Questions on the wavelet analysis functions of Mathematica.

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3
votes
1answer
83 views

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) ...
1
vote
1answer
85 views

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 ...
1
vote
1answer
84 views

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 ...
10
votes
3answers
293 views

Disentangling the data

An experiment yields a functional dependence on two variables $F(x,y)$, can be imagined as a 2D map. It is known that the function can be factored as follows $F(x,y)=fx(x) gy(y) +gx(x) fy(y)$. Given ...
4
votes
3answers
838 views

Signal processing by means of WaveletTransform

I updated my question to explain what I want. I have the voltage-time curve from the real industial object. This curve was gotten from the digital oscilloscope: As you can see it has ...
1
vote
1answer
154 views

Is wavelet a Nonlinear transform, or Not? [closed]

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 ...
10
votes
1answer
271 views

Wavelet transform order problem

I have a signal that I'm trying to study its time-frequency features by continuous wavelet transform. By choosing different wavelet order, I get some differences in the results. ...
4
votes
3answers
375 views

How to increase Spectrogram resolution?

I have a time-domain signal that I want do a time-frequency analysis on it. When I tried the Spectrogram, I always get very low resolution. For example: I have a ...
9
votes
1answer
765 views

Extracting information from the result of ContinuousWaveletTransform

I'm trying to analysis a signal and identify some time-frequency information of it. For example, around which time the specific frequency arrives. It appears that Mathematica has very powerful wavelet ...
4
votes
1answer
796 views

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 ...
11
votes
3answers
447 views

WaveletScalogram in polar coordinates

For given dataset data = Re[Zeta[1/2 + I Range[0, 100, 0.01]]]; It is nice that Mathematica can plot data in both Cartesian and Polar coordinates. ...
2
votes
1answer
191 views

Daubechies scaling function

In Mathematica in wavelet package with the following codes Phi[x_, j_, k_] := 2^(j/2) WaveletPhi[DaubechiesWavelet[3], 2^(j) x - k] Mathematica computes ...
2
votes
0answers
159 views

Is there a relatively easy way to add the “Cone of Influence” to a waveletscalogram?

I am analyzing time series data using the ContinousWaveletTransform function and plotting the results with WaveletScalogram. I ...
1
vote
1answer
213 views

Function definition and delayed assignment

I need to define the following function MyWavelet[n_]["PrimalLowpass", prec_ : MachinePrecision] := Table[(-1)^(j - 1) h[[2*n - j]], {j, 0, 2*n - 1}] which ...
3
votes
1answer
221 views

Wavelets: Relative error vs compression ratio

I need to plot the relative error vs compression ratio diagram of a discrete wavelet transform on an image, but no luck so far .. Here's the problem in short: random_image.jpg compress the image ...
16
votes
2answers
1k views

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 ...
5
votes
2answers
744 views

Wavelet Packet Transform in Mathematica 7 and 8

For finding location of spikes in a time series I used to transform the data into wavelet space using DiscreteWaveletPacketTransform [ data, filter, 0] and then ...