Linked Questions

23 votes
2 answers
12k 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?
OverLordGoldDragon's user avatar
12 votes
1 answer
7k 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?
OverLordGoldDragon's user avatar
11 votes
4 answers
5k views

What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform?

At a glance, the constant-Q fourier transform and the complex Gabor-Morlet wavelet transform seem the same. Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, ...
endolith's user avatar
  • 15.8k
4 votes
6 answers
589 views

instantaneous frequency for a sum

In the literature, the instantaneous frequency for a signal $s(t)=e^{-j \phi(t)}$ is given by: $$f(t)=\tfrac{1}{2\pi}\frac{d\phi(t)}{dt}$$ This my problem: I have a signal $$u(t)=e^{-j \alpha_1 \phi(...
user46213's user avatar
6 votes
3 answers
1k views

Intuition behind the Continuous Wavelet Transform?

I was thinking sometime back about how to explain the Continuous Wavelet Transform ELI5. So this is what I came across. The correlation of two exact signals is 1. So if I have an input signal $f(x)$ ...
user1343318's user avatar
1 vote
1 answer
546 views

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
2 votes
2 answers
474 views

The uncertainty principle - Why does it imply that we can't localise

The uncertainty principle states that if you have a signal which is very concentrated in time, then its Fourier transform will be rather outspread and vice versa. However, I don't really understand ...
Richard's user avatar
  • 129
1 vote
1 answer
841 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 ...
vibe's user avatar
  • 290
1 vote
1 answer
162 views

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) &&...
OverLordGoldDragon's user avatar
0 votes
1 answer
347 views

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 ...
Jokerp's user avatar
  • 189
1 vote
1 answer
232 views

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 ...
User's user avatar
  • 55
1 vote
2 answers
209 views

How to objectively measure how "good" a time-frequency representation of music is?

I've been studying the time-frequency uncertainty principle of Dennis Gabor, and the tradeoff of the STFT window size in representing the tonal and transient characteristics of the musical signal ...
Sevag's user avatar
  • 205
0 votes
2 answers
166 views

Is it possible that the value of a continuous mother wavelet at origin is zero, i.e. $\psi(t=0)=0$?

According to Fourier transform, a continuous wavelet could be written as $$ \psi(t)=\frac{1}{2\pi}\int\hat\psi(k)\text{e}^{-ikt}\text{d}k $$ From the equation above, we know that $\psi(t=0)$ is $$ \...
Wang Yun's user avatar
  • 124
2 votes
1 answer
85 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?
Eddy Piedad's user avatar
1 vote
1 answer
78 views

How to understand the statistical noise level of wavelet bicoherence?

Wavelet bicoherence was given by Van Milligen1995, which used to analyze turbulence. And the normalized squared wavelet bicoherence (usually called wavelet bicoherence) is shown below. $$ WBC(a_1,a_2)=...
Wang Yun's user avatar
  • 124

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