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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 ...
• 8,954
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Wavelet Scattering explanation?

Wavelet Scattering is an equivalent deep convolutional network, formed by cascade of wavelets, modulus nonlinearities, and lowpass filters. It yields representations that are time-shift invariant, ...
• 8,954
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What Is the Difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat Wavelet?

Laplace of Gaussian The Laplace of Gaussian (LoG) of image $f$ can be written as $$\nabla^2 (f * g) = f * \nabla^2 g$$ with $g$ the Gaussian kernel and $*$ the convolution. That is, the Laplace ...
• 2,584
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Which transform most closely mimics the human auditory system?

In designing such transformations, one should take into account competing interests: fidelity to the human auditory system (that varies with people), including non-linear or even chaotic aspects (...
• 31.9k

• 153
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Wavelet "center frequency" explanation? Relation to CWT scales?

The "frequency" in "center frequency" does refer to Fourier frequency - rate of sinusoidal oscillation - but measures (and interpretations) can vary depending on the wavelet. Said ...
• 8,954

Continuous Wavelet Transform vs Discrete Wavelet Transform

The CWT & DWT implementations differ in how they discretize the scale parameter used to stretch or shrink copies of the basic wavelet. The finer grain scale parameter in the CWT can be useful for ...
• 1,770
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What is "spin" for the 2D (separable) Morlet?

cause it s p i n Explanation, ground up When there's complex numbers, there's rotation. Recall, multiplying by $e^{j\theta}$ rotates a number by $\theta$ radians: and since $|e^{jX}|=1$ for any (...
• 8,954

How to Map CWT to Synchrosqueezed wavelet transform?

Let me explain the intuition briefly. The authors of the paper you've cited assume that the signal $x(t)$ can be written in the form \begin{align*} x(t) &= \sum_{k=1}^K a_k(t) \exp(2\pi\mathrm{i} ...
• 41

Slow Down Music Playing While Maintaining Frequency

The tool/theory you describe is really a large area of research in music technology, broadly called audio time-scale modification. A large component of this field is how you might prevent audible ...
• 436

"Fourier Transform can localize signals in frequency domain, but not in time domain." -- What does it mean in layman's terms?

To localize here means: to find where the signal is mostly concentrated, and with what precision. This could be either in the time or the frequency domain. An answer could be: the signal's center of ...
• 31.9k
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Difference(relation?) between filter banks and wavelet decomposition

If we stick to the linear version and discrete versions of filter banks and wavelets, filter banks represent the generic tool, and wavelets can be implemented as a specific instance of iterated $2$-...
• 31.9k
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What are the known use cases for different wavelet families?

Answer 0: ask yourself if you really need wavelets Say yes. Let us concentrate on 2-band real discrete wavelet first. JPEG 2000 is a special case, where CDF9/7 and 5/3 biorthogonal wavelets are used. ...
• 31.9k
Accepted

Bandpass filter to get EEG frequency bands?

As the frequency bands are simple frequency ranges, I wonder if I can use several bandpass filters to get them (instead of using WPT / FFT)? Sure! That's how it's usually done! Is there any ...
• 31.1k