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Your cell phone wouldn't exist without the Fourier Transform, or the discrete fourier transform, to be correct. Image compression is another application, albeit

Your cell phone wouldn't exist without the Fourier Transform, or the discrete fourier transform, to be correct. Image compression is another application, albeit, a 2-dimensional version. Software defined radios, or SDR, are completely dependent on the DFT. Radar processing. Earthquake analysis. The list goes on and on. Basically, our technological society would not exist in its current form without the fourier transform. To me, it is one of the key mathematical algorithms of the 20th century.

kkapelon 3y ago
> Your cell phone wouldn't exist without the Fourier Transform, or the discrete fourier transform, to be correct Yes that is great to know. But where can I find an article that explains how exactly FT helps in my cell phone? What exactly do we do with FT in a cell phone?
- rjeli 3y ago
  For example, to create a JPEG, part of the process is removing the "high frequency" parts of your image, since those take the most information to store. Here, high frequency refers to noise, or any large difference between neighboring pixels, as opposed to low frequency parts, which are averages over larger groups of pixels. So, at the extreme, if you average the whole image, you only have to store one pixel, so it's obviously less data to store, vs storing info about every single pixel. JPEG (and other lossy compression formats) tries to find a good middle ground between storing every pixel perfectly and storing just one pixel. So, how do you remove the high frequency parts? You apply a Fourier transform to the image (in this case, it's a "Discrete Cosine Transform", which is extremely similar to a DFT and has no differences for the purpose of this explanation) and get a 2d array. This 2d array has the low frequency parts in the upper left corner, and the high frequency parts everywhere else (to the right and down for horizontal and vertical frequencies). So your compression algorithm will simply zero out the high frequency parts so you don't have to store them. In the simplest case, this is equivalent to a simple blur of the image, but there are some heuristics about how much to remove (zero out) to minimize image degradation. To decode the image, you take the 2d array and apply the inverse FT to get the original image (now slightly blurry because it's been compressed). More details here: https://en.wikipedia.org/wiki/JPEG#Discrete_cosine_transform https://en.wikipedia.org/wiki/JPEG#Discrete_cosine_transform
cmehdy 3y ago
We went from mostly fearing vibrations in a mechanical world to harnessing them in a chemical and electrical world. It entirely reshaped our relationship to the world and perhaps so fast that our brains haven't entirely caught up yet. I wonder how many well controlled oscillations of mostly electrical charges happened between me swyping this and you hearing it in your head. We rely on them instead of fearing them now.

kkapelon 3y ago

> Your cell phone wouldn't exist without the Fourier Transform, or the discrete fourier transform, to be correct Yes that is great to know. But where can I find an article that explains how exactly FT helps in my cell phone? What exactly do we do with FT in a cell phone?

rjeli 3y ago
For example, to create a JPEG, part of the process is removing the "high frequency" parts of your image, since those take the most information to store. Here, high frequency refers to noise, or any large difference between neighboring pixels, as opposed to low frequency parts, which are averages over larger groups of pixels. So, at the extreme, if you average the whole image, you only have to store one pixel, so it's obviously less data to store, vs storing info about every single pixel. JPEG (and other lossy compression formats) tries to find a good middle ground between storing every pixel perfectly and storing just one pixel. So, how do you remove the high frequency parts? You apply a Fourier transform to the image (in this case, it's a "Discrete Cosine Transform", which is extremely similar to a DFT and has no differences for the purpose of this explanation) and get a 2d array. This 2d array has the low frequency parts in the upper left corner, and the high frequency parts everywhere else (to the right and down for horizontal and vertical frequencies). So your compression algorithm will simply zero out the high frequency parts so you don't have to store them. In the simplest case, this is equivalent to a simple blur of the image, but there are some heuristics about how much to remove (zero out) to minimize image degradation. To decode the image, you take the 2d array and apply the inverse FT to get the original image (now slightly blurry because it's been compressed). More details here: https://en.wikipedia.org/wiki/JPEG#Discrete_cosine_transform https://en.wikipedia.org/wiki/JPEG#Discrete_cosine_transform

cmehdy 3y ago

We went from mostly fearing vibrations in a mechanical world to harnessing them in a chemical and electrical world. It entirely reshaped our relationship to the world and perhaps so fast that our brains haven't entirely caught up yet. I wonder how many well controlled oscillations of mostly electrical charges happened between me swyping this and you hearing it in your head. We rely on them instead of fearing them now.