Questions on the wavelet analysis functions of Mathematica.

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20
votes
3answers
576 views

Detecting components in timeseries

I'm looking at this sequence of values: I'd like to detect the points where the center of the time-series shifts (around x=1000 and x=2000). Many of the transforms and smoothing methods I have ...
16
votes
3answers
461 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 ...
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 ...
13
votes
1answer
3k 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 ...
12
votes
3answers
607 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. ...
10
votes
1answer
408 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. ...
7
votes
1answer
395 views

How to extract notes and chords from audio?

I have a 3-second recording of a guitar chord which you can safely download here. I'm trying to use Mathematica's wavelet features to find out the notes in the chord, at least the docs says that ...
6
votes
3answers
1k 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 ...
6
votes
0answers
1k views

Create “Ostagram” like Images using Wavelet Transforms

I am trying to make an "ostagram" like image using wavelet transforms and image keypoints. See the following link: https://www.facebook.com/ostagram/ This is done using neural networks, which I at ...
5
votes
2answers
864 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 ...
5
votes
1answer
2k 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 ...
5
votes
1answer
82 views

InverseWaveletTransform not recreating the original image exactly

I am trying to do DWT steganography. I first obtain the DiscreteWaveletTransform of the image as follows ...
5
votes
0answers
455 views

Wavelet Transform Modulus Maxima (WTMM) method

Has anyone already coded the Wavelet Transform Modulus Maxima (WTMM) method for computing the singular spectrum using multi fractal formalism in Mathematica? The goal is to analyse 1D, 2D and 3D ...
4
votes
3answers
1k 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 ...
4
votes
2answers
202 views

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 ...
3
votes
1answer
304 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 ...
3
votes
1answer
327 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 ...
3
votes
1answer
730 views

Wavelet vs instantaneous power spectrum

Following on from a previous question posted by @xslittlegrass and answered by @Sector and others, Extracting information from the result of ContinuousWaveletTransform I'd like to know if it is ...
3
votes
1answer
237 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) ...
2
votes
1answer
249 views

Wavelet transform of data with sliders

I saw a beautiful application of wavelets applied to a randomly created data series of about 500 data points. It used the Haar wavelet and had two sliders. The first slider allowed the user to view a ...
2
votes
1answer
105 views

How many arguments does a function require, and how to use that in `Manipulate`

The goal is to vary the order parameters in wavelet transforms in the Manipulate environment. The various transformations have arguments of different rank. For ...
2
votes
0answers
45 views

Modified WaveletImagePlot

When performing Wavelet Transform img = ExampleData[{"TestImage", "Lena"}]; dwd = DiscreteWaveletTransform[img, HaarWavelet[], 2] WaveletImagePlot[dwd] I get ...
2
votes
0answers
98 views

How to obtain amplitude and phase of tidal data using wavelets

I have a time series of tidal data for one month and success with identifying tidal characteristic such as semidiurnal or diurnal spring and neap position power spectrum However, I don't have ...
2
votes
0answers
186 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
274 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 ...
1
vote
1answer
119 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 ...
1
vote
1answer
200 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 ...
1
vote
2answers
79 views

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 ...
1
vote
1answer
114 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
0answers
42 views

Detrending a time-series by means of Discrete Wavelet Transform

I plot a time-series for observation as you can see in the plot: I tried to detrend the time series by 3 different approaches which are: 1) differences, 2) detrended fluctuation analysis, and 3) ...
1
vote
0answers
91 views

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

Due to ContinuousWaveletTransform[...] I can obtain information about wavelet-coefficient for example ...
1
vote
0answers
92 views

Problem with DiscreteWaveletTransform for DaubechiesWavelet

I am trying to use Mathematica's wavelet transform. In preparation I entered: ...
0
votes
1answer
43 views

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[]: ...