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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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 ...
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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 ...
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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 ...
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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
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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 ...
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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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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 ...
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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
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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 ...
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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(...
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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 ...
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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 ...
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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
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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
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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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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 ...
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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 ...
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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 ...
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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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MODWT looses properties after thresholding

The haar modwt has the shift invariance property, it is causal on the right edge so it has no border distortion and it has the perfect reconstruction property. So the sum of the coefficients is equal ...
Emiliano Rosso's user avatar
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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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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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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
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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....
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Wavelet Multilevel with EBWS

0 I have an important question. I'm using a wavelet multilevel transform using the wavedec (pywt on python), but I need to change the mother wavelet on each level. It's possible to perform it? def ...
Allan David Da Costa Silva's user avatar
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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 ...
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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 ...
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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 ...
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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
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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 ...
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How to temporally align detail coefficients with original signal after stationary wavelet transform (PyWavelets SWT)

I am using pywavelets and the Stationary wavelet transform to decompose a signal into scale dependent details and fluctuations. However, it is important for my application to have the details ...
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Using the inverse discrete wavelet transform (DWT) to provide the derivative of the original signal

I was wondering if anyone familiar with python's pywt and ptwt libraries knew of a way to extract the derivative of the wavelet? I have a time-series, x, and find it's wavelet coefficients, W using ...
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How do I determine how many noise components are numerically contained in the Wavelet Transform Image?

How do I determine how many noise components are numerically contained in the Wavelet Transform Image? I used Matlab's DWT2 to convert the wavelet to check the vertical, horizontal, and diagonal noise ...
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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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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
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Why is the vertical pattern noise FFT result of the image vertical?

A vertical pattern of noise is mixed in an image. I did FFT (Fast Fourier Transform) for this. When I studied the theory of FFT, I learned that vertical patterns appear horizontally as a result of FFT....
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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 ...
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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
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2 answers
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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
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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
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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) &&...
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Question about constructing orthonormal wavelet bases

Consider multi-resolution analysis and the two-scale equation for $\phi(t)$ and $\psi(t)$ given in $$\phi(t) = \sqrt2\sum_{n}h_0[n]\phi(2t-n)$$ $$\psi(t) = \sqrt2\sum_{n}h_1[n]\phi(2t-n)$$ is it ...
WilliamW's user avatar
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Implement a simple Continuous Wavelet Transform for specifics frequency

I have a question. I am worked with the Wavelet Transform, Continuous and Discrete. With the Discrete Wavelet I implemented a noise reduction in a signal, using Python library. Now i have a signal ...
LordJota's user avatar
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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
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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
292 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
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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
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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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Question about the definition of wavelet

From the definition, we will use wavelet for expanding signals the same way Fourier series use sinusoids: $$f(t) = \sum a_{l}ψ_l(t)$$ The definition then defines that if $ψ_l(t)$ form an orthonormal ...
WilliamW's user avatar
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Discrete Wavelet Transform With Overlaps

Maybe this is a trivial question, but I couldn't find an answer yet. Is there some discrete wavelet transformation which works with overlapping wavelets (half on half)? In other words, is there some ...
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