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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.

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closed as off-topic by MarcoB, dr.blochwave, user9660, m_goldberg, Jens Mar 12 '16 at 18:15

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "The question is out of scope for this site. The answer to this question requires either advice from Wolfram support or the services of a professional consultant." – MarcoB, dr.blochwave, Community, Jens
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