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The unreasonable effectiveness of the Fourier transform

joshuawise.com

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Re: The unreasonable effectiveness of the Fourier transform

#101

Post by Rzor »

hedgehog wrote: post #33

Once you start looking at the world through the lens of frequency domain a lot of neat tricks become simple. I have some demo code that uses fourier transform on webcam video to read a heartrate off a person's face, basically looking for what frequency holds peak energy.

>Once you start looking at the world through the lens of frequency domain a lot of neat tricks become simple.

Not the first time I've heard this on HN. I remember a user commenting once that it was one of the few perspective shifts in his life that completely turned things upside down professionally.

Re: The unreasonable effectiveness of the Fourier transform

#102

Post by [deleted] »

pastrami_panda wrote: post #26
derektank wrote: post #23

My favorite story about the Fourier Transform is that Carl Friedrich Gauss stumbled upon the algorithm for the Fast Fourier Algorthim over a century before Cooley and Tukey’s publication in 1965 (which itself revolutionized digital signal processing).[1] He was apparently studying the motion of the asteroids Pallas and Juno and wrote the algorithm down in his notes but it never made it into public knowledge. [1] http…

Gauss's notes and margins is riddled with proofs he didn't bother to publish - he was wild. Not sure if true, but allegedy he insisted his son not go into maths, as he would simply end up in his father's shadow as he deemed it utterly Impossible to surpass his brilliance in maths :'D

[deleted]

Re: The unreasonable effectiveness of the Fourier transform

#104

Post by isolli »

hedgehog wrote: post #33

Once you start looking at the world through the lens of frequency domain a lot of neat tricks become simple. I have some demo code that uses fourier transform on webcam video to read a heartrate off a person's face, basically looking for what frequency holds peak energy.

There is also a loose analogy with finance: act (trade) when prices cross a certain threshold, not after a specific time.

Re: The unreasonable effectiveness of the Fourier transform

#105

Post by zipy124 »

derektank wrote: post #96
refulgentis wrote: post #78

Earlier quoted context omitted.

It’s unusual to tell others not to do something because you’re projecting they’re secretly doing it to compete with you, or that they’ll be depressed when they don’t do what you did. Doubly so when the rationale is “I’m so fucking awesome” Triply so when it’s something you’re passionate about, presumably inherently. Quadruply so when it’s your child. Its tough as a kid hearing your parents come up with elongated excu…

For what it’s worth, his children were quite successful by all accounts. Two of the boys became successful businessmen after emigrating to the US and one of the boys became a director of the railway network in Hannover. Seems as though they weren’t harmed by their upbringing.

I mean just like most scientists at the time Gauss was rather wealthy, so it is unsurprising they were fine.

Re: The unreasonable effectiveness of the Fourier transform

#106

Post by tgv »

greenwallnorway wrote: post #52
observationist wrote: post #18

Earlier quoted context omitted.

Unreasonable effectiveness is all you need.

I did some analysis on top title patterns. Both of these make the list pretty handily: https://projects.peercy.net/projects/hn-patterns/index.html

Funny. You might want to do that modulo capitalization, and perhaps some other common substitutions (LLM/LLMs/Large Language Model/Large Language Models, it's/ it is, what's/what is, I am/I'm), but they change the number of words, so better opt for the shortest alternative.

Re: The unreasonable effectiveness of the Fourier transform

#107

Post by zipy124 »

Chrupiter wrote: post #48
hedgehog wrote: post #33

Once you start looking at the world through the lens of frequency domain a lot of neat tricks become simple. I have some demo code that uses fourier transform on webcam video to read a heartrate off a person's face, basically looking for what frequency holds peak energy.

I don't think pulsing skin (due to blood flow) is visible from a webcam though.

It totally is. Look for motion-magnification in the literature for the start of the field, and then remote PPG for more recent work.

Re: The unreasonable effectiveness of the Fourier transform

#108

Post by rocqua »

So he explains OFDM in a way that implicitly does Amplitude shift keying.

I guess if you want to use different modulations you treat the complex number corresponding to the subcarrier as an IQ point in quadrature. So you take the same symbols, but read them off in the frequency domain instead of the time domain.

And I guess this works out quite equivalently to normally modulating these symbols at properly offset frequencies (just by the superposition principle)

Re: The unreasonable effectiveness of the Fourier transform

#109

Post by [deleted] »

zamadatix wrote: post #71
javawizard wrote: post #53

Earlier quoted context omitted.

Plenty of sources suggest it is: https://github.com/giladoved/webcam-heart-rate-monitor https://medium.com/dev-genius/remote-heart-rate-detection-us... The Reddit comments on that second one have examples of people doing it with low quality webcams: https://www.reddit.com/r/programming/comments/llnv93/remote_... It's honestly amazing that this is doable.

My dumb ass sat there for a good bit looking at the example in the first link thinking "How does a 30-60 Hz webcam have enough samples per cycle to know it's 77 BPM?". Then it finally clicked in my head beats per minute are indeed not to be conflated with beats per second... :). Non-paywalled version of the second link https://archive.is/NeBzJ

[deleted]

Re: The unreasonable effectiveness of the Fourier transform

#110

Post by srean »

libraryofbabel wrote: post #65
rcxdude wrote: post #57

Earlier quoted context omitted.

Well, in that time it was more or less how mathematics worked. It was a way of showing off, and often it would be a case of "Hey I've solved this problem, bet no-one else can". It was only later it became a lot more collaborative (and a bit more focused on publishing proofs).

You're correct that the culture of mathematics has changed a lot, and has become much more collaborative. The rise of the modern doctoral training system in Germany later in the 19th century is also relevant. So really Gauss's example points primarily to how much mathematics has changed. But at the same time, I think you could reasonably take Gauss to task even applying the standards of his own era - compare him with…

There's also this notion of holding themselves to their own standards.

They, Newton included, would often feel that their work was not good enough, that it was not completed and perfected yet and therefore would be ammunition for conflict and ridicule.

Gauss did not publicize his work on complex numbers because he thought he would attacked for it. To us that may seem weird, but there is no dearth of examples of people who were attacked for their mostly correct ideas.

Deadly or life changing attacks notwithstanding, I can certainly sympathize. There's not in figuring things out, but the process of communicating that can be full of tediousness and drama that one maybe tempted to do without.

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