UCD4IDS / ContinuousWavelets.jl

wide array of continuous wavelet transforms using Julia
https://dsweber2.github.io/ContinuousWavelets.jl/dev/
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Simple access to a wavelet ? #47

Open SimonCoste opened 1 year ago

SimonCoste commented 1 year ago

Hi, is there any simple way to directly access any wavelet as a function ? For example,

m = Morlet()
m(0.5) # should output the value of the Morlet wavelet at the point 0.5.

Thanks ! Simon

dsweber2 commented 1 year ago

So there currently isn't a way to directly get the space domain of just the unscaled mother, as they're mostly represented internally in the Fourier domain. If you're looking for plotting purposes (e.g. the ones on the readme landing page), there's a space domain representation ψ given by

m = Morlet()
ψ, ω = computeWavelets(n, m; space = true)

though to get the values its computed at, you'd also have to convert the frequency ω to time.

I think probably the "proper" way to do this would be include the analytic version of the space domain, which in principle isn't too hard. Though the orthogonal wavelets, with their recursive definition, would be more involved.