring naturally in Nature is a Prism, and a Prism splits light, and that's sort of, kind of analogous to what a Fourier Transform does, although, perhaps there's a limited range of frequencies at which the effect is applicable...
So now the next question is, is there anything in Nature, that is, naturally occurring, which acts like a Prism does?
Although, perhaps we're not looking for something that necessarily splits light, perhaps we're looking for something that splits other electromagnetic radiation, that is, waves of some sort...
Also, maybe there's some kind of naturally occuring shape of rock that could be used to "split" ocean waves into one or more component parts... while perhaps not a true Fourier Transform, it might be a step in the right direction for conceptualization purposes...
Anyway, just thinking aloud... It would be interesting to know all of the systems, both natural and man-made, which are capable of Fourier Transforms -- or even just splitting waves of different sorts into component parts...
Prisms and diffraction pattern gratings split light according to the frequency of the photons (colours) in the input. That's a Fourier transform in a certain sense, and you'd use that to make a spectral analyzer. But what about the Fourier transform of an image, according to the frequency components of objects in the image? Like fence posts at a regular spacing, and such?
Well you might be excited to learn that optical lenses actually compute the Fourier transform of their input image:
Your average water droplet acts as a dispersive element (a prism). Dispersive elements can act as temporal Fourier transforms. Lenses act as spatial Fourier transforms. Going further, any mechanical device that exhibits resonance can be claimed to act as a Fourier transform (but that starts sounding meaninglessly vague).
Don't think prism and FT are analogous. Fourier transform is a symmetric operation between dual expressions of the same thing - frequency form and amplitude form.
What effect do yall think this could have on AI? There is literature describing performance advantages of using Fourier transform space for convolutional neural networks
The fourier transform is a linear operator (implementable as a dense NN layer) so I wouldn't be surprised if some NNs learn it or an approximation during training.
[+] [-] peter_d_sherman|5 years ago|reply
If a Fourier Transform can be computed from something in which Quantum Bits are implemented by some underlying physical system, then is there anything self-existing in Nature which could be used to (or does in actuality) implement a Fourier Transform?
Now, I don't know the answer to that.
Something not occuring naturally in Nature is a Prism, and a Prism splits light, and that's sort of, kind of analogous to what a Fourier Transform does, although, perhaps there's a limited range of frequencies at which the effect is applicable...
So now the next question is, is there anything in Nature, that is, naturally occurring, which acts like a Prism does?
Although, perhaps we're not looking for something that necessarily splits light, perhaps we're looking for something that splits other electromagnetic radiation, that is, waves of some sort...
Also, maybe there's some kind of naturally occuring shape of rock that could be used to "split" ocean waves into one or more component parts... while perhaps not a true Fourier Transform, it might be a step in the right direction for conceptualization purposes...
Anyway, just thinking aloud... It would be interesting to know all of the systems, both natural and man-made, which are capable of Fourier Transforms -- or even just splitting waves of different sorts into component parts...
[+] [-] jbay808|5 years ago|reply
Prisms and diffraction pattern gratings split light according to the frequency of the photons (colours) in the input. That's a Fourier transform in a certain sense, and you'd use that to make a spectral analyzer. But what about the Fourier transform of an image, according to the frequency components of objects in the image? Like fence posts at a regular spacing, and such?
Well you might be excited to learn that optical lenses actually compute the Fourier transform of their input image:
http://web.mit.edu/2.710/Fall06/2.710-wk10-a-sl.pdf (the ideal thin lens as a Fourier transform engine, PDF)
[+] [-] krastanov|5 years ago|reply
[+] [-] Randor|5 years ago|reply
The lens in the human eye is continuously doing Fourier transforms via the lens:
https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transfo...
[+] [-] sacredcows|5 years ago|reply
[+] [-] zkmon|5 years ago|reply
[+] [-] domrally|5 years ago|reply
[+] [-] domrally|5 years ago|reply
[+] [-] IdiocyInAction|5 years ago|reply