The Most Underrated Algorithm

What Hacker News said

Strong rec kevlened · 2022-11 · on “Demystifying Fourier analysis”

The 2-minute brute-force explanation of Fourier transforms in a recent Veritasium video was my "aha!" moment. [this video]

Strong rec kippinitreal · 2023-01 · on “Ask HN: Concepts that clicked only years after you first encountered them?”

That video did the same for me. I also like the reducible video for Fast Fourier Transforms as well as the Veratasium piece that shares some fun history. Reducible - FFTs the most ingenious algorithm ever [LINK] Veritasium - The Most Important Algorithm of All Time [this video]

Recommends yunruse · 2022-11 · on “I over-engineered a Fast Fourier Transform for Arduino”

If you have 26 minutes spare, Veritaserum's video [0] on the history of FTs and FFTs is quite good. Effectively, a Fourier Transform can turn a signal into its underlying frequencies using a neat property of maths. For a piece of music, say, you could produce a spectrogram [1] – Foobar2000 [2] has a nice one built in – to visualise the frequency of music with time. In general, this is all sorts of useful applications any time you have a signal – electronics, climate physics, astrophysics, detecting nuclear explosion testing underground, and so on. It's essential to modern medical imaging, and a whole bunch of differential equations can be solved a lot faster by using this. The FFT takes the

Recommends psychphysic · 2022-12 · on “Fascinating Interview with Martin Hellman of Diffie-Hellman Fame (2004)”

You might also like this recent Veritasium video on the link between the Nuclear test ban treaty and FFT. [this video]

Recommends ourmandave · 2023-01 · on “The Fourier Transform, explained in one sentence”

Veritasium has an explainer of the Fast Fourier Transform on youtube. From how it's used and an interest history. [this video]

Cites watersb · 2022-11 · on “What is interferometry?”

I recommend learning about the Fourier Transform, and then peeking at how frequency transformations are used to represent everyday images, like the Cosine Transform used in JPEG. 3 blue 1 brown FFT: [LINK] JPEG components [LINK] I worked at the Very Large Array radio telescope for a while, and even so the language didn't click for me until I thought about the signal transforms that have become ubiquitous in everyday life. And a co worker described the telescope as a double-slit experiment, with multiple 2-D holes instead of slits; imagine the interference pattern that you get when you have multiple slits. The elements of an interferometer are the "slits", but they are receiving the light rat

Cites graycat · 2024-04 · on “Not so fast, Mr. Fourier”

Consider ordinary 3 dimensional space: Go to a corner of the room, where the floor and two walls meet, and see three lines, each line the intersection of the two walls or a wall and the floor. In usual building architecture, these three lines are mutually perpendicular, i.e., orthogonal . Regard each of these three lines as an axis of a coordinate system. In particular, pick a point on each of the three axes to give us points with coordinates: (1,0,0) -- the X axis (0,1,0) -- the Y axis (0,0,1) -- the Z axis Soooo, now we have a standard coordinate system for ordinary 3 dimensional space. Now consider a point P in the room (in my case, the end of the pony tail of that sweet, gorgeous blond I

Cites AndrewOMartin · 2024-07 · on “The Fourier Transform: What's Wrong with It?”

I saw this one a while ago. [this video] - The Remarkable Story Behind The Most Important Algorithm Of All Time In summary, FFT is just a "dynamic programming" version of Fourier Transforms, in that it's the same idea, just with avoiding repeating a lot of duplicated calculations.