# 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 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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1 vote
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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

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 ...
1 vote
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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 ...
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 ...
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1 vote
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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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### 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
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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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### 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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### 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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### 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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### 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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### 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 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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### 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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### 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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### PyWavelets CWT: resampling vs recomputing wavelet

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