# Wavelet Data Visualization (modus and phase) ListPlot [closed]

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[]], Frame -> True,
LabelStyle -> {Black, FontFamily -> "Times New Roman",
FontSize -> 14},
ColorFunction -> (ColorData[{"GrayTones", "Reverse"}]),
AspectRatio -> 1/2, PlotLegends -> Automatic]

ListDensityPlot[ArcTan[Im[cwd[]]/Re[cwd[]]], 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[]], 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.

## closed as off-topic by MarcoB, dr.blochwave, user9660, m_goldberg, JensMar 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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