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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.

130 questions with no upvoted or accepted answers
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1answer
12k views

Discrete Wavelet Transform - Visualizing Relation between Decomposed Detail Coefficients and Signal

I'm trying to directly visualize the relation between discrete wavelet transform (DWT) detail coefficients and the original signal/its reconstruction. The goal is to show their relation in an ...
9
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1answer
250 views

What is the normalization factor for the quincunx lattice wavelet transform, and how do you find it?

On pages 57-60 (preview was available last I checked, images here in case), there is a quincunx lattice transform described. Lattice: ...
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1answer
1k views

Issues with the smoothing operator in coherence estimation using the complex Morlet (Gabor) wavelet

The goal I wish to compute the coherence estimate using the continuous wavelet transform (CWT) of a real-valued signal with the complex Morlet (a.k.a. Gabor) wavelet. I compute the cwt of the signal ...
6
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231 views

What's the similarities and differences between Wigner transform and wavelet transform?

Wigner transform and continuous wavelet transform are both some kind of time-frequency representation of a signal. What are the similarities and differences between them? Could you give some ...
4
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1answer
407 views

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 ...
3
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1answer
33 views

At what stage do we compute the approximations and details while performing a DWT?

$$ \int_{-\infty}^{+\infty}{f(t)\psi_{j,k}^\ast(t)dt}\ \textrm{with}\ \psi_{j,k}(t)\ =\ a_0^{-j/2}\psi(a_0^{-j}t\ -\ b_0k) $$ If this is the expression for the wavelet transform, how does this lead to ...
3
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0answers
61 views

Clarification about wavelet thresholds

I am trying to wrap my head around the original wavelet shrinkage papers of Donoho and others from the mid-90s. There are a couple of curious things that confuse me, and I'd appreciate some input: ...
3
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0answers
267 views

Why does the Stationary Wavelet Transform shift this image?

I am running a stationary wavelet transformation on a brain image. I can't understand why it shifts with each level so that the image is no longer centered. You can see that the X component shifts to ...
3
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0answers
262 views

Hints and helps to implement an accurate wavelet packet transfrom

I want to implement a Time-Freqency analysis by wavelet packets. I don't know what level and sampling rate should I use. I've tried different value for level(3,4,5,6,). but I couldn't get an accurate ...
3
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0answers
161 views

understanding discrete wavelets

I was reading section 4.3.3 from chapter 4 of "A Wavelet Tour of Signal Processing", "...Let $\bar{f}(t)$ be a continuous time signal defined over $[0,1]$. Let $f[n]$ be the discrete signal obtained ...
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0answers
299 views

Wavelet computation with filter bank - differing results

I'm trying to get a grip on Wavelets. I've read "Wavelets, Their Friends, and What They Can Do for You" which lead me to an implementation of the discrete DWT with filter banks. Basically, I'm using ...
2
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1answer
76 views

Non-Linear, Non-Stationary spectral analysis methods! When and where?

I have been reading about non-linear non-stationary signal analysis methods and it seems to do this type of analysis the go-to method is the Empirical Mode Decomposition (EMD), then Hilbert Transform (...
2
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1answer
172 views

Extract approximation and detail coefficients

I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)?
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74 views

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 ...
2
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0answers
70 views

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 ...
2
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0answers
131 views

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 ...
2
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1answer
651 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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0answers
2k views

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. ...
2
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0answers
512 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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0answers
160 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 ...
2
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0answers
510 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 ...
2
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1answer
246 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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0answers
611 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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27 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 ...
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0answers
158 views

Plotting a scalogram of a signal's Continuous Wavelet Transform (CWT) in python

So I've been learning about wavelets for a few weeks because I'd like to use them in a research project I'm working on and I've been trying to grasp the general ideas behind them.I've been struggling ...
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60 views

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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0answers
13 views

Expectation of power spectrum for nonorthogonal wavelets

I'm working through "A Practical Guide to Wavelet Analysis" by Torrence and Compo, and I am confused about section 3d ("Wavelet Power Spectrum"). Let $x_n$ denote the signal, sampled at increments $\...
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0answers
86 views

Discrete Wavelet Transform: Specifics of Filter Bank

So I have been given to understand that the discrete wavelet transform is able to provide both time and frequency resolution in ways that classic Fourier and even short time Fourier cannot. By ...
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0answers
173 views

Connecting DWT matrix operations to Daubechies D4 scaling $\left(\phi(x)\right)$ and wavelet $\left(\psi(x)\right)$ functions by plotting

I'd like to duplicate the plot in the Wikipedia entry for Daubechies D4 scaling and wavelet functions: I don't have Matlab or Mathematica, and my question is not about hacking the curve, but rather ...
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0answers
68 views

Can I have some feedback on this research paper on vibration diagnostics?

I have submitted this paper "Detecting a Valve Spring Failure of a Piston Compressor with the Help of the Vibration Monitoring" to figshare.com. I would like to get some feedback on the methodology ...
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0answers
51 views

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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0answers
54 views

Does a “chirp”-like generalization of the Gabor or Morlet wavelets definitions exist in the lit somewhere?

I have asked this at the Math SE also. Predicating this on the definition of the continuous Fourier Transform preferred by most electrical engineers: $$ X(f) \triangleq \mathscr{F} \Big\{ x(t) \Big\}...
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22 views

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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0answers
147 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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0answers
200 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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1answer
138 views

Continuous wavelet transform subsampling at lower frequencies?

I am not completely confident in my understanding of wavelet theory, but since I am currently in the process of creating a CWT scalogram tool, I have to ask: Is there a theorem allowing us to ...
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0answers
78 views

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 ...
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0answers
758 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 ...
1
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1answer
197 views

2D DWT computation order

In 2D the discrete wavelet transform (DWT) of an image using lifting based 5/3 filter, if I perform a row-wise operation first then perform column-wise operation then I will get 4 sub-band LL, LH and ...
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0answers
45 views

DWT initialization from nonuniform samples

Let $D\subset\mathbb R$ be compact, let $f:\mathbb R\to\mathbb R$ be a contintinuous function with support $D$. Let $\phi(x)$ be a well-defined scaling function, in the sense that it generates a ...
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0answers
252 views

Transfer functions from wavelet transform

So I have this problem where I need to measure the phase of a signal and correct for a delay associated with the travel time of the signal while simultaneously determining the transfer function of my ...
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0answers
421 views

What the difference between the family of Discrete Wavelet Transform?

When I useed Mathematica,If found many Transforms in the list of Discrete Wavelet Transforms. For example: discrete wavelet transform (DWT) stationary wavelet transform (SWT) lifting wavelet ...
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42 views

Example of radial frequency functions that give scale shiftability

Simoncelli's "Shiftable multi-scale transforms" paper talks about shiftability of the parameters of a wavelet transform, in particular translation, rotation and scale. The first two are used in his ...
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0answers
122 views

Are wavelets for audio spectrograms available as a simple FIR filter?

I have read that "Debauchies Wavelet is simply a short FIR" so i am searching for a single FIR that i can make into a filterbank, a precise "bandpass filter" that detects narrow frequencies, i.e. 1Hz ...
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0answers
173 views

Singularity Detection from 2D Wavelet Modulus Plot

I was wondering if I could get some tips/resources on how to pick out the singularity from my 2D Continuous Wavelet Transform Coefficient Plot (scalogram) using the Gaussian Derivative as the mother-...
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0answers
40 views

Matrix expansion into bases

I have an image (that is a matrix), let's say of dimensions NxN. I then want to expand this matrix into M basis matrices (for the moment I'm still unsure how many M of these basis matrices I should ...
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0answers
442 views

Are discrete wavelet transform based statistical features invariant to rotation/translation/scale?

I'm reading a paper where image classification is done. Their approach is to use the discrete wavelet transform with bi-orthogonal wavelets of degree 3.5 and decomposition of level 3 on images. Based ...
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0answers
513 views

Selecting the number of cycles for wavelet transform

I'm trying some wavelet analysis of EEG signals, using the phase lock measures from [1], specifically the S-PLV measure. In order to calculate that we perform a wavelet transform on the signals and ...
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0answers
72 views

What is the difference between Time-Frequency Represenation and TF Decomposition

I'm asking as I'm looking at Wavelet transforms, and I see that it is possible to have a TF decomposition or a representation of the signal. Looking for example at the code here we can see that the ...