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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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
46 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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10 views
How to define and use custom wavelet filters in python?
I would like to define custom analysis and synthesis filters for wavelet implementation in pyhton. How it can be cone using pywt library?
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1answer
69 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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27 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
33 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
219 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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16 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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43 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
33 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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40 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
55 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
48 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
136 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
37 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
34 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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38 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
764 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
62 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
40 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
54 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
185 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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29 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
76 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
122 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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0answers
59 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?
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384 views
How does the Scipy implementation of CWT actually work?
I'm trying to use the SciPy implementation of the Continuous Wavelet Transform to analyze EEG data.
I am using The problem is that I have no idea what the width parameter should be. It says that it's ...
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0answers
194 views
How to interpret Discrete Wavelet Transform Coefficients?
I want to extract features from DWT coefficients like Power Spectral Density, Max frequency, Min frequency etc.
After taking DWT, we get coefficients D1, D2, A2 etc. But my question is, Are D1, D2, ...
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1answer
134 views
Wavelet transform and FFT using to extract feature power bands with EEG signals
I am using 5 channels [ fz , cz , c3 , c4 , pz] to detect drowsiness of driver
My First Question is, what is the right input to get feature power band ( Theta , alpha , gamma , beta ) to wavelet ...
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15 views
Do the magnitude of the signal changes in the wavelet filtering
I am using Daubechies 4 wavelets to extract a required signal.
In my signal there is a magnitude change. My raw signal lies from $-3$ to $3$, but when I choose the detail coefficients of the Db4 ...
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1answer
43 views
Isolating frequency-specific oscillation from transient
I am performing time-frequency analysis on electrophysiological data with complex morlet wavelets. Each decomposition in the attached figure shows total power following the onset of a stimulus (top ...
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44 views
Determine scales for continuous wavelet transform (cwt) obtained
How to obtain the corresponding scales for frequencies while computing cwt in Matlab or any other formulae?
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31 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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54 views
Wavelet central frequency
What is the definition of the central frequency of a Wavelet and the bandwidth of a Wavelet? How do they affect the resultant waveform of the wavelet?
Thanks.
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51 views
Algorithm Question for Haar Scaling Function and Discrete wavelet transform
Let $\displaystyle f(x)= \begin{cases} 4x^2-4x+1 & 0\le x\le 1, \\ 0 & \text{otherwise}. \end{cases} $
a) Find the approximation $f_{-3}$ of $f \in V_{-3}$ using the Haar scaling function
...
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306 views
Plot CWT (Continuous Wavelet Transform) in 3D using Python
I am working on a project using signal processing.
Part of my work is to apply the CWT on the signal I have.
As I read, that I can plot the signal in the frequency-time domain using CWT.
So my ...
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0answers
15 views
Implementing Wavelet family matrices
I want to use CS to reconstruct an image from fewer samples, and I would like to use wavelet coefficients but I don't know how to define them when making a Psi matrix.
I have written wavelets ...
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0answers
13 views
Wavelet Quality factor
I read in my lectures that a wavelet should have a constant quality factor Q but without any explanation. Can anyone please explain what do we mean by a quality factor. Thanks..
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1answer
53 views
Can I apply CWT on a digital signal?
First, I am so sorry for my dumb and stupid question, I am very beginner with signals.
Say that I have an ultrasonic sensor cabled to an ADC (Analog to Digital Converter).
The ADC converts the analog ...
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0answers
31 views
Daubechies orthogonal Wavelets
I read a document that it said: "Daubechies orthogonal wavelets D2-D5". Then I've searched on the Internet to get information about this kind but I haven't found any information about it. Moreover, to ...
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0answers
25 views
Qrs complex detection using haar wavelet
I am using this algorithm to detect QRS complex from ECG signal that is samled at 360Hz that is decomposed to level 5 with haar wavelet
In the fourth step it says that the duration of the QRS ...
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0answers
18 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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1answer
60 views
Alternative function for Matlab Stationary Wavelet Transformation
I'm currently working on a project of mine where I have to use stationary wavelet transformation. I found a perfect way to do the transformation using wavelet toolbox of the Matlab. But since it is ...
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92 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
53 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 ...
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2answers
632 views
How to implement a filter associated to a specific wavelet
I am working on ECG signals, to eventually extract features in order to detect an arrhythmia and classify it.
I am using Discrete Wavelet Transform with biorthogonal wavelet bior6.8
During my research,...
2
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2answers
298 views
How to extract features of individual spikes in non-negative signal?
I have data of non-negative (in the sense there's no signal below baseline) spiking waveforms, which are in the form of a 1D array of numbers:
Spikes that cross some threshold are considered real ...
2
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3answers
113 views
Denoise techniques when clean signal and pure noise is available
I have the clean version of the signal.
I can obtain the environmental noise.
I want to apply an effective denoising technique on a noisy signal (i.e., clean plus environmental noise).
Some ...
