Due to ContinuousWaveletTransform[...] I can obtain information about wavelet-coefficient for example
sampleRate = 2^7*100/84.08964152537143`; tMin = 0; tMax = 10; analyzedFunction[t_] = Sin[t*2 \[Pi]] - Sin[4 t*2 \[Pi]]; data = Table[analyzedFunction[t], {t, tMin, tMax, 1/sampleRate}]; cwd = ContinuousWaveletTransform[data, MorletWavelet[], SampleRate -> sampleRate]; Further how I can visualizate spectral wavelets-information? I would like to draw three graphs: distribution of modus, phase, and the evolution of local maxima of modus.
Using ListDensityPlot[...]
ListDensityPlot[Abs[cwd[[1]]], Frame -> True, LabelStyle -> {Black, FontFamily -> "Times New Roman", FontSize -> 14}, ColorFunction -> (ColorData[{"GrayTones", "Reverse"}]), AspectRatio -> 1/2, PlotLegends -> Automatic] ListDensityPlot[ArcTan[Im[cwd[[1]]]/Re[cwd[[1]]]], Frame -> True, LabelStyle -> {Black, FontFamily -> "Times New Roman", FontSize -> 14}, ColorFunction -> (ColorData[{"GrayTones", "Reverse"}]), AspectRatio -> 1/2, PlotLegends -> Automatic] We may obtain only qualitative graphics without scale. How we can restore a corresponding axes scale to plot wavelet scalogram and phase disribution in common unit (time-frequency)? Moreover frequency-axis should be in Log-scale.
Perheaps there is another way to plot wavelet phase distribution - but I don't know about that.
Another Question is plotting wavelet skeleton. That is a line of local maxima of specral distribution in each time.
For this example data that is only two lines on 1 and 4 Hz.
Related topics (as I think)
How to increase Spectrogram resolution?
Extracting information from the result of ContinuousWaveletTransform
How to do the log scale plot for ListContourPlot
Why I not want use standart WaveletScalogram[...] - this function graph normalized wavelet coefficient modus, not absolute values.
Compare numerical values:
WaveletScalogram[cwd, Frame -> True, LabelStyle -> {Black, FontFamily -> "Times New Roman", FontSize -> 14}, ColorFunction -> (ColorData[{"GrayTones", "Reverse"}]), AspectRatio -> 1/2, PlotLegends -> Automatic] ListDensityPlot[Abs[cwd[[1]]], Frame -> True, LabelStyle -> {Black, FontFamily -> "Times New Roman", FontSize -> 14}, ColorFunction -> (ColorData[{"GrayTones", "Reverse"}]), AspectRatio -> 1/2, PlotLegends -> Automatic] But in a good case, of course we would like to have exactly the same appearance graph.
