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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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Detecting and fixing clipped positive waveforms

I have a large number of audio files recorded using custom IOT devices. When analysing the data I noticed that a portion of them seems to have their positive amplitude ramp up, but the negative ...
zaza's user avatar
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Time step (skipping) in CWT function with PyWavelets

I am using cwt function from pywavelet to perform time-frequency decomposition of a large signal (several million samples). The computational requirements for this is huge, sin it performs the ...
Juan Luis Ferrando Chacón's user avatar
1 vote
1 answer
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Normalisation of Complex Morlet Wavelet

I am currently writing an essay on Wavelet transforms, and as part of such, I am trying to show that the Morlet wavelet satisfies the standard criteria: $$ \int^\infty_{-\infty} \psi(t) dt = 0 $$ $$ \...
Isaac Mortiboy's user avatar
4 votes
1 answer
142 views

Wavelet basis orthonormality

I recently started learning about wavelet transforms, and there's something that is confusing me. My understanding was that most wavelet decompositions are simply a decomposition of a given signal in ...
Sahand Tabatabaei's user avatar
1 vote
1 answer
55 views

Correlation Matrix Problem of Three Decomposition Level of DWT

I'm trying to apply a DWT with 3 composition levels and the following question arose when calculating the composition matrix. The step I'm trying to follow is: The DWT coefficientes are obtained from ...
Dragnovith's user avatar
1 vote
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Wavelet Scattering features extraction

I want ask about the wavelet scattering feature extraction with machine learning -- if it is correct to use it for fault detection in induction machines?
Asli Farook's user avatar
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24 views

How to implement scale-dependent Gaussian averaging using Morlet wavelet envelope in Python?

I'm trying to reproduce the scale-dependent Gaussian averaging of a time series as described in this paper: https://arxiv.org/pdf/1706.01126.pdf The process involves performing a continuous wavelet ...
Jokerp's user avatar
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2 votes
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Online Noise Reduction on Non-Stationary, Broadband Signals

im capturing ultrasonic waves using an analog MEMS mic and other components on a PCB. My signal is similiar broadband and non-stationary (see 2) and im trying to remove/reduce environmental noise. I ...
Tom's user avatar
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1 answer
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Why window functions can't have both narrow main lobe and low-level side lobes?

Why window functions can't have both narrow main lobe and low-level side lobes? i got a hint from my mentor that it's quite often expained in books about wavelets... I thought it could be associated ...
Alexander's user avatar
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1 answer
60 views

scalogram shows black image

my goal is to generate scalogram from .wav file and save as jpg or png format,i used following code : ...
dato's user avatar
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41 views

Why no Daubechies wavelet from Continuous Wavelet Transform?

thank you for considering this question. Do you know any reason why Daubechies wavelet can't be used for Continuous Wavelet Transfrom, but only for Discrete Wavelet Transform ? Matlab toolbox and ...
Yannick Daviaux's user avatar
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Identify variation patterns in image time series

I am working on time series of 12 remote sensing images obtained at irregular intervals. The pixels of all images are of exact same region. Pixels of some areas in these images vary in time with ...
sat_P's user avatar
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Avoiding latency distortion at high denoise levels with DWT

I am denoising biological signals using the DWT, and for UI reasons would prefer the smoother waveform afforded by denoise level 5. However, higher denoise levels seem to distort the latency of ...
Brian Barry's user avatar
1 vote
0 answers
52 views

PyWavelets CWT : error when differentiating after convolution?

I'm trying to understand the implementation of CWT in PYWT. This topic has already helped me quite a lot but there is still a thing that is unclear to me : why is the result differentiated only after ...
Tanguy Jonv's user avatar
1 vote
1 answer
36 views

How to get approximation coeff. Of WT of all levels

I am running a WT using pywt.wavedec on a gait signal (accelerometer and gyroscope data), I'm setting level to 5 and using a db4 Wavelet. I am wondering why we only get the approximation coefficient ...
Syrine's user avatar
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1 answer
158 views

CWT: selection of scales and filtering

I am using CWT to obtain scalograms of ECG signals as the one below: In my research, most articles contain a pre-processing step before performing CWT (that usually includes signal normalization and ...
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49 views

Does filtering by wavelet decomposition and reconstruction introduce a phase shift in the filtered signal?

I am removing low frequency noise from a signal using Matlab using the DWT and then reconstruction at a specific level: I am removing the approximation signal at level 10 which approximates the low ...
HP W's user avatar
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High Resolution Spectral Analysis

Inspired by this post and this video I have been playing around with different methods in Matlab to do spectral analysis. In the past I have simpy used digital fourier transforms and played around ...
Matthias La's user avatar
2 votes
1 answer
62 views

3D wavelet transform in the form of a matrix?

I was wondering if anyone may know of any method for the construction of a 3D wavelet transform in matrix form? I've been able to build matrices to perform 1D & 2D transforms. Yet, am finding very ...
hubble's user avatar
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2 votes
1 answer
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Integrating over the translation on a DWT

I'm really a begginer at Wavelet transform and I'm starting to use the pywt module. I have some difficulties understanding the link between the following integral and the coefficients of the DWT: $$ W(...
user68569's user avatar
1 vote
1 answer
150 views

Why are analytical wavelets said to have no negative frequency?

I have been reading about analytical wavelets and came across this definition: An analytic wavelet is a complex wavelet such that its Fourier transform is null for negative frequency. If it is a ...
KRISHNAPRIYA G B's user avatar
1 vote
0 answers
86 views

Adding noise to ECG to mimic Electrode Motion Artifacts, Muscle Artifacts, and Baseline Wander in Python

I have clean ECG signals and I want to add noise to them. Specifically, I want the noisy signals to be closest to "real life" type of noise. Reading this paper, I noticed that the ...
David Harar's user avatar
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How can we prove using matlab that after each level of decomposition of a signal using DWT the frequency content is halved?

I was trying to decompose an EMG signal, which was sampled at 200 Hz, into 7 levels of decomposition using DWT. And the result is shown in the figure( only up to level 3 is shown here) However, I ...
KRISHNAPRIYA G B's user avatar
1 vote
1 answer
92 views

How to find median position of a contour that represents a peak?

I was reading some papers on time-frequency methods of signal analysis and I am confused about one concept. The idea in these works is to plot a power spectrum in time-frequency plane and then to ...
Wave_Rider03's user avatar
2 votes
1 answer
70 views

How can Haar basis be written as the impulse response of an LTI system?

Haar wavelets are defined as: $$\phi_{0,0}(t) = \begin{cases} 1, & \text{ for } 0<t< 1/2\\ -1, & \text{ for } 1/2<t<1 \\ 0, & \text{ ...
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3 votes
3 answers
297 views

Wavelet Coefficients Algorithm for Haar System

In my DSP class a few lectures ago my professor shared a basic algorithm with us for computing wavelet coefficients when the wavelet basis belong to the Haar system. He also shared a circuit with us ...
user avatar
2 votes
0 answers
54 views

Is using cross-correlation with a reference wavelet a good approach for vibration detection?

This is my first time actually applying signal processing to a real problem. I'm trying to monitor some equipment for vibrations. The vibrations aren't constant but occur at some point in time - I've ...
Nick S.'s user avatar
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1 answer
277 views

Python's equivalent of MATLAB's cwtfilterbank

I am learning signal processing and would like to know what's the python equivalent of matlab's cwtfilterbank. I looked through pywt but did not find anything. Some ...
JXuan's user avatar
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2 votes
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35 views

Relation between discrete wavelet transform and filter banks

I have approached wavelet transformation from a projection perspective. Specifically, we can show for a certain class of functions (in the continuous setting) that they can be written in terms of a ...
Rudolf 12345's user avatar
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60 views

In continous wavelet transform, all wavelets must have the same energy regardless of their scales,why?

In Continuous Wavelet Transform (CWT) To achieve energy normalization and to ensure that all wavelets have the same energy regardless of their scales, each wavelet is divided by the square root of the ...
Hend Ibrahim's user avatar
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1 answer
48 views

Zeroing input frequencies to improve inverse CWT

This is a follow up of my previous question Why is inverse CWT inexact / inaccurate? Rephrasing its accepted answer in my own words: The filterbank's transfer function gives information on what band ...
G. Fougeron's user avatar
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1 answer
472 views

Why is inverse CWT inexact / inaccurate?

I'm all new to wavelet analysis. I'm trying to get a working understanding of the continuous wavelet transform and its inverse. By "working understanding", I really mean "getting some ...
G. Fougeron's user avatar
1 vote
0 answers
27 views

Reconstruction of batch-acquired signal

I am currently working on a project which requires evaluating slow changes over time in the magnitude of a signal's high frequency (over 10 kHz) components. This signal was acquired in tests with a 25....
G. Thaler's user avatar
1 vote
1 answer
222 views

What do computed CWT frequencies and color values correspond to?

I wanted to make wavelet transform and represent the frequencies as function of time instead of the scale of the wavelet as function of time. This example that uses ...
User's user avatar
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1 answer
209 views

why is the output length of the inverse wavelet transform the double of my original signal?

I have an input signal of 30000 samples. I perform the Stationary wavelet transform in python to get the 4th level od decomposition. Then I perform an array mathematical operation over the decomposed ...
GGChe's user avatar
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2 votes
2 answers
99 views

Natural frequencies

Given the acceleration response time history of a multi-story structure, how can I find natural frequencies using time-frequency analysis techniques? If you just provide some references or articles, I ...
Praham's user avatar
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2 votes
1 answer
67 views

Can finite Multi-Resolution Analysis satisfy the Littlewood-Paley Criterion (unity partition)?

Suppose we are working with a multi resolution analysis (MRA) of $L^2(\mathbb{R})$ and let $\phi$ be the corresponding scaling function and $\psi$ the derived wavelets. Using standard notation with $\...
WedgeAntilles's user avatar
3 votes
1 answer
106 views

Littlewood-Paley Conditions, Scattering, and Multi-Resolution Analysis

So I am trying to understand the scattering transform on graphs (GST). There are many formulations but I am stuck on equation 8 in this paper. Here they give a condition on a wavelets that looks like ...
WedgeAntilles's user avatar
0 votes
1 answer
415 views

Inverse continuous wavelet transform off by constant factor in the y axis

I have implemented the Continuous Wavelet Transform using the pycwt library(https://github.com/regeirk/pycwt/blob/master/pycwt/wavelet.py) and its inverse using Morlet wavelets, however, upon ...
Jokerp's user avatar
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2 votes
0 answers
59 views

Best 'SNR-like' detection statistic for time series signal in the wavelet domain?

What is the best way to define a detection statistic for a time series event trigger generator, which computes the wavelet transform of some time series data? I want such quantity to be similar to a ...
GWSurfer's user avatar
0 votes
1 answer
509 views

Signal Reconstruction Using Scipy.signal.cwt

Can someone explain to me how I can reconstruct a signal using the scipy.signal.morlet2? The codes in the link only allows one to do a fourier transform using the morlet wavelet, but there is no such ...
VA157's user avatar
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1 vote
1 answer
834 views

Power/Energy from Continuous Wavelet Transform

How can power or energy be computed from Continuous Wavelet Transform? Is it just $\sum |\text{CWT}(x)|^2$, or are there other considerations, particularly if interested in a subset of frequencies? Do ...
OverLordGoldDragon's user avatar
2 votes
2 answers
189 views

Reconstruction of a Ricker Wavelet using inverse discrete fourier transform - signal cut in a half?

I am new here and new to DSP, so maybe my question is really basic. I have the formula for the Ricker wavelet (Mexican Hat) in frequency-domain and I wish to do an inverse Fourier transform to recover ...
Luis Fraga's user avatar
1 vote
1 answer
532 views

How to validate a wavelet filterbank (CWT)?

I've seen many different implementations of CWT, especially in generating the wavelets. Often these implementations produce significantly different outputs - e.g. ...
OverLordGoldDragon's user avatar
1 vote
1 answer
162 views

What is "spin" for the 2D (separable) Morlet?

The 2D Morlet formed separably as product of 1D Morlets, used in JTFS, is said to have "spin": $$ \begin{align} \Psi_{{\mu, l, +1}}(t, \lambda) &= \psi_\mu(t) \psi_{l}(+\lambda) &&...
OverLordGoldDragon's user avatar
1 vote
0 answers
88 views

What are frequencies in a scaleogram generated using pywavelet?

I am using PyWavelet to do continous wavelet transform of a 1D signal. The pywavelet continous wavelet transform function works with this line of code: ...
User's user avatar
  • 55
1 vote
1 answer
187 views

Limited cross-correlation for multiple signals

I have $N$ signals, each of length $\tau$, with $N\ll \tau$, eg. $\tau=10^8$ samples and $N=100$. I want the $r=10$ first components of all pairwise cross-correlation for the $N$ signals. The naive ...
wavelet_surfer's user avatar
3 votes
1 answer
340 views

Why does a signal with constant frequency have spots that changes colors at a specific value of scale (and so frequency) in the scalogram?

I am studying the Wavelet transform and I am considering this example that I took from PyWavelets documentation. The signal in time domain has the following shape: Till the value of zero on the ...
User's user avatar
  • 55
0 votes
0 answers
27 views

What is "modified frequency slice wavelet transform"?

What is "modified frequency slice wavelet transform"? It was written in an article but It's not been described on the web.
mohammad rezza's user avatar
0 votes
0 answers
25 views

Question about the derive of a theory of the scaling function in the wavelet analysis

Page 5 in link: For the scaling function, it holds: $\int \phi(x)dx = 1 $ or, equivalently: $\Phi(0) = 1$ How is this derived?
WilliamW's user avatar

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