Fourier's frequency decompositions (Version 0.0.1)
I first saw this representation of a Fourier series from a senior student's dissertation at Uni in 1995. Through the years it occasionally cropped up. Most recently was a post from DineshNG in r/Python
Below is basically a summary of that post. The repo contains my own re-worked version of the visualization.
Fourier series and transform resources
3Blue1Brown has an excellent video on the topic explaining Fourier transforms visually like this
This interactive webpage that's very well-coded and easy to use. You can probably run through the whole page in 15 minutes or less, depending on how much you choose to interact.
Mary Boas' Mathematical Methods for the Physical Sciences. A world-class resource in math "crash courses" if you will, this book will be a lifelong resource for learning and relearning heavy math topics that you will use for the rest of your academic life. There's a lengthy section on Fourier Series and one on Fourier Transforms.
This lecture series from Stanford. It's all about the Fourier Transform, and it's a very inviting course that will leave you entirely without questions or confusion by the end. By far the best resource on this list, but it would easily take you weeks to get through the 30 lectures, each I think 50 minutes long. Also, I believe this is the set of lecture notes and practice problems that goes along with this lecture series. It would be well worth your time to work with these materials once you've gained a decent front-end understanding from the first two sources I listed.
Install
To install pygame on Arch Linux you need to install these dependencies:
$ yay -S sdl_image sdl_mixer sdl_ttf portmidi
Other systems may have pygame already, the setup below should install all dependencies.
Now do pip install -e . in a virtualenv as usual. Type fourier to get the
animation.
You can set a few parameters like these:
❯ fourier --help
pygame 1.9.6
Hello from the pygame community. https://www.pygame.org/contribute.html
Usage: fourier [OPTIONS]
Options:
-t, --terms INTEGER Number of terms [default: 3]
-r, --radius INTEGER Radius [default: 100]
--version Show the version and exit.
--help Show this message and exit.