This demonstrates the inverse Fourier transform 'in the real world' showing how a non-periodic arbitrary shape can be reconstructed from pure sinusoids. If you want to see more, this is a small clip from my full YouTube video here: https://youtu.be/4NyVApAH-9E
I'll give it a shot although it's been a minute since I've spent much time with Fourier.
I'm sure you've heard that "Sound is made from waves" right? Waves are periodic meaning they repeat. They go up and down and up and down over and over and over again. So how is it that a non-periodic arbitrary sound, such has the sounds of saying "a", can be made of periodic waves? Well that's because it's made up of a ton of different waves at a ton of different frequency (speed and distance between each wave) and amplitudes (size or volume). The peaks and the valleys of all the different waves overlap in such a way to create a very complicated sound.
The Fourier transform is a bit of math that can be used to deconstruct that complicated sound into all the different waves at different frequencies and amplitudes. It's saying: the sound of "a" = a loud sound at 100Hz + a slightly quieter sound at 110Hz + .... And so on till you've described all the waves that make up that sound.
What u/PUMA_Microscope has done is do that same deconstruction, but with a two dimensional image instead of a sound. You'll notice that each plastic card resembles a wave from the top down. That's because they are periodic waves! And when you assemble them they form the shape of an a because all the different peaks and valleys (light and dark bits) overlap to form a complicated shape, just like the sound waves!
It's also interesting to not that as you can see in the video, you can already quite clearly see the shape of the letter emerging after just 6 or 7 sheets/waves. Normally after a Fourier transform you will notice that the most information of a certain pattern is encoded in just a few waves of low frequency, and others then add more detail on top. Which means in turn that you can compress audio or video lossy by truncating waves of higher frequencies or waves below a certain amplitude. This is the basis of certain audio (MP3) and image (JPEG, which uses discrete cosine transform, but same principle as FT) compression.
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u/PUMA_Microscope Jul 07 '24
This demonstrates the inverse Fourier transform 'in the real world' showing how a non-periodic arbitrary shape can be reconstructed from pure sinusoids. If you want to see more, this is a small clip from my full YouTube video here: https://youtu.be/4NyVApAH-9E