Quantum circuit for the fast Fourier transform
link.springer.com
link.springer.com
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...
So, now the next question is, could we prove that a cochlea implements a Fourier Transformation? Note that this Fourier Transform isn't applicable to all frequencies, that is, our ears cannot hear vibrations beyond a certain high pitch, so if a Fourier Transformation could be proved, we could almost think of this as a Fourier Transformation inside of a specific range of frequencies...
But anyway, an interesting observation!
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)
Also (since I didn't know what a "thin lens" was prior to reading this (I never studied Optics)) I Googled it, and found the Wikipedia page for it:
https://en.wikipedia.org/wiki/Thin_lens
>"In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called thick lenses.
The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations."
Which makes me wonder if there's a link between Fourier Transformations and Ray Tracing, and if so, how does it express itself?
Although, that's probably going seriously off-topic for this HN article! <g>
Anyway, thanks again for the link/info!
The lens in the human eye is continuously doing Fourier transforms via the lens:
https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transfo...