
In Noisy Equations, One Who Heard Music (2014) - _Microft
https://www.quantamagazine.org/hearing-music-in-noise-martin-hairer-wins-the-fields-medal-20140812/
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nyanpasu64
> He suddenly realized that he could tame the distributions in SPDEs using an
> approach modeled on the mathematical properties of “wavelets” — brief,
> heartbeatlike oscillations that encode information in JPEG and MP3 files.

Wavelets are not used in JPEG or MP3 files. They're used in JPEG 2000 and
video codecs like Dirac, which have failed to outperform DCT-based codecs like
JPEG and MP3 and h.264.

Most of this article flew over my head though.

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d0mdo0ss
FTA: "... any wavelet can be reconstructed by adding together a finite series
of identical wavelets squashed to fractions of its initial width: a half, then
a fourth, then an eighth and so on."

I may not follow or there's a typo above. Should the first 'wavelet' be
replaced with function/signal/distribution/etc? this sounds a lot like a
taylor or fourier analysis

~~~
mhh__
A wavelet is a well-defined mathematical idea, not a euphemism for any old
function.

[https://en.wikipedia.org/wiki/Wavelet](https://en.wikipedia.org/wiki/Wavelet)

~~~
TheOtherHobbes
Wavelets are basically a generalisation of Fourier with an arbitrary basis
function which can be selected to highlight/match specific features in the
data.

They've been used in image filtering for a long time. I remember a wavelet-
based grain removal and denoising plugin for Photoshop from around 15 years
ago.

In this work I suspect that trying to implement wavelets in an audio editor -
which generates some useful but slightly quirky representations and editing
options - cued the realisation they could be applied to stochastic PDEs.

