The Fast Fourier Transform (FFT)

Here I introduce the Fast Fourier Transform (FFT), which is how we compute the Fourier Transform on a computer. The FFT is one of the most important algorithms of all time.

Book Website: http://databookuw.com
Book PDF: http://databookuw.com/databook.pdf

These lectures follow Chapter 2 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

Amazon: https://www.amazon.com/Data-Driven-Science-Engineering-Learning-Dynamical/dp/1108422098/

Brunton Website: eigensteve.com

But what is the Fourier Transform? A visual introduction.

An animated introduction to the Fourier Transform.
Home page: https://www.3blue1brown.com/
Brought to you by you: http://3b1b.co/fourier-thanks

Follow-on video about the uncertainty principle:

Interactive made by a viewer inspired by this video:
https://prajwalsouza.github.io/Experiments/Fourier-Transform-Visualization.html

Also, take a look at this Jupyter notebook implementing this idea in a way you can play with:
https://github.com/thatSaneKid/fourier/blob/master/Fourier%20Transform%20-%20A%20Visual%20Introduction.ipynb

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Animations largely made using manim, a scrappy open-source python library. https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

Final Fantasy Tactics Complete Soundtrack

Subscribe for more: http://tiny.cc/exj1tz

Music from the video game Final Fantasy Tactics from 1998, by Square
Music by Hitoshi Sakimoto and Masaharu Iwata.

If you liked this video please, subscribe, like, comment and SHARE! :)

Tracklist:

[Disc One]

1. Bland Logo ~ Title Back (0:00)
2. Backborn Story (1:08)
3. P. R. Movie (2:41)
4. Unit Introductions (3:27)
5. Player Creation (7:16)
6. Prologue Movie (9:01)
7. Chapel (11:53)
8. Enemy Attack (12:51)
9. Trisection (13:49)
10. Cadets (16:24)
11. Attack Team (18:19)
12. Unavoidable Battle (19:06)
13. Mission Complete (20:49)
14. Hero's Theme (21:12)
15. A Chapel (22:22)
16. Meeting with Algus (24:54)
17. World Map (26:57)
18. Shop (27:50)
19. Soldier Office (28:44)
20. Pelt, Bone, and Meat Trader (29:45)
21. Formation Screen (30:39)
22. Brave Story (31:35)
23. Pub (32:52)
24. Data Screen (33:54)
25. Desert Land (34:49)
26. Alma's Theme (37:38)
27. Suspicious Atmosphere (38:48)
28. Decisive Battle (40:41)
29. Cry of Pain (43:04)
30. Remnants (43:58)
31. Anxiety before the Battle (47:01)
32. Tension 1 (49:02)
33. Game Over (51:41)
34. Tutorial (52:03)
35. Random Waltz (54:11)
36. Ovelia's Theme (56:03)
37. Apoplexy (58:43)
38. Zalbag, the Holy Knight (1:02:51)
39. Run Past Through the Plain (1:04:53)
40. Strategy (1:06:48)
41. Delita's Theme (1:09:29)
42. Back Fire (1:11:11)

[Disc Two]

1. Memories (1:14:11)
2. Dycedarg's Theme (1:15:53)
3. Antipyretic (1:17:20)
4. Saint Ajora's Theme (1:20:59)
5. Bloody Excrement (1:23:50)
6. And I Ran Away (1:26:34)
7. Espionage (1:27:00)
8. Advent (1:29:23)
9. Ovelia's Anxiety (1:32:44)
10. Under the Stars (1:36:24)
11. Battle on the Bridge (1:39:39)
12. The Cardinal's Anger (1:43:07)
13. In Pursuit (1:45:47)
14. Shock!! ~ Despair (1:48:18)
15. Saint Ajora's Theme Deluxe (1:50:36)
16. Cry of Pain! (1:51:44)
17. Requiem (1:54:22)
18. Terror 1 (1:57:33)
19. The Pervert (1:59:38)
20. Antidote (2:03:29)
21. Thunder God Cid's Theme (2:06:39)
22. Treasure (2:08:29)
23. Night Attack (2:11:14)
24. Terror 2 (2:14:03)
25. Ultema, the Nice Body (2:16:03)
26. Ultema, the Perfect Body (2:18:20)
27. Final Battle Fanfare (2:21:46)
28. Epilogue Movie (2:22:01)
29. Staff Credits (2:23:36)

...