# Questions tagged [wavelet]

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.

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### Wavelet filter coefficients from the Morlet wavelet

How can I obtain the wavelet filter coefficients ( i.e. lowpass decomposition filter, highpass decomposition filter, lowpass reconstruction filter, highpass reconstruction ...
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### wavelet reconstruction

I am doing mtech project now. Actually I am working on discrete wavelet transform.I have done till wavelet decomposition. I have been stuck in reconstructing the signal back to original .please help ...
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### Selection of transforms, windows, wavelets for current signal analysis

I am new to this topic but I already read about the propperties of different signal analysis methods. I am stuck with the obvious advantages of FFT, STFT and Wavelet transforms but can't find good ...
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### Perfect reconstruction of 2 channel filter bank

I am studying Perfect reconstruction of 2 channel filter bank for using Biorthogonal Spline wavelet for decomposing ECG signal. I am using Wavelets and Filter Banks By Gilbert Strang, Truong Nguyen to ...
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992 views

### Relationship between Wavelet transform and Fourier Power Spectral Density

Is there anyway to obtain the Fourier Power Spectral Density from a wavelet transform of a time series? I am particularly interested in this problem because I was wondering if there is any ...
1answer
715 views

### MATLAB: Generating and Visualizing Mother Wavelet of different scale

In MATLAB, there is a function wavefun that outputs both the scaling and wavelet functions. To generate a Daubechies, the following command can be used: ...
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### How can I specify the scale parameter of the wavelet in PyWavelets (pywt)?

When computing wavelet transforms with PyWavelets (Discrete Wavelet Transform in Python), e.g. ...
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584 views

### Shifting of Shift-Invariant Wavelet Transforms

Main Question: Why would iterative wavelet/inverse-wavelet transforms cause a shift along the x-axis for undecimated (shift-invariant) wavelet transforms? I am attempting to remove backgrounds from ...
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170 views

### Any idea how can I optimize morlet wavelet parameters by Heisenberg uncertainty principal and Shannon entropy?

Based on a paper in here, they have proposed a method to optimize morlet function parameter. I have tried to implement their technique, but I can't get rational results. any idea? In here you can see ...
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513 views

### Audio watermark embedding text attack resistant

I'm developing an audio watermarking algorithm which embeds text (binary form) in DWT-DCT coefficients. The goal of the algorithm is to hide song information (like artist, song, album,...). Everything ...
1answer
282 views

### Image watermarking in wavelet domain (data hiding in images)

I am working and researching on Image watermarking/steganography and I'm stuck at a point and want to know which technique is better in image processing for data hiding. Bit Plane Complexity ...
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619 views

### why wavelet (CWT) doesn't show accurate results always?

hmm any one can help please? I have a signal that contains some modes in it. I've run a CWT transform but I haven't got my desired results. so I implement a test signal that contains freqs [0.1,0.3,0....
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24 views

### Alternatives to Meyer Windows as Curvelets?

I am looking for alternative to Meyer window functions (Section 4.1) from which one can define a curvelet system. Are there any similar window functions which would be as easy to implement?
1answer
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### Why does each node in the wavelet scattering transform split into multiple paths?

Why does each node in the wavelet scattering transform split into multiple paths as in this figure from https://arxiv.org/abs/1304.6763? I understand roughly what’s happening along a single path, but ...
1answer
91 views

### 3D (time, scale, amplitude) plot in Continuous Wavelet Transform

I will be extremely grateful if someone could please answer this basic question. How can one plot a 3D (translation, scale, amplitude) plot from the Continuous wavelet transform (CWT) coefficients? ...
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### Pros/Cons to using Spectral and Diffusive Graph Wavelets

As I understand, there are two major methods of constructing wavelets on graphs. Spectral wavelets, from David K Hammond et. al, and diffusive wavelets from Coifman and Maggioni. I can't quite parse ...
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107 views

### One integral inverse CWT

MATLAB's icwt docs state inversion to be done by a single integral:  f(t) = 2 \Re e\left\{ \frac{1}{C_{\psi, \delta}} \int_0^\infty \left< f(t), \psi(t) \right> \frac{da}{a} \tag{1} \...
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### What are the wavelet packet functions and how are they different from the wavelet and scaling functions?

I understand that in the decomposition process, wavelet and scaling functions are used to split the signal to approximation and detail coefficients. Most of the time I saw the wavelet and scaling ...
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### Why should wavelet re-synthesis produce an output when the main component is suppressed and what does this mean for denoising?

I understand that aliasing occurs in DWPT if the wavelet used is of low order since the "filters" are not perfect and the combination of down sampling and overlapping between bands causes ...
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### How well can discrete wavelet packet transform reduce noises that are similar to the input signal in the same frequency band?

If I had 50Hz noise coming from power line, and signals in the same frequency range (EEG for example 0.1Hz to 100Hz). If my sampling frequency is 30kHz but I downsample my signal to 937kHz and use the ...
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33 views

### Best way to measure effectiveness of discrete wavelet denoising?

I am using matlab wavelet toolbox to denoise physiological signals, I am plotting the denoised signal on top of the original noisy signal and making sure spikes were not removed as a measure of ...
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### Can thresholding in wavelet transform be implemented on the approximation coefficients?

Sorry as it might be a silly question since I am a beginner in wavelets. I have been using the matlab wavelet toolbox for denoising purposes and saw that thresholding is only applied on the detail (...
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23 views

### Continuously tunable low-pass filter that "interpolate" wavelet filter for multi-resolution analysis

I am using wavelets to analyse some complicated 1D signal, where I am able to come up with multiple filtered signals with different level of details. However, the cutoff of wavelet filters follow a ...
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33 views

### Difference between these two Continuous Wavelet Transforms?

I am porting Synchrosqueezing to Python, and came across an implementation difference on CWT between mine and PyWavelets' - details below. The idea is to merge this implementation to PyWavelets if ...
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32 views

### How to create different Time frequency images from a data

I'm new to Python. I have a time series in a CSV file that has about 5000 rows and 3 columns. I have split the data into training and testing in ratio 70:30 respectively. However, I have a problem ...
1answer
165 views

### Fourier Transform of the full Morlet wavelet

In 2014 someone asked here the Fourier transform of the Morlet wavelet; link below: Fourier Transform of Morlet wavelet Function? However, it was the approximated Morlet wavelet not written with the ...
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### how can we calculate Mathieu wavelet filter coefficients from its design equation? a detailed explanation will be highly appreciated

Elliptic-Cylindrical Wavelets: The Mathieu Wavelets
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### Difference in the meaning of kernel, filter, and dictionary atoms

While reading literature on wavelets, I have encountered keywords filters and dictionary atoms and their exact meaning is confusing for me. Basically, one can use them interchangeably and I won't see ...
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### Efficient audio power spectrum estimation

I am working on a small personal project where I want to control a matrix of roughly 100 actuators with an audio stream. The goal would be that the user can see/feel the music features in the movement ...
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### why is my inbuilt function is not matching with the db5 CA and CD coefficients generated by my code

I am working on wavelet decomposition.As read by the theory i have implemented wavelet decomposition in MATLAB. CA and CD for wavelet decomposition of db1 matches with the inbuilt function but not ...
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160 views

### How to define the scales in a biorthogonal, dyadic Discrete Wavelet Transform in Python

I am sorry if this has been discussed before but I could not find any answer. I am trying to implement an algorithm that I found in a paper which asks for a biorthogonal, dyadic DWT with scales 1 and ...
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301 views

### Log energy and Shannon entropy?

For best tree decomposition using wavelet packets, i have tried both Shannon and log energy entropy functions. I noticed that log energy leads to images with higher PSNR values. Could you please help ...
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### Values (amplitudes) of the CWT and their relationship to waveform amplitudes?

I'm coding up a scalogram in C++. Right now it calculates a single row of the CWT matrix and immediately maps it to a line of pixels. Trouble is my colouring scales with the values of the transform ...