161–170 of 214 posts
Earlier quoted context omitted.
> Never perceived algebra as useful in anything programming related Image, video, and audio processing and synthesis, compression algorithms, 2D and 3D graphics and geometry, physics simulation, not to mention the entire current AI boom that's nothing but linear algebra… yeah, definitely algebra isn't useful in anything programming related.
Yea that's not what I work with my guy
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
https://youtu.be/spUNpyF58BY?feature=shared
Edit: In fact it was already mentioned in the comments, but I haven't noticed
Earlier quoted context omitted.
When I did EE, didn't have access to any kind of computer algebra system. Have 'fond' memories of taking Laplace transform transfer functions and converting to z-transform form. Expand and then re-group and factor. Used a lot of pencil, eraser and line printer fanfold paper for doing the very basic but very tedious algebra. Youngsters today don't know how lucky.. (ties onion to belt, etc., etc.)
No worries, as a self proclaimed youngster I didn't manage to understand Fourier in 2 days and never bothered again. Also had no other prior knowledge to algebra so maybe that's why I struggled. Never perceived algebra as useful in anything programming related, will continue to do so as most problems are solvable without it. I'll let the degree havers do all that stuff.
> Fourier argued that the distribution of heat through the rod could be written as a sum of simple waves. How do you even begin to think of such things? Some people are wired differently.
Other mathematicians before Fourier had used trigonometric series to study waves, and physicists already understood harmonic superposition on eg a vibrating string. I don't have the source but I believe Gauss even noted that trigonometric series were a solution to the heat equation. Fourier's contribution was discovering that almost any function, including the general solution to the heat equation, could be modelled this way, and he provided machinery that let mathematicians apply the idea to an enormous range of problems.
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
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 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.
Isn't this essentially a quantum-mechanical concept?
If you like Fourier, you're going to love Laplace (or its discrete counterpart, the z transform). This took me down a very fascinating and intricate rabbit hole years ago, and is still one of my favorite hobbies. Application of Fourier, Laplace, and z transforms is (famously) useful in an incredibly wide variety of fields. I mostly use it for signal processing and analog electronics.
When I did EE, didn't have access to any kind of computer algebra system. Have 'fond' memories of taking Laplace transform transfer functions and converting to z-transform form. Expand and then re-group and factor. Used a lot of pencil, eraser and line printer fanfold paper for doing the very basic but very tedious algebra. Youngsters today don't know how lucky.. (ties onion to belt, etc., etc.)
I guess what i want to know, in the examples it always shows like 3 or 4 constituents frequencies as output, but why not hundreds or a million? Is that decided upfront /paramtetizable?
The article isn't helpful, it just says something like "all possible frequencies".