In Noisy Equations, One Who Heard Music (2014)

Re:In Noisy Equations, One Who Heard Music (2014) by d0mdo0ss on Friday September 11, 2020 @05:11PM (#24447354)

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

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Re:In Noisy Equations, One Who Heard Music (2014) by mhh__ on Friday September 11, 2020 @05:20PM (#24447422)

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

https://en.wikipedia.org/wiki/Wavelet

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Re:In Noisy Equations, One Who Heard Music (2014) by TheOtherHobbes on Friday September 11, 2020 @07:40PM (#24448500)

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.

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Re:In Noisy Equations, One Who Heard Music (2014) by chewbaxxa on Saturday September 12, 2020 @10:15AM (#24452613)

Your comment is grey, but I think you’re right.

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