Available Wavelet Families

ContWave{Boundary,T}

The abstract type encompassing the various types of wavelets implemented in the package. The abstract type has parameters Boundary<:WaveletBoundary and T<:Number, which gives the element output type. Each has both a constructor, and a default predefined entry. These are:

• Morlet: A complex approximately analytic wavelet that is just a frequency domain Gaussian with mean subtracted. Morlet(σ::T) where T<: Real. σ gives the frequency domain variance of the mother Wavelet. As σ goes to zero, all of the information becomes spatial. Default is morl which has $\sigma=2\pi$.

  $\psi\hat(\omega) \propto \textrm{e}^{-\frac{\sigma^2}{2}}\big(\textrm{e}^{-(\sigma - \omega)^2} -\textrm{e}^{\frac{\omega^2-\sigma^2}{2}}\big)$

• Paul{N}: A complex analytic wavelet, also known as Cauchy wavelets. pauln for n in 1:20 e.g. paul5

  $\psi\hat(\omega) \propto \chi_{\omega \geq 0} \omega^N\textrm{e}^{-\omega}$

• Dog{N}: Derivative of a Gaussian, where N is the number of derivatives. dogn for n in 0:6. The Sombrero/mexican hat/Marr wavelet is n=2.

  $\psi\hat(\omega) \propto \omega^N\textrm{e}^{-\frac{\omega^2}{2}}$

• ContOrtho{OWT}. OWT is some orthogonal wavelet of type OrthoWaveletClass from Wavelets.jl. This uses an explicit construction of the mother wavelet for these orthogonal wavelets to do a continuous transform. Constructed via ContOrtho(o::W) where o is from Wavelets.jl. Alternatively, you can get them directly as ContOrtho objects via:

  • cHaar Haar Wavelets
  • cBeyl Beylkin Wavelets
  • cVaid Vaidyanathan Wavelets
  • cDbn Daubhechies Wavelets. n ranges from 1:Inf
  • cCoifn Coiflets. n ranges from 2:2:8
  • cSymn Symlets. n ranges from 4:10
  • cBattn Battle-Lemarie wavelets. n ranges from 2:2:6