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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75 views

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 ...
1 vote
1 answer
154 views

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 ...
1 vote
2 answers
106 views

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 ...
2 votes
2 answers
124 views

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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1 vote
1 answer
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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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1 answer
51 views

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 ...
2 votes
1 answer
33 views

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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1 answer
51 views

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 ...
0 votes
1 answer
44 views

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 ...
0 votes
0 answers
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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 ...
3 votes
1 answer
99 views

Calculating signal power from Continuous Wavelet Transform

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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1 answer
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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 ...
2 votes
1 answer
31 views

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 ...
-1 votes
1 answer
100 views

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 ...
0 votes
1 answer
287 views

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 ...
1 vote
1 answer
169 views

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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8 votes
4 answers
932 views

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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1 answer
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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 ...
0 votes
1 answer
145 views

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 ...
1 vote
1 answer
317 views

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?
0 votes
1 answer
59 views

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, ...
0 votes
1 answer
90 views

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 ...
5 votes
1 answer
694 views

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?
7 votes
1 answer
2k views

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?
2 votes
2 answers
103 views

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 ...
1 vote
1 answer
128 views

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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4 votes
1 answer
101 views

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 ...
4 votes
3 answers
954 views

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 ...
2 votes
2 answers
300 views

How does the scale of a wavelet relate to the Fourier frequency (or period) under CWT?

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....
1 vote
1 answer
152 views

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 ...
1 vote
1 answer
72 views

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 ...
0 votes
1 answer
136 views

Define frequencies present in the time-frequency spectrum using scipy.signal.cwt

I have a very basic question, but I didn't find a definite answer elsewhere. When we use scipy.signal.cwt we specify only one parameter ...
1 vote
2 answers
218 views

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 ...
1 vote
1 answer
130 views

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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1 answer
106 views

Pywavelets CWT returning 0 after scale 64

I am running continuous wavelet transform in mexican hat wavelet basis on a data set (with millions of samples) using pywavelets. The command used is ...
1 vote
1 answer
40 views

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?
4 votes
1 answer
2k views

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 ...
0 votes
2 answers
295 views

3D (time, scale, amplitude) plot in Continuous Wavelet Transform

I will be extremely grateful if someone could please answer this basic question. How can one plot a 3D (translation, scale, amplitude) plot from the Continuous wavelet transform (CWT) coefficients? ...
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2 votes
2 answers
226 views

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\...
2 votes
2 answers
1k views

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^...
2 votes
2 answers
366 views

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 ...
14 votes
2 answers
4k views

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?
2 votes
2 answers
286 views

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} \...
2 votes
1 answer
737 views

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 $\...
1 vote
2 answers
385 views

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"). ...
3 votes
1 answer
388 views

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 ...
1 vote
1 answer
644 views

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 ...
0 votes
2 answers
111 views

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. ...
0 votes
1 answer
84 views

PyWavelets CWT: resampling vs recomputing wavelet

Related. The implementation pre-integrates a wavelet once, and resamples it at each scale, finally differencing to implement ...
1 vote
1 answer
1k views

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 ...