Questions tagged [cwt]
Continuous Wavelet Transform. Time-frequency localization method with a wavelet kernel correlating against signal across scales and translations. Is non-orthogonal and overcomplete (unlike Discrete WT), varies time & frequency resolution across scales (unlike STFT), and is invertible. Usage includes image compression, multi-resolution analysis, instantaneous frequency estimation, transient detection, feature extraction.
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Wavelet admissibility and orthogonality
I have been studying the continuous wavelet transform and came across the following result on the Wikipedia:
A wavelet $\psi(t) \in L^1(\mathbb{R})\cap L^2(\mathbb{R})$ is admissible if it has a ...
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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 ...
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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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ICWT filtering signal with a cut-off frequency
In ssqueezepy, by finding a certain scale is it possible to do an icwt only for the scales above (or bellow) ? For exemple if I have a double sin (with $f_1$ and $f_2$), by taking the frequency $f_c$ ...
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Wavelet signal analysis approach for multi-mode, noisy signal
I have a signal that I am trying to analyze via Matlab's CWT functions. The signal has two distinct oscillating components and I would like to extract the decay factor from each of them. Here is what ...
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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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Integrating CWT around nominal frequency with amplitude and phase
I have a real signal f sampled at 96Hz composed of clusters of harmonics scattered tigthly around evenly central frequencies close to 1Hz and 2Hz (multiples of 0.966Hz) that I'll call features. These ...
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Inverse of wavelet transform modulus gives poor results
I just want to understand, why is the result of my wavelet(?) transform so bad.
For $0\le i< k$, where I set $k$ to $10$, I split the signal in blocks of length $s_i:=2^{i+2}$, overlapping by $s/2$...
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How best analyze a very short data record (~100 data points) windowing and padding data to perform CWT
I have short segments of a biological signal interpolated at 10 Hz (anywhre from about 8.5 sec to 10 sec length). I want to use a cwt to then convert this segment to frequency over the short time ...
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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 ...
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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 ...
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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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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 $\...
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Why are wavelet transforms implemented in Python/Matlab often called Continuous wavelet transform when they take discrete-time input?
The implementations of Synchrosqueezing wavelet transform in Python (ssqueezepy) and MATLAB both write in their documentation that they implement the synchrosqueezing algorithm on the Continuous ...
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Inverse continuous wavelet transform, how to obtain fluctuations at a given scale with ssqueezepy?
How can I obtain the fluctuations of a timeseries at a specific scale using the ssqueezepy library for inverse continuous wavelet transform (ICWT)?
I have a minimum reproducible example that uses the ...
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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 ...
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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 ...
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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. ...
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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 ...
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Wavelet transformation to analyse time series
I am new to wavelet transformation. I am learning it as a tool for signal processing. I have a time series that I want to analyze. I tried to learn wavelet transformation by applying it to a periodic ...
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Weird Noise arises on the small scales: one question about the fast CWT algorithm implemented in real space
Background:
I am learning an interesting Fast CWT algorithm(PPCWT) by reading this paper published in 2019. The algorithm is summarized as below. The continuous wavelet transform of a signal can be ...
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Questions about the paper titled "Rapid computation of the continuous wavelet transform by oblique projections"
This paper introduced a fast method for computing the real CWT and achieved $O(N)$ complexity per scale.
However, in the context of this article, I'm not sure what the definition of oblique projection ...
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Interpretation of wavelet trasformation (synchrosqueezing)
I'm working on a dataset of spectroscopies and i'm classifying them by transforming the 1D signal into a 2D one by the ssqueezepy library.
For instance, consider to ...
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Inverse continuous wavelet transform output has significant error in magnitude and phase
For the inverse continuous wavelet transform, I am using a for-loop which runs through each frequency. At each frequency, I convolve the corresponding morlet wavelet with the signal at that frequency, ...
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Not showing the right frequency in ssqueezepy CWT plot
I am following the ssqueezepy simple example.
The plot should show f=12 but it shows around 33.
Is this a bug or have I scaled the y-axis wrong?
Also the plot is not a straight plot as it waves at ...
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what are the advantages of higher-order Generalized Morse Wavelets?
What are the advantages of the higher-order Generalized Morse Wavelets in comparison with the first-order ones?
Are they also more computationally expensive?
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Is online Continuous Wavelet Transform possible?
I have recently created a real-time STFT with 50% overlap.
I wanted to know if this window-based is possible for scalogram, especially continuous wavelet transform. I haven't found anyone ...
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Does Fast Continuous Wavelet Transform (fCWT) have theory-supported novelty or just simply a computation optimization?
A recent publication, The fast Continuous Wavelet Transform (fCWT), enables real-time, wide-band, and high-quality, wavelet-based time–frequency analysis on non-stationary noisy signals.
I'm a ...
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Is it possible to update wavelet packet from fixed-sized window of data without repeating the whole process?
Assume that a scalogram is generated from performing wavelet packet in a fixed size window of data. Then, is it possible to update the scalogram with the incoming and outgoing data points without ...
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Calculating signal power from Continuous Wavelet Transform in MATLAB
I would like to ask a question about the calculation of the signal power using CWT in Matlab. Assume a signal of length N points with sampling frequency $f_{s}$. Using conventional approach, the power ...
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How to achieve a periodized Mexican hat wavelet with period L by using Python?
Now I have a scaled Mexican hat wavelet, i.e.
$$
\psi(a,x)=\frac{1}{\sqrt{a}}…\left(1-\frac{x^2}{a^2}\right)e^{-x^2/(2a^2)},
$$
which decays quickly along the x-axis. Here I want to define a ...
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When is a continuous wavelet in the Schwartz space?
I was thinking if the continuous wavelet transform can be in the Schwartz space or not? If someone knows can help me and tell me what are the conditions on the mother wavelet or the signal so that the ...
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Why does using a log scale ruin (warp) my scaleograms?
I'm trying to make a scaleogram of neural data using the continuous wavelet transform (with Morlet wavelets). As a starting point, I use just a simple sine wave built from two frequencies, 50 and 80 ...
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How to set the "widths" parameter for continuous wavelet transform using Morlet wavelets? (scipy.signal.cwt)
I'm trying to use scipy.signal.cwt() to do a time-frequency decomposition of neural data. However, I don't completely understand the "widths" parameter.
I ...
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How to make a time/period (1/frequency) plot with CWT
This is a question about producing a time/period (1/frequency) plot from a CWT, instead of the time/scale output. I am trying to use the ssqueezepy python library to perform the CWTs. Then I ...
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Advantage of STFT over wavelet transform
I have learned about STFT and wavelet transform recently, and wavelet transform seems better than STFT in my opinion.
So, I wonder if there is any advantage of using STFT than WT, and if so, what are ...
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Result of convolution using FFT method not accurate in time
I am trying to implement fast convolution between a signal and complex Morlet wavelets. To make the result equivalent to a linear convolution, I let the MATLAB fft function zero-pad both the signal ...
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Joint Time-Frequency Scattering structure & implementation?
How does JTFS differ from wavelet time scattering in its computation graph, and how does FDTS discriminability work, at a lower level? How is it implemented in practice, and how can one visualize ...
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Joint Time-Frequency Scattering explanation?
How does JTFS work, intuitively? What are its motivations, and how's it differ from the Wavelet (time) Scattering transform? Can it be visualized?
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Wavelet Scattering time-warp equivariance
Is scattering equivariant to multiplicative time warps? Defined as
$$
x(t) \rightarrow x(\tau(t)t),\ \text{sup}|\tau'(t)| < 1
$$
This post claims it holds approximately - what are the arguments, ...
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Inverting a scalogram
A scalogram is said to discard phase information with modulus; is it still possible to recover the signal to some extent?
Algorithms like Griffin-Lim can invert within an error, but what's the ...
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Wavelet Scattering properties & implementation?
What are the properties of the scattering transform, besides shift invariance and warp stability? How is it implemented in practice, and how can one visualize its computational graph?
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Wavelet Scattering explanation?
How does Wavelet Scattering work, intuitively? What are its motivations, and how's it differ from the (continuous) Wavelet Transform? Can it be visualized?
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What is the importance of the translational invariance of the CWT?
Translational invariance is a property that the continuous wavelet transform (CWT) has but the discrete wavelet transform (DWT) does not have. It says that a shift of the signal, i.e. $x(t)\rightarrow ...
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What exactly is meant by "translation invariant dictionaries/wavelets"?
I'm trying to wrap my head around the notion of translation invariance in terms of dictionaries/wavelets. For example in Lecture Notes, Page 41 its written that one starts with a family of atoms/...
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log(conv) vs conv(log)
Suppose an arbitrary, strictly positive $x[n]$, transformed as
$$
x_l[n] = \log(1 + C x[n]) \tag{0}
$$
where $C$ is freely chosen. Given the following, where $h[n]$ is a Gaussian lowpass filter (or ...
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Continuous Wavelet Transform vs Discrete Wavelet Transform
The discrete wavelet transform is applied in many areas, such as signal compression, since it is easy to compute. I notice that, However, the continuous wavelet transform (CWT) is also applied to ...
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Wavelet "center frequency" explanation? Relation to CWT scales?
I noticed that there are many ways to relate the scale factor of wavelets to some characteristic frequency, such as the peak frequency, the central instantaneous frequency, and so on(plz see section 2....
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What scheme of padding should I choose if my 1D data satisfy the periodical boundary condition under CWT?
By CWT, I mean the continuous wavelet transform. The usual padding schemes are zero padding, periodic padding, and decay padding.
If I adopt the periodic padding, can I avoid the edge effects for the ...
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