MorletWavelet
represents a Morlet wavelet.
Details
- MorletWavelet defines a family of non-orthogonal wavelets.
- The wavelet function (
) is given by 
. - MorletWavelet can be used with such functions as ContinuousWaveletTransform, WaveletPsi, etc.
Examples
open all close allBasic Examples (1)
Scope (1)
MorletWavelet is used to perform ContinuousWaveletTransform:
data = Table[Sin[100 t^2], {t, 0, 1, 1. / 2000}];cwt = ContinuousWaveletTransform[data, MorletWavelet[], {Automatic, 16}, Padding -> 0.0, SampleRate -> 2000]Use WaveletScalogram to get a time scale representation of wavelet coefficients:
WaveletScalogram[cwt]Use InverseWaveletTransform to reconstruct the signal:
ListLinePlot[{data, InverseContinuousWaveletTransform[cwt]}]Properties & Relations (3)
MorletWavelet is similar to GaborWavelet with a certain frequency:
ω0 = N[πSqrt[(2/Log[2])]];Plot[{WaveletPsi[MorletWavelet[], x], Re@WaveletPsi[GaborWavelet[ω0], x]}, {x, -5, 5}, PlotStyle -> {{Red, Dashed}, Blue}, PlotRange -> All]Wavelet function and its Fourier transform:
ψ = WaveletPsi[MorletWavelet[], x]Plot[ψ , {x, -5, 5}, PlotRange -> All, Frame -> True, GridLines -> Automatic]Overscript[ψ, ^ ] = FourierTransform[ψ, x, ω, FourierParameters -> {0, -2Pi}]//FullSimplifyPlot[Overscript[ψ, ^ ], {ω, -3, 3}, PlotRange -> All]MorletWavelet does not have a scaling function:
WaveletPhi[MorletWavelet[], x]Text
Wolfram Research (2010), MorletWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/MorletWavelet.html.
CMS
Wolfram Language. 2010. "MorletWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MorletWavelet.html.
APA
Wolfram Language. (2010). MorletWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MorletWavelet.html