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In Noisy Equations, One Who Heard Music (2014)
- d0mdo0ss 6y agoFTA: "... 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__ 6y agoA 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 6y agoWavelets 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.
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- chewbaxxa 6y agoYour comment is grey, but I think you’re right.
- nyanpasu64 6y ago> 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.