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dsweber2
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.github/workflows/docsBuild.yml

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- docs/*
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- Project.toml
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jobs:
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docs:
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name: Documentation
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runs-on: ubuntu-latest
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steps:
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- uses: actions/checkout@v2
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- uses: julia-actions/setup-julia@latest
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with:
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version: '1.6'
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- name: Install dependencies
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run: |
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sudo apt install libxt6 libxrender1 libxext6 libgl1-mesa-glx libqt5widgets5
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- run: |
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julia --project=docs -e '
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using Pkg
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Pkg.instantiate()
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Pkg.develop(PackageSpec(path=pwd()))
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Pkg.instantiate()'
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- name: Build and deploy
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run: julia --project=docs docs/make.jl
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env:
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GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
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DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }}
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name: Documentation
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runs-on: ubuntu-latest
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steps:
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- uses: actions/checkout@v2
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- uses: julia-actions/setup-julia@latest
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with:
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version: '1.6'
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- name: Install dependencies
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run: |
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sudo apt install libxt6 libxrender1 libxext6 libgl1-mesa-glx libqt5widgets5
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run: |
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julia --project=docs -e '
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using Pkg
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Pkg.instantiate()
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Pkg.develop(PackageSpec(path=pwd()))
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Pkg.instantiate()'
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- name: Build and deploy
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env:
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GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
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DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }}
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run: julia --project=docs --code-coverage=user docs/make.jl
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- uses: julia-actions/julia-processcoverage@v1
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- uses: codecov/codecov-action@v1

README.md

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[![Build Status](https://travis-ci.com/dsweber2/ContinuousWavelets.jl.svg?branch=master)](https://travis-ci.com/dsweber2/ContinuousWavelets.jl)
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[![Coverage](https://codecov.io/gh/dsweber2/ContinuousWavelets.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/dsweber2/ContinuousWavelets.jl)
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[![](https://img.shields.io/badge/docs-dev-blue.svg)](https://dsweber2.github.io/ContinuousWavelets.jl/dev/)
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This package is an offshoot of [Wavelets.jl](https://github.com/JuliaDSP/Wavelets.jl) for the continuous wavelets.
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Thanks to [Felix Gerick](https://github.com/fgerick) for the initial implementation there, with extension and further adaptation by David Weber and any other contributors listed on the right.
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Currently, it implements 1D continuous wavelet transforms with the following mother wavelets:

docs/make.jl

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using Documenter, ContinuousWavelets
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ENV["GKSwstype"] = "100"
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makedocs(sitename="ContinuousWavelets.jl",
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format=Documenter.HTML(),
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authors="David Weber",
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clean=true,
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pages=[
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"basic usage" => "index.md",
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"Install" => "installation.md",
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"CWT" => [
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"Available Wavelet Families" => "coreType.md",
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"CWT Construction" => "CWTConstruction.md",
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"Wavelet Spacing" => "spacing.md",
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"Wavelet Frequency Spacing" => "spacing.md",
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"Boundary Conditions" => "bound.md",
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"Inversion" => "inverse.md"
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],

docs/src/CWTConstruction.md

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# CWT type
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# CWT Construction
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```@docs
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CWT
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ContinuousWavelets.wavelet(::WC) where {WC<:ContinuousWavelets.ContWaveClass}
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In more detail, the parameters, along with their defaults, are:
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+ `wave::ContWaveClass`: is a type of continuous wavelet, see the [Available Wavelet Families](@ref).
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+ `scalingFactor`, `s`, or `Q::Real=8.0`: the number of wavelets between the octaves ``2^J`` and ``2^{J+1}`` (defaults to 8, which is most appropriate for music and other audio). Valid range is $(0,\infty)$.
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+ `β::Real=4.0`: As using exactly `Q` wavelets per octave leads to excessively many low-frequency wavelets, `β` varies the number of wavelets per octave, with larger values of `β` corresponding to fewer low frequency wavelets(see [Wavelet Spacing](@ref) for details).
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+ `β::Real=4.0`: As using exactly `Q` wavelets per octave leads to excessively many low-frequency wavelets, `β` varies the number of wavelets per octave, with larger values of `β` corresponding to fewer low frequency wavelets(see [Wavelet Frequency Spacing](@ref) for details).
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Valid range is $(1,\infty)$, though around `β=6` the spacing is approximately linear *in frequency*, rather than log-frequency, and begins to become concave after that.
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+ `boundary::WaveletBoundary=SymBoundary()`: The default boundary condition is `SymBoundary()`, implemented by appending a flipped version of the vector at the end to eliminate edge discontinuities. See [Boundary Conditions](@ref) for the other possibilities.
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+ `averagingType::Average=Father()`: determines whether or not to include the

docs/src/bound.md

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# Boundary types #
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# Boundary Conditions #
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```@docs
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WaveletBoundary

docs/src/coreType.md

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# Wavelet types
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# Available Wavelet Families
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There are two tiers of wavelet types in this package. The most abstract is the `ContWave` type, representing a class of wavelets.
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This is split into several strictly continuous wavelets, and a `ContOrtho<:ContWave` type, which is a supertype of continuous versions of the orthogonal wavelets defined in [Wavelets.jl](https://github.com/JuliaDSP/Wavelets.jl).
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```@docs
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using ContinuousWavelets, Plots, Wavelets, FFTW, Logging
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using Plots; gr()
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Plots.reset_defaults()
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global_logger(Logging.SimpleLogger(stderr,Logging.Error))
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n= 2047;
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function mapTo(waveType, isReal=true,window=1:2047; d=1, kwargs...)
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if isReal

docs/src/index.md

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# ContinuousWavelets Documentation #
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Originally included in Wavelets.jl, this is a fork containing the types and
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methods specifically for doing continuous wavelet transforms. Current methods
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only include 1D wavelet transforms and their inverses.
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Originally included in Wavelets.jl, this is a fork containing the types and methods specifically for doing continuous wavelet transforms. Current methods only include 1D wavelet transforms and their inverses.
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The basic structure is similar to that of Wavelets.jl; first you choose one of
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the ![Wavelet types](@ref) of the `ContWaveClass` type, e.g. `Morlet(2π)`.
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Then you set the general transform parameters by constructing a ![CWT
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type](@ref), which specifies such properties as whether to average,
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the scaling rate, or the boundary conditions. Finally, you perform the actual
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transform with`cwt`.
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The basic structure is similar to that of Wavelets.jl; first you choose one of the [Available Wavelet Families](@ref) of the `ContWaveClass` type, e.g. `Morlet(2π)`.
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Then you set the general transform parameters via [CWT Construction](@ref), which specifies such properties as whether to average, the scaling rate, or the boundary conditions.
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Finally, you perform the actual transform with`cwt`.
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```@example basicEx
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using Plots; gr(); #hide
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Plots.reset_defaults(); #hide
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using ContinuousWavelets, Plots, Wavelets, FFTW
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using Logging #hide
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global_logger(Logging.SimpleLogger(stderr,Logging.Error)) #hide
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n=2047;
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f = testfunction(n, "Doppler");
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p1=plot(f,legend=false,title="Doppler",xlims=(0,2000));
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c = wavelet(Morlet(π), averagingType=NoAve(), β=2);
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res = cwt(f, c)
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res = ContinuousWavelets.cwt(f, c)
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p2=heatmap(abs.(res)', xlabel= "time index",
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ylabel="frequency index",colorbar=false);
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l=@layout [a{.3h};b{.7h}]

docs/src/inverse.md

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using ContinuousWavelets, Plots, Wavelets, FFTW, Logging
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using Plots; gr()
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Plots.reset_defaults()
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global_logger(Logging.SimpleLogger(stderr,Logging.Error))
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```
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# Wavelet Inversion #
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The continuous wavelet transform is a redundant shift-invariant frame transform. As such, there isn't a single inverse transform, although there is a canonical pseudo-inverse. For more see, for example, chapter 5 of [A Wavelet Tour of Signal Processing](https://wavelet-tour.github.io/).

docs/src/spacing.md

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# Wavelet Frequency spacing #
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# Wavelet Frequency Spacing #
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Frequently, using a fixed ratio for scaling the wavelets results in too many large scale wavelets.
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There are several ways of dealing with this; in this package, the scaling factors have the form $2^{a(mx+x_0)^{^1/_\beta}}$, for suitable choice of $a$,$m$, $x_0$, and $\beta$.
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The user chooses $\beta$ and $Q$, and the rest are chosen to match the derivative at the last frequency to be $^{1}/_{Q}$, as in the figure.
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using ContinuousWavelets, Plots, Wavelets, FFTW, LaTeXStrings, Logging
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using Plots; gr();
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Plots.reset_defaults();
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global_logger(Logging.SimpleLogger(stderr,Logging.Error))
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dRate = 4
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waveType = Morlet()
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Ψ1 = wavelet(waveType, s=8, β =dRate, averagingLength=2)

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