Linked Questions

23 votes
2 answers
11k 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
8 votes
4 answers
2k 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 ...
lemoncake's user avatar
  • 103
1 vote
3 answers
328 views

Increasing STFT resolution by repeating the window? Ways to improve STFT resolution?

In theory of FT(Fourier transform) and STFT(Short Time Fourier Transform) it is said that "A narrower window gives good ...
google dev's user avatar
2 votes
2 answers
338 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 ...
Wang Yun's user avatar
  • 124
2 votes
2 answers
122 views

Is downsampling LTI for bandlimited inputs?

This question stems from the discussion we had on a previous question of mine. The point of contention is whether the downsampling operator is time invariant or not. Which gives us a new condition to ...
Ahsan Yousaf's user avatar
  • 1,533
0 votes
1 answer
487 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 ...
OverLordGoldDragon's user avatar
1 vote
2 answers
201 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
2 votes
1 answer
90 views

Understanding stability in frame theory. Wavelets

I'm trying to grasp some understanding of the concept of stability in the context of the frame theory. The definition of frame in ref1 states that a sequence of functions $\{ \phi_n \}_{n \in \Gamma}$ ...
dac's user avatar
  • 77
0 votes
1 answer
140 views

Wavelet Scattering (Kymatio) Zero Divison Error

I'm attempting to make use of wavelet scattering to analyse my signal samples. The example IQ Wav file I am using is as follows: https://www.dropbox.com/s/dd6fr4va4alpazj/...
rshah's user avatar
  • 77
1 vote
1 answer
122 views

Building the low pass filter in the wavelet scattering transform

In 1, analyzing the equivalence between MFCC and wavelet transform, the scaled wavelets are truncated for $\lambda < 2\pi Q/T$ to fit the time spread of the wavelets within the length $T$ of the ...
dac's user avatar
  • 77
2 votes
1 answer
112 views

Choosing a good low pass filter in the wavelet scattering transform

What's the impact of a specific filter $\phi$ when building the wavelet scattering transform? I mean, if I compute the MFCC choosing different windows, (Hamming, Blackman, etc.), the behaviour ...
dac's user avatar
  • 77
3 votes
1 answer
99 views

Littlewood-Paley Conditions, Scattering, and Multi-Resolution Analysis

So I am trying to understand the scattering transform on graphs (GST). There are many formulations but I am stuck on equation 8 in this paper. Here they give a condition on a wavelets that looks like ...
WedgeAntilles's user avatar
0 votes
1 answer
125 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, ...
OverLordGoldDragon's user avatar