What Is the Fourier Transform?

This video [1] from a visual effects channel (Captain Disillusion) has an excellent visual illustration of how the Fourier tranform works and how its used in visual effects in his video about blurring and unblurring ("ENHANCE!") images.

1. https://youtu.be/xDLxFGXuPEc?feature=shared

The Carl Sagan bit is also an amusing tribute.

While I like CD's works, I would say "CD / Blur" is the least informational of all the CD slash series. I guess it's a fun and more accessible option, but it certainly lacks depth compared to something like 3B1B's video on FT.

I found this video from 3Blue1Brown more informative in terms of mathematics involved:

https://youtu.be/spUNpyF58BY?feature=shared

Edit: In fact it was already mentioned in the comments, but I haven't noticed

I like his videos and most of this particular video. For example, I agree with his choice to not discuss the nasty details of the FFT. Also, I think the "blur" part is fine, but the "unblur" part is too oversimplified.

I think he could have explained how the Gaussian filter almost kills all details / high frequency features, then rounding completely destroy them and then they can not be magically reconstructed to "unblur". He gives some hints about this, but they are to few and too general.

PS: There are some non lineal ticks "enhance" the "unblur" version , like minimizing the L1 norm of the gradient (or something like that). It helps with some images. I'm not sure which is the current state of the art.