# Questions tagged [wavelet-analysis]

Questions on the wavelet analysis functions of Mathematica.

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### 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 tried ...
5k 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 ...
619 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 ...
2k 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 ...
852 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. ...
568 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. ...
3k 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 ...
3k 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 ...
2k 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 ...
304 views

### How to detect discolorations in an image?

I'm evaluating the technical quality of an images and I'd like to scan it for defects from dirty sensors. Are there any filters to quickly detect a blob of discoloration? Here are a few examples:
2k 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 hight-frequency ...
224 views

### How to calculate the amount of offset about two list

You can get my data by this code {data1, data2} = Uncompress[FromCharacterCode@ Flatten[ImageData[Import["https://i.stack.imgur.com/ShSMY.png"], "Byte"]]]; We ...
1k 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 data....
938 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 ...
3k 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 ...
186 views

### 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-...
121 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 ...
420 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 ...
375 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) ...
152 views

### How to extract a single image from the output of the DiscreteWaveletTransform[]?

So, I use the following code to carry out the discrete wavelet transform on an image of Lena. I am interested in then doing some changes to a single image out of the obtained 4. How do I extract any ...
98 views

### Why does Continuous Wavelet Transform have phase information at high frequencies?

I'm playing around with ContinuousWaveletTransform using a sine wave of a constant frequency: ...
350 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 plot ...
239 views

### Solve 1D Wave Equation

I wanna model 1D wave equation and plot it, Here is my try so far, ...
162 views

### How to detect the singular value in 3-dimension with wavelet analysis

Actually this question is related with this post,but this is about point of 3-dimension ...
531 views

### Daubechies scaling function

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

### <<WaveletsWavelets Not Found [closed]

please i'm a student and i need help in my project which is based on an already existing program. The problem that the program is ancient( Mathematica 5.0) and doesn't fit with the new versions of ...
2k 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 ...
205 views

### 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 ...
150 views

### Integrating a function containing a wavelet

How do I evaluate the integral c? ...
176 views

### Computing FundamentalFrequency

How does Mathematica use AudioLocalMeasurements to compute the fundamental frequency? Is there any formula? I can't seem to find what method Mathematica makes use ...
577 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 ...
73 views

### Integral of a Wavelet function

I ran into problems integrating a function which contains both an If condition and a Wavelet which is an ...
777 views

### How to generate a Wavelet Matrix?

The Wavelet Matrix, also called the Haar matrix, is very useful. We can find some useful information in MathWorld on how to generate it, but this document is too hard for me. From my reading of the ...
395 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 ...
157 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 ...
70 views

### WaveletListPlot: Broken in 11.2?

I'm trying to create a WaveletListPlot, following the reference code exactly: ...
151 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 ...
100 views

### Coefficients of continuous wavelet transform

I am fiddling with wavelet coefficients in Mathematica, and for simplicty only a real valued Wavlet. Lets say we have the data: ...
878 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) ...
67 views

### Modified WaveletImagePlot

When performing Wavelet Transform ...
253 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 ...
215 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 ...
300 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 ...
160 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 ...
131 views

### How to detect the singular value with wavelet analysis

I have a series data data=Uncompress[ FromCharacterCode[Flatten[ImageData[Import["http://i.stack.imgur.com/ApipY.png"], "Byte"]]]]; We can show it ...
103 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 ...
96 views

### Numerical solution to approximate the singular integration using collocation method

I am working to solve "numerically" the following integral equation IE: u[x]=f[x]+Integrate[(1/(x-t)^(1/4))*u[t],{t,0,x}]+Integrate[(1/(x-t)^(1/4))*u[t],{t,0,1}] ...
102 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 ...