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Questions tagged [wavelet-analysis]

Questions on the wavelet analysis functions of Mathematica.

See Wavelet Analysis for Mathematica functions related to wavelets. See Defining Your Own Wavelet if you want to implement a wavelet that is not currently supported by Mathematica. Consider using the tags , , and/or whenever appropriate.

70 questions
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Detecting spikes by shrinking WaveletPacket basis using a specific threshold

Last time, I asked how I can use the command DiscreteWaveletPacketTransform[data, filter, 0] for spike detection and I got answers mostly based on an automatically defined threshold. In my case it is crucial to first define a threshold to…
K-1
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Continuous wavelet transform with complex Morlet function

The complex Morlet function is defined as: $$Ψ(t,f_c,f_b)= \frac{1}{\sqrt[]{ \pi f_{b} } }\exp(-t^2/f_b)\exp(\jmath 2πf_ct)$$ where $f_b$ and $f_c$ are two important parameters in modifying the complex Morlet wavelet. It seems that Mathematica…
SAH
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Is there a way to add a cone of influence to waveletscalogram?

This question was asked in 2013, but didn't get an answer. Can Mathematica plot the cone of influence in wavelet analysis. Matlab will do it. Follow up question. Does it make good mathematical sense to show the cone of influence?
Chris
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5
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2 answers

Getting rid of "glitches" in DiscreteWaveletTransform-de-noised data

Typical glitch Dear all, I have been using discrete wavelet transforms for de-noising simulated (and real) radiation counting data and from time to time encounter "glitches" in the resulting de-noised data. An example is shown above. Does anyone…
DMWood
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5
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1 answer

InverseWaveletTransform not recreating the original image exactly

I am trying to do DWT steganography. I first obtain the DiscreteWaveletTransform of the image as follows dwd = DiscreteWaveletTransform[carrierImage, HaarWavelet[], 1] (* Out: DiscreteWaveletData[<< DWT >>, < 1 >, {256, 256}] *) This splits the…
Ramya Mendharkar
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4
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1 answer

Wavelet expansion of given function (as opposed to DWT of given data)

To illustrate, say I take the following function (the reason for the square root will be apparent soon) dist = NormalDistribution[0.5,0.1]; f[x_] := Sqrt[PDF[dist,x]]; Then I can grab the Haar wavelet to calculate coefficients like data =…
carlosayam
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How to define a new wavelet type?

I have a problem in understanding how to create my own wavelets in Mathematica's wavelet framework. There is a tutorial. I have read the tutorial, but I don’t understand what exactly is needed to define my own wavelet type. I tried to implement a…
Dan
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3
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1 answer

Wavelet filter artifact

I would like to denoise some data using wavelet filters. My current approach is to employ the stationary wavelet transform with Haar wavelets. However, this leads to undesirable artifacts at the top and bottom boundary of the dataset, as you can…
Oscillon
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2
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1 answer

LiftingWaveletTransform with irregular grids

One of the properties mentioned in the literature about the lifting wavelet transform is that it can be applied on irregular meshes or grids (i.e. not equally spaced samples); but I don't seem to see that as an option in LiftingWaveletTransform. Any…
carlosayam
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Is wavelet a Nonlinear transform, or Not?

Is wavelet a Nonlinear transform, or Not? specifically, continuous wavelet transform with morlet function. I am studying behavior of a dynamic system, and it has nonlinear behaviour. can I employ wavelet transform?
SAH
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Modified WaveletImagePlot

When performing Wavelet Transform img = ExampleData[{"TestImage", "Lena"}]; dwd = DiscreteWaveletTransform[img, HaarWavelet[], 2] WaveletImagePlot[dwd] I get the plot: But I want to subdivide image 4 instead of image 1 -- any ideas ?
Ramya Mendharkar
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Problem with DiscreteWaveletTransform for DaubechiesWavelet

I am trying to use Mathematica's wavelet transform. In preparation I entered: n = 8 Clear[dataTest] dataTest = Table[0, {n}] For [i = 1, i < n + 1, i++, dataTest[[i]] = i; ] dataTest wave2 = DaubechiesWavelet[2] dwd =…
cadri
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2 answers

InverseWaveletTransform of a list of rules

I want to extract coefficient images from a DiscreteWaveletTransform and replace them by modified images of the same dimensions. However, when I use DiscreteWaveletData without specifying the input image dimensions the dimension of the…
Lex Toet
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1 answer

Calculate support of given wavelet

I am calculating approximations using wavelets but outside the multi resolution analysis framework; particularly, I am not using the built-in wavelet transforms. Still, I need to calculate coefficients and therefore I am wondering how to calculate…
carlosayam
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How to recover data from a DiscreteWaveletTransform with Battle-Lemarie Wavelets?

The question is why can data be recovered perfectly from a discrete wavelet transform with a Haar wavelet but not with some Battle-Lemarie wavelets? A simple example with the HaarWavelet[]: data3 = Table[Random[Real, 10], {k, 30}] {0.702135,…
Dan
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