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.
74 questions
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Synchrosqueezing Wavelet Transform explanation?
How does Synchrosqueezing Wavelet Transform work, intuitively? What does the "synchrosqueezed" part do, and how is it different from simply the (continuous) Wavelet Transform?
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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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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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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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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 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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Inverse Continuous Wavelet Transform derivation?
Wiki writes iCWT as
$$
f(t) = C_{\psi}^{-1} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} W_f(a,b) \frac{1}{|a|^{1/2}} \tilde\psi \left(\frac{t - b}{a}\right) db \frac{da}{a^2}, \tag{1}
$$
where $\...
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Scalograms in python
I am reading this paper to learning basic concepts of dsp and I want to reproduce the following scalogram of a test signal (fig 4.2 of the paper):
It has been produced from the discretization of the ...
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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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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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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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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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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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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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Why is CWT implemented with FFT convolution?
Some implementations generate wavelets in frequency domain.
Besides speed per FFT convolution, is there any reason?
All wavelets will be sampled at same length - 100,000 samples even for those having ...
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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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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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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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Why does a synchrosqueezed wavelet transform show oscillating behavior?
This question came up in the context of the ssqueezepy library. As a basic experiment I did compute the synchrosqueezed wavelet transform of three basic signals:
A ...
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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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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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How is wavelet time & frequency resolution computed?
Mallat gives analytic wavelet time & frequency widths/uncertainties as
$$
\begin{align}
\sigma_{ts}^2 &= \int_{-\infty}^{\infty} (t - u)^2 |\psi_{u, s}(t)|^2 dt
= s^2 \sigma_t^...
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Wavelet transformation to analyse time series
I am new to wavelet transformation. I am learning it as a tool for signal processing. I have a time series that I want to analyze. I tried to learn wavelet transformation by applying it to a periodic ...
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Synchrosqueezed STFT phase transform
Synchrosqueezed STFT paper, Synchrosqueezing based Recovery of Instantaneous Frequency from Nonuniform Samples, defines STFT phase transform as:
$$
w(u, \xi) = \xi - \frac{\partial_tS_{g}f(u, \xi)}{j2\...
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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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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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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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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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One integral inverse CWT
MATLAB's icwt docs state inversion to be done by a single integral:
$$
f(t) = 2 \Re e\left\{
\frac{1}{C_{\psi, \delta}} \int_0^\infty \left< f(t), \psi(t) \right> \frac{da}{a} \tag{1}
\...
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PyWavelets CWT implementation
I seek to understand PyWavelets' implementation of the Continuous Wavelet Transform, and how it compares to the more 'basic' version I've coded and provided here. In particular:
How is integrated ...
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2
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CWT Disapointing Frequency Separation
I'm attempting to perform multi-resolution analysis via Continuous-Wavelet Transform (CWT) using Pywavelets. I've heard that CWT is supposed to be superior to STFT due to varying frequency content as ...
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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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STFT with varying window lengths (like the continuous wavelet transform)
I was wondering if it is possible to use windows of varying lengths when making a spectrogram based on the short-time Fourier transform (STFT). That is, for higher frequencies I would use shorter ...
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How is wavelet center frequency computed?
PyWavelets (1) takes index of max DFT magnitude, (2) adds 1 to it, (3) divides by domain, which is the range of input values to the wavelet ("support"). ...
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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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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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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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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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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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1
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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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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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Is single integral inverse CWT possible with real-valued wavelets?
Where the CWT in the title refers to the continuous wavelet transform. Torrence1998 proposed a reconstruction formula as shown below
Obviously, Eq.(11) is a single integral. However, Torrence1998 ...
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How to test wavelet transforms?
One pertinent attribute is normalization, which measures performance in describing signal spectral amplitude and energy, like here. Others are robustness to noise, time vs frequency resolution. ...
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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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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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Understanding the units of wavelet time & frequency resolution
While using a continuous wavelet transform for my research project, I came up with some questions.
Having a set of equations for a Morlet wavelet,
$\psi(t)=\sqrt{\frac{2}{\pi}}e^{-t^2/2}e^{i6t}$
$\...
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wavelet_transform
I have a signal
$$Y=f(t),$$
which I want to show the anomalies, using the wavelets transform.
I don't know if I use the CWT or the DWT and which mother wavelet could I use?
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CWT at low scales: PyWavelets vs Scipy
Low scales are arguably the most challenging to implement due to limitations in discretized representations. Detailed comparison here; the principal difference is in how the two handle wavelets at ...
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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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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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