34
votes
Accepted
Synchrosqueezing Wavelet Transform explanation?
Synchrosqueezing is a powerful reassignment method. To grasp its mechanisms, we dissect the (continuous) Wavelet Transform, and how its pitfalls can be remedied. Physical and statistical ...
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9
votes
Synchrosqueezing Wavelet Transform explanation?
Low-level intuition can be obtained by inspecting the phase transform, visually. Answer complements and is complemented by this one. (-- Answer code)
We consider a pure sinusoidal tone; ideas extend ...
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3
votes
Why does a synchrosqueezed wavelet transform show oscillating behavior?
This answer delves deeper into low-level aspects of the phase transform to better understand the wavy phenomenon; complements main answer.
2. How wavy is w?
Recall,...
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3
votes
Accepted
Why does a synchrosqueezed wavelet transform show oscillating behavior?
This was interesting to figure out. The key lies in the phase transform, and how CWT interacts with own derivative upon insufficient component separation. Relevant are, and I'll be answering, the ...
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2
votes
Synchrosqueezing transform
It looks like a forgotten scale or frequency factor in the integral over scales / frequencies.
In panel 2, the "power" of the CWT is either the CWT squared or its modulus, in the "norm $...
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1
vote
Why are wavelet transforms implemented in Python/Matlab often called Continuous wavelet transform when they take discrete-time input?
Good question.
From nomenclature standpoint
Sampling a continuous-time result (called discretization) most often inherits the original name. For example, we still say "IIR filters", though ...
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1
vote
Interpretation of wavelet trasformation (synchrosqueezing)
Any time-frequency representation with hop_size=1 is subject to the one-integral inverse, either directly or with a normalization step. This means we recover ...
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1
vote
Synchrosqueezed STFT phase transform
Why 'modified' STFT?
Authors merely state it's "convenient for our purposes", which isn't much. My exploring reveals: extreme numeric instability in reassignment and component inversion of '...
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1
vote
Accepted
Synchrosqueezed STFT phase transform
TL;DR:
CWT's $\partial_t$ is taken with respect to wavelet timeshifts, STFT's with respect to window time samples, with CWT's FT taken along rows, and STFT's along columns.
The $2\pi$ is per assuming ...
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