OverLordGoldDragon
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Role of window length and overlap in uncertainty principle?
2 votes

Overlap is and isn't related to time resolution: in sense of the uncertainty principle, only the window width plays a role. However, any overlap other than maximum (hop_size = len(window) - 1) will ...

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How to train a FCNN with Spectrogram images?
0 votes

Spectrograms will work with any network that can operate on images. A spectrogram, however, is not an image, and many image techniques will be inapplicable: Data augmentation via rotation: a rotated ...

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Choosing a good low pass filter in the wavelet scattering transform
1 votes

The choice of $\phi$ affects: Time-shift invariance: slower decay in time will increase it Time-warp stability: slower decay in time will increase it mainly for deformations along time (but not only ...

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Time support for wavelets in scattering transform
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1 votes

It's indeed only a statement on proportionality. Wavelets aren't compat, so any notion of "support" invokes a heuristic (engineered criterion). However, it's not applicable to all wavelets: ...

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Building the low pass filter in the wavelet scattering transform
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1 votes

It keeps the scale of the largest scale wavelet $\leq T$ while still tiling the entire frequency axis. using a single low pass filter built with a single scaling function would not achieve this: $\...

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Advantage of STFT over wavelet transform
4 votes

STFT is frequency-shift equivariant - same absolute shift has same effect on representation regardless of original frequency${}^1$: $$ \hat x(\omega) \rightarrow \hat x(\omega - c) \Leftrightarrow \...

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Understanding stability in frame theory. Wavelets
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3 votes

They aren't equivalent; "stability" is used differently in each context. $(1)$ guarantees a stable inverse. If $A=0$, we lose information. Existence of such $A$ and $B$ ensure the ...

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Convolutions in log-scale axis
1 votes

Worth looking into the log Fourier transform (and FFTLog), which I know nothing about except that its abstract reads exactly like what you seek: We present an exact and analytical expression for ...

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Identify and remove repeated audio chunks
1 votes

What I'd do: Transform data into a representation that maximizes "similarity" of chunks that are otherwise "alike" but have large Euclidean distance in terms of raw waveforms ...

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Joint Time-Frequency Scattering structure & implementation?
0 votes

JTFS overview provided in this post. Computational structure JTFS breaks the tree structure by convolving along frequency, exploiting the joint time-frequency geometry: $$ \begin{align} S_{(J, J_{fr})}...

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Joint Time-Frequency Scattering explanation?
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1 votes

JTFS is an extension of Wavelet Scattering that exploits time-frequency structure, adding sensitivity to frequency-dependent time shifts, invariance to frequency transposition, and stability against ...

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

This is subject of ridge analysis. The "quality" of a representation can be quantified as follows: Component extraction Ability to separate intrinsic modes / independent time-frequency ...

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Why is CWT implemented with FFT convolution?
0 votes

The answer is wavelet design. In brief, sampling in frequency domain offers precise control over certain desired filtering properties and is often subject to less discretization error. Discretization ...

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What is the importance of the translational invariance of the CWT?
2 votes

CWT is translation-invariant in feature sense: translating a pattern translates its representation but not modify it. In coefficient sense, it is translation equivariant: shift signal $\Leftrightarrow$...

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Wavelet Scattering time-warp equivariance
0 votes

Time-warp-frequency equivariance (multiplicative) The argument is simple: CWT center frequencies are distributed exponentially. Adjacent coefficients are hence related multiplicatively in frequency: ...

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Inverting a scalogram
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Algorithms aside, a scalogram is proven to be strongly invertible - perfectly for recovering instantaneous frequency and amplitude; see "Invertibility". Besides Griffin-Lim and alike, since ...

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Wavelet Scattering properties & implementation?
Accepted answer
4 votes

Scattering overview provided in this answer. Computational structure Fig 4, Deep Scattering Spectrum In steps: (First order begins) $x$ convolves with $\psi1_i$ --> $W1_i$ Modulus, $W1_i \...

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Wavelet Scattering explanation?
Accepted answer
6 votes

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, ...

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Why are there copies of a signal in the frequency domain?
2 votes

It's the spectrum of a discrete signal: sampling in time $\Leftrightarrow$ periodizing in frequency - explained in detail here. Overlap means there's aliasing, and we require a higher sampling rate. ...

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How to remove heartbeat signal from blood pressure signal?
0 votes

If $A(t)$ is known, it can be zeroed in the synchrosqueezed representation - the remainder is then $B(t)$, recovered by inversion. $A(t)$ need not be known perfectly - just enough to indentify its ...

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How to plot the shape of a 2D wavelet?
Accepted answer
1 votes

Transform to time domain Center Plot real & imag separately, or use complex colormap, or take modulus Results below. Python code -- more examples -- other examples Minimal code import numpy as ...

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FFT of a Time series data
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0 votes

np.linspace(0, 100, 1000, endpoint=False) to yield full integer periods np.sin(2*np.pi * 1 * t) np.imag for np.sin and np.real for np.cos t = np.linspace(0, 100, 1000, 0) S_t = np.sin(2*np.pi*1*t) ...

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Regularity in EEG data
1 votes

TP9 and AF7 are definitely not brain waves. AF8 is more realistic, but still too clean; I suspect both it and TP10 were heavily filtered. Possibly TP9 and AF7 had negligible activity and were ...

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Computable Time-Frequency Distribution without Cross-Terms
2 votes

Synchrosqueezing. Diminishes Wigner-Ville interaction disadvantages as described here.

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scipy.signal.spectrogram() - how to handle gaps in the timeseries data
1 votes

OP's time vector is What I'd do: Treat it as piecewise-lienar, i.e. ignore that the time vector isn't uniformly spaced except for jumps. This should work reasonably - but if greater accuracy is ...

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scipy.signal.spectrogram() with noverlap=nperseg-1, what are the possible side-effects?
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1 votes

noverlap = nperseg - 1 provides maximum possible information - it is the 'ideal' configuration. A spectrogram is $|\text{STFT}|$, and $\text{STFT}$ is input convolved with windowed complex sinusoids. ...

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Is it possible to "determine"/"evaluate" the perceived quality of a music audio/video record by using software in an automatic way?
2 votes

Is it possible to analyze a recording in a software way ... to "determine"/"evaluate" its subjective quality Yes, very possible; all one needs is to define, mathematically, what &...

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Explain the Process of Spectral Pooling and Spectral Activation in the Context of CNN in Frequency Domain
0 votes

Update: after a closer look, activation follows pooling, not precedes; this is much more explicit in the original paper. Furthermore, the cited paper uses linear approximations of nonlinearities (but ...

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Can i represent a Time series signal as a spectogram image with desired shape
0 votes

Yes, just adjust hop_size and n_fft such that width matches height. But mind: hop_size <= window_length must hold to not lose information (NOLA) (width, height, 3) can't be done with spectrogram, ...

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What exactly is meant by "translation invariant dictionaries/wavelets"?
Accepted answer
2 votes

It's rather translation equivariant: $$ \text{CWT}_{s, t}x(t - t_0) = \text{CWT}_{s, t - t_0}x(t) \tag{1} $$ and $$ \langle x(t−t_0),\psi(t) \rangle= \langle x(t), \psi(t+t_0)\rangle \tag{2} $$ That ...

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