But what is the Fourier Transform? A visual introduction.

This is an explanation (from the amazing three blue one brown) of the DFT not the DCT, but this was the first thing that ever really made sense to me. It is explained by someone who really knows math incredibly well and is an amazing teacher, with amazing visuals: ▶ this video

in “Discrete Cosine Transform in Video Compression – Explain Like I'm Five” · View on HN

I found the 3Blue1Brown explanation to be more intuitive to understand, but this article has more practical examples/details. Here's the 3Blue1Brown explanation: ▶ this video [link]

in “What Is the Fourier Transform?” · View on HN

(Almost-)linear models do linear things, it seems, and the Fourier transform is the quintessential linear thing. It is also an extremely neat piece of the real world, but I’m hesitant to guess your background and offer an explanation because your phrasing makes me suspect an engineering one. With concepts usually being the first to be culled in a course targeted at engineers, there could be quite a bit of concept debt to pay off before I could really offer something I could honestly call an explanation. Have you tried the 3Blue1Brown video on the topic[1]? It does not AFAIR offer any answers as to why the Fourier transform should exist or be useful, but it does show very well what it does in the immediate sense. [1] ▶ this video

in “Pre-Trained Large Language Models Use Fourier Features for Addition (2024)” · View on HN

Just a nit. The pair of equations the author showed at the beginning of the article are not the equations of the Fourier Transform and its inverse. The Transform is a continuous function operating on an infinite input. The equation for the Transform involves the use of the integral taken over +/- infinity. What is shown, using the summation operator, is a discrete form on the Transform where the input is a limited time series. A good alternative explanation can be found on Grant Sanderson's 3 Blue 1 Brown channel ▶ this video

in “An Interactive Guide to the Fourier Transform” · View on HN

There's no all in one stop for understanding radio but these 5 resources helped me a lot. The RF Get Down courses. This is by far the best material online to learn RF and how modulation works: [link] 3blue1brown's video tutorial on the fourier transform: ▶ this video AT&T Archives: Similiarities of Wave Behavior [link] Quadrature Signals: Complex, But Not Complicated by Richard Lyons, [link] [link] Antenna Theory's website and forums, [link] I also highly recommend getting a $20 rtl-sdr USB software defined radio dongle. They're great toys for learning RF, what modulation is , and exploring the spectrum.

in “What Is Radio Spectrum?” · View on HN

If the part about the tack on the board under the clocks wasn't clear, and you're a visual learner, this video from 3Blue1Brown about the [classic] Fourier Transform might help clarify the relationship to periodicity: ▶ this video

in “Shor, I’ll do it (2007)” · View on HN

What about the 3 blue 1 brown video on it? I think that is pretty concise and intuitive too but does not seem to appear on this thread ▶ this video

in “An Interactive Guide to the Fourier Transform (2012)” · View on HN

3blue1brown is great, e.g. his Fourier transform animation is super intuitive: ▶ this video He has opensourced his animation engine "manim" used in his videos: [link]

in “Show HN: SHA-256 Animation” · View on HN

I recommend watching the "But what is the Fourier Transform? A visual introduction." ▶ this video . Beautiful.

in “The “Windmill” Problem on the 2011 International Mathematical Olympiad [video]” · View on HN

3Blue1Brown has an extremely good explanation[1] of the intrinsic uncertainty, and why it's separate from measurement uncertainty. (the previous episode[2] is a recommended prerequisite for background on how the Fourier Transform works) > emerges through a different, as yet unknown, mechanism. In 3Blue1Bron's explanation[1], he shows how the intrinsic uncertainty is an inherent trade-off of trying to measure both position and frequency. A short wave packet only a few wavelengths long correlates with a narrow (precise) range of positions, but also correlates well with a very wide range of frequencies due. A Heisenberg-like uncertainty exists any time you are working with weave packets with length near the wavelength. 3Blue1Brown gives a very good example using Doppler radar. [1] [link] [2] ▶ this video

in “Why have so many physicists shrugged off the paradoxes of quantum mechanics?” · View on HN

This is a combination of things that almost breaks my brain, but it works, and it's brilliant! First, you need to understand coded masks[1,2]. This is a way to use an LCD or other array to mask off parts of a scene so that very specific parts of it are sampled, but the rest aren't, to get a single, high resolution analog value. Then you switch to other masks, and get more values. You can then work backwards in the math through the known mask shapes, to get the original image with far fewer samples that would be required one at a time. Think of the above as a 2d visual version of the Fourier transform[3,4]. This transform is used heavily to compress images throwing away most of the bits in an image without losing it's essence. The analysis they're talking about uses a very specially printed card. It isn't just something generated with a standard 4 ink printer, each "dot" is a separate unique ink with tightly controlled spectral curves, these form a virtual version of the above masks. When you view these through a sample, it can then give an idea of the spectral response of the camera, and the liquid, by using the many different known response curves of the "dots" to work backwards, and generate the 1 dimensional very tight response curve of a hyperspectral imager, by figuring out where each "dot" is in the scene, then averaging that dot's intensity across the RGB values of the picture taken by the camera. Today's cameras have sufficient resolution and bit depth that you get th

in “Smartphone Cameras Go Hyperspectral” · View on HN

Because it's a fast way to get that interactivity, rather than having to explicitly code it yourself. A good example are modern math videos on youtube, like this one (not saying that they're using G9.js in particular): ▶ this video It's 20 minutes of changing graphics. You could code all of that with P5, and it would be an excruciatingly long process. G9.js would get you there in a fraction of the time.

in “G9.js: Automatically Interactive Graphics” · View on HN

This is one of the few people who connects math and music in a way that's both useful and interesting. I followed this channel back when I found the video on Fourier transforms[1], but never looked at other videos. I've never really thought about the math of consonance and dissonance, but I use it all the time without realizing it. For example: a hypersaw. That's 7 saws slightly detuned played at the same time. The more you detune them, the worse it sounds. If you own Serum, you can hear this in realtime if you make a 7 voice saw and play with the detune knob. You can use an LFO to modulate this and get a sound that's a little uneasy while still somehow being harmonious. It's perfect for dark/spooky music. [1] ▶ this video

in “Music and Measure Theory (2015) [video]” · View on HN

Ted Nelson's Computers for Cynics probably doesn't contain technical information that's new to any of you, but Ted has a knack for reframing things in ways that make the arbitrariness of certain historical decisions clear: [link] On the subject of hypertext, The Web That Wasn't gives a nice history of the idea (for anybody who thinks it starts with TBL -- surprisingly many people!): [link] Another reframing-oriented talk is Clay Shirky's "It's not information overload, it's filter failure", which ultimately leads to Shirky suggesting the kinds of user-oriented filtering features that Mastodon has implemented: [link] At the intersection of neurology and information science, Peter Watts always has something interesting to say, and as a former marine biologist focusing on the nervous system of starfish, this is absolutely in his wheelhouse: [link] This one ("moving away from defensive programming") justified strong typing in a pretty clear way: [link] Dan Dennett is just as relevant as Doug Hofstadter when it comes to metacognition: [link] Forgotten Ideas in Computer Science starts slow, but if you don't have much of a historical background (like, if you're only vaguely aware of what happened in CS in the 70s), it's a laundry list of things you should look up and be aware of before you start your next project: [link] Everybody should understand procedural generation: [link] Likewise, since AI is hyped up right now, we should all remind ourselves that IA is a thing too: [link] Mo

in “Ask HN: What is your favourite tech talk?” · View on HN