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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.

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Obtaining Continuous Wavelet Transform coefficients from Discrete Wavelet Transform

On an earlier StackExchange question, I read that for a given signal, "From the resulting DWT the corresponding full CWT can be obtained by convolving the DWT with the reproducing kernel of the ...
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15 views

Discrete Wavelet Transform (DWT) Filter Bank

I have some stumbling block in my thesis writing. Do we use the same filter pair while implementing DWT filter bank with downsampling of the filter output, or filters do change also from level to ...
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15 views

Is the convolution between a decomposition and reconstruction filter a scalar?

I'm very new in a research topic about wavelet filtering and I received an observation by a professor, but I actually cannot understand it, so I ask you to help me. Suppose to perform a stationary ...
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1answer
32 views

High frequencies disappear when applying discrete wavelet transform

Trying to decompose and reconstruct a signal using a to some extent self-made implementation of DWT for some reason fails. The result looks highpass filtered and/or shifted. I wanted to write the code ...
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16 views

What's the difference between Wavelet transform coherency and Singular Spectrum Analysis

I know that Wavelet transform Coherence is the most common method to find the linkage between two time series, in field of finance. Can we use Singular Spectrum Analysis to find out the linkage of ...
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1answer
41 views

Down sampling an EEG signal

I have a set of 10 minute EEG signals that were sampled at 400 Hz and have 16 channels which corresponds to a 16x240000 matrix. These EEG signals belong to two different classes. I am trying to ...
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33 views

What's the maximum allowable amplitude modulation frequency for a given carrier frequency?

I'm currently studying wavelets and had an interesting thought experiment: If you were to calculate the wavelet transform of a signal using a wavelet of a fixed frequency, you would get time varying ...
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1answer
20 views

What does it mean for a Wavelet transform to commute with translations?

Referencing this article here https://arxiv.org/pdf/1203.1513.pdf It states "A wavelet transform commutes with translations, and is therefore not translation invariant". Now I understand why it is a ...
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22 views

scalogram for huge data

I have a huge data for which I want to apply wavelet and plot scalogram. the below code works for small data. However, I have a huge signal, for which I am not able to plot scalogram. Can anyone ...
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1answer
33 views

Please help me understand this paper about Discrete Wavelet Transform!

I am trying to understand this paper says. I have found this paragraph to be vague: (a) Preprocessing Stage. The first step in this stage was to apply the Discrete Wavelet Transform (DWT). This ...
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8 views

Continuous Wavelet Filter Bank Frequencies

I have followed instructions on how to create a single Morlet wavelet, and can change the centre frequency of the wavelet. My question now, is I would very much like to create a filter bank. How do ...
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43 views

How to calculate Continuous Wavelet Transform (CWT) for specific frequency range in Python?

My first question what is a scale and how to convert it into a frequency? Secondly, I want to get CWT of a signal, but I want to have the option to choose the frequency range to work on. I found ...
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16 views

Wavelet Transform Implementation Method

I have been watching the wonderful youtube videos here: https://www.youtube.com/watch?v=4TTpwIZrUAo&list=PLn0OLiymPak2G__qvavn3T8k7R8ssKxVr&index=3 detailing morlet wavelets and fit ...
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44 views

Using Wavelet Transform on a 1D signal while updating the values

I'm working on a NN that uses Wavlet Transformed signals (with different wavelets and levels) and combines them with an additional Statistical Features input (input_4) to provide one step ahead ...
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20 views

Can coefficients of a DWT be computed using least squares approximation?

I assume that it can be computed given function values for each sample as a vector and wavelet values for each scale and translation packed in a matrix. Can anyone clarify the matrix construction and ...
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1answer
49 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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20 views

Take a wavelet function as a transfer funtion

Is there anyone having the experience of taking the wavelet funtion as a transfer function? That is: if we have $\psi_{m,n}(x)=a^{-m/2}\psi(a^{-m}x-nb)$, $\psi_{m,n}$ is the dilated and shifted ...
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33 views

For discrete wavelet transforms, is redundancy needed to ensure perfect reconstruction?

So I was using pywt and I noticed that in the padding mode documentation they explain the following: DWT performed for these extension modes is slightly ...
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47 views

CWT matlab function [closed]

i'm trying to apply the cwt function from matlab in the first graph and from the different articles that i've read i should get something that shows different peaks to determine the location of damage,...
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1answer
29 views

Is there a reason why with symmetric padding, the inverse wavelet transform is not the adjoint of the wavelet transform?

I recently stumbled upon a bothering fact when using the pywavelet library in Python. When we use the default "symmetric" ...
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1answer
31 views

Daubechies Wavelets in mulitresolutional analysis decomposition

I have an understanding problem with Daubechies wavelets. When I use a multiresolutional analysis, I want to approximate the given input Signal $f\in L^2(\mathbb{R})$ on the subspaces $V_i$. By ...
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31 views

What are the constraints in design of discrete orthogonal wavelets?

Can anyone point me to literature that explains a quote from here : Why is a wavelet transform implemented as a filter bank? So not all wavelets can be implemeted perfectly (invertible) with ...
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173 views

Filter ECG signal with Wavelet and Python

I have to filter the signal of an ECG with the wavelet method with Python. The data is in a txt file. I can create my dataframe with pandas, display that with seaborn, but can not find a way to apply ...
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31 views

Calculating the Mean Square Error (MSE) in Wavelet Denoising

I´m currently reading the paper (to be more precise: it´s a chapter from the book "Shearlets, Multiscale Analysis of Multivariate Data" by Kutyniok and Labate) "Image Processing Using Shearlets" by G....
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11 views

Why packet wavelet transform for frequency analysis gets non-informative results for some frequencies and phase?

I wrote the following code in Julia for packet wavelet transform. It uses Haar transform (I've chosen low-pass filter to keep average value of the signal). As usual, it works recursively filtering ...
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2answers
53 views

Wavelet is a small wave, what is problem with using sin(x) of one cycle?

As far as I know a $\sin(x)$ which is one cycle long can be made into a wavelet and then we can use its dilated and translated versions to represent another function, effectively a wavelet transform. ...
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1answer
74 views

Constrained LASSO Problem - $ {L}_{1} $ Regularized Least Squares with Linear Equality Constraints

I have an optimization question. I want to solve the following problem: $$ \arg\min_S\frac{1}{2}\|s-c\|_2^2 +\lambda\|\Phi s\|_1 \mbox{ s.t. } As = 0 $$ in which $\Phi$ is the wavelet transform ...
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18 views

Which algorithms can efficiently identify rectangular regions in noisy greyscale image?

I have a large number (~50000) of square greyscale images, about 180x180 pixels. I need to efficiently scan them for containing significant block like regions. See the following pictures where I have ...
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54 views

Multifractal analysis of an image using wavelets

I want to measure the fractal character of images using a wavelet approach (if possible) in python. (E.g., maybe things like roughness, anisotropy, or just the fractal dimension - perhaps just ...
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1answer
63 views

Wavelet Transform and STFT

How wavelet transform is different from STFT. I'm not able to understand what is resolution in frequency domain means?
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3answers
244 views

Why does decimation make a system time variant?

On Wikipedia I read this : "The Discrete Wavelet Transform, often used in modern signal processing, is time variant because it makes use of the decimation operation." Why does decimation makes system ...
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21 views

Threshold both detail and analysis coefficients?

Suppose I perform a discrete wavelet transform on some noisy signal $x$ and obtain ${a_1, d_1, d_2, \ldots, d_n}$ where $a_1$ is the set of analysis coefficients and $\{d_j\}$ are the detail ...
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63 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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1answer
35 views

Why is the sound field intensity due to $K$ point sources given by $ I(p,\omega) = \sum_{k=1}^K \sigma_k^2(\omega) \delta(p - p_k)$?

I am trying to understand the following piece of text. I am not used to dealing with sound intensity and power so I'm not familiar with the derivation of the formula $(*)$ below. Statement: 1. We ...
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80 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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60 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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1answer
101 views

Wavelet transform of a spatial convolution

Does anyone know if there exist a kind of convolution theorem for the discrete wavelet transform (decimated or undecimated)? In other words can I find a simple form of $W\left[ \int f(t) g(x-t) \, ...
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2answers
188 views

Other time-frequency-plane tiling than STFT, DWT, ConstantQ-Transform: multiresolution STFT?

It is known that a) the STFT gives a rectangular tiling of the time-frequency plane b) the Wavelet transform gives a non-linear tiling (better frequency resolution for low-frequencies, and better ...
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1answer
52 views

RMS value from wavelet coefficients

I am confused on how to calculate the RMS value fo a signal from the wavelet coefficients. Here is a minimal python code for a sinusoidal sigmal of amplitude $1$ and $RMS=1/\sqrt{2}$ ...
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1answer
35 views

Find Fourier series $f(t) = e^{jx t}$ , $−\pi < t < \pi$ [closed]

I need to find the Fourier series of the $f(t) = e^{jxt}$ , $− \pi < t < \pi$ What will be the first step to solve it?
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44 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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1answer
1k views

wavelet decomposition for time series signal

Is it possible to use stationary wavelet decomposition as a tool to extract wavelet features for a time series? I can see how it works for image cases, but for a time series prediction problem say $...
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1answer
91 views

Reproducing paper results about a wavelet transformation using python [closed]

I have been reading this PhD theis about wavelets and I am trying to reproduce some of the results but I don't know the specific code to use to generate similar results. The original time series ...
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1answer
46 views

Phase of a signal with multi delayed windowed (rectangular window) signal with different amplitudes

I have a signal $x(t)$ which is composed of multi delayed linear chirps with different amplitudes and phases but they share the same $w$ and $\alpha$, the signal can be expressed as follows: $$\...
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1answer
75 views

Dimensional reduction from DWT with threshold

I have been trying to find out how can the discrete wavelet transform (DWT) be possible to reduce dimension of data. Then I saw the question which is seemingly related to my work: Feature extraction/...
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3answers
345 views

Denoising a signal

I'm starting hydraulic experiments, where I'd have to measure velocity in an unsteady flow with a device called Acoustic Doppler Velocimeter. In DSP terms, I'd have a nonstationary signal in a shape ...
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33 views

From Fourier (k space) to wavelet domain in MRI sensing

In compressed sensing MRI (cSENSE MRI) technology the idea seems to entail sampling from the Fourier domain (k space) in a way that, when transformed to the wavelet domain ("sparsification"), the ...
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2answers
77 views

Orthonormal Dictionaries for Band Limited Signals

If $\mathbf{x} = [x_0, x_1, \ldots, x_{N-1}]^T$ is the time sampled input signal and $\mathbf{Y} = [Y_0, Y_1, \ldots, Y_{N-1}]^T$ is the Fourier transform of the input signal, then a linear ...
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1answer
191 views

Detection of Troughs and Notches in a PPG Signal

I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below... I'm having problem in finding the troughs and dicrotic notch for ...
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80 views

signal denoising by continuous wavelet transform

i want to use Morlet mother wavelet for signal denoising so i should employ cwt only. Is there any proper MATLAB code for this target?