# 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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### 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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### 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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### 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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### 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 ...
53 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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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...