https://reddit.com/r/space/comments/f4l2jv/_/fhrgh2r/?context=1
An explanation of the whole comment would be great. I tried to look up Fourier transform on Wikipedia but it was a lot of math.
In: Mathematics
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A Fourier Transform is a way to split something complex into its simpler parts.
ELI5: Imagine you get served a cup of coffee with milk and sugar. You didn’t make it, so you don’t know how much beans, milk and sugar are in it. You only know the sum of the combined ingredients.
If you want to find out how much the constituent parts are, a Fourier transform could help you split it back out again. But then for maths (e.g. sines) and not for drinks of course.
It’s used a lot in signal processing.
The Fourier transform converts horizontal information to perpendicular information by extracting many waveforms of different wavelengths. For example, if the horizontal information is an image, the Fourier transform can describe the amount of each color the image contains: more red than green.
Rendering an image requires a lot of processing. An image is composed of pixels. Each pixel is calculated and multiplied several times. What if you had a way to speed up the multiplication by performing an addition.
Enter Fourier Transform. Which shows that the addition of two numbers in the time domain is the same as multiplying in the frequency domain. And frequency is nothing but the inverse of time.
To speed up the multiplication, we take the numbers apply the Fourier transform, perform an addition and then apply an inverse Fourier transform. We get the same result as the multiplication.
Say you want to draw a circle but only have rectangles. So you draw a single square, and it’s pretty far from the circle you want. You draw additional rectangles filling the area left between the square and the circle, and it’s still a lot of edges, but closer to the circle now. You draw more and more rectangles getting smaller and smaller, and it gets closer to the circle every time. So that’s essentially digitization : you want to model something analog, but only have one and zeroes. The more of those you have, the closer you get. At one point, you’re still not perfect, but the difference doesn’t matter anymore.
One more thing you can do is not only draw the rectangles, but find a formula to describe how the series of rectangles would need to look. That means, you don’t end up with an actual circle, but with a formula describing how to get as close to it as you want. The more iterations you calculate of this formula, the better its results represents the circle.
Determining this formula is what the Fourier Transform does for waves (ie signals).
Explain Fourier transforms to a 5 year old? Huh…
A Fourier transform for a picture will transform it into an image that describes the patterns in the picture. For example if you took a picture through a screen door, after the transform you can just erase the part the describes the screen and when you transform it back into a picture, the screen will be gone.
Lots of correct answers about Fourier transforms, but no one has directly addressed the second part of the question: why it was needed to render that image. The answer is that when you take an image of an eclipse, the photo has a mixture of fuzzy/cloudy features, sharp edges, and everything in between. Using the Fourier transform you can break down the original image into all the constituent parts (fuzzy stuff, sharp stuff, edges, noise, etc) and then you can selectively pick just the one you want to recreate the image.
More technically, you will generally omit the features that have lower frequencies, and retain certain higher frequencies for an image like this. You can also recreate the original image using multiples of a certain frequency. So, say there’s a sharp feature that shows up well in a certain frequency, you might add multiples of that specific feature into the final image. It takes a surprising amount of experience to get really good at processing images like this, but the outcomes can be amazing.
A fourier transform changes a signal from being in the time domain to being in the frequency domain. In other words, if you have a page of text, the fourier transform will provide you with the number of “the’s”, “a’s” and “becauses” instead of the whole text. Using this you can then get rid of the words you aren’t interested in like the “So’s”, leaving you with only the important information. In relation to the solar eclipse, a series of images is transformed and the best bits of each can be taken out and put together in one image.
Its basically an easy way to apply a filter to a signal.
Well, I didn’t know about Fourier Transform before this question, but I don’t think the answers given do a great job at ELI5, so here’s my take: the Fourier Transform uses math to take a whole bunch of pictures, choose the best parts from each, and mash it together to form one great picture. Done.
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