OverLordGoldDragon
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## 146 Answers

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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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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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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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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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: $\... View answer 4 votes STFT is frequency-shift equivariant - same absolute shift has same effect on representation regardless of original frequency${}^1: $$\hat x(\omega) \rightarrow \hat x(\omega - c) \Leftrightarrow \... View answer Accepted answer 3 votes They aren't equivalent; "stability" is used differently in each context. (1) guarantees a stable inverse. If A=0, we lose information. Existence of such A and B ensure the ... View answer 1 votes Worth looking into the log Fourier transform (and FFTLog), which I know nothing about except that its abstract reads exactly like what you seek: We present an exact and analytical expression for ... View answer 1 votes What I'd do: Transform data into a representation that maximizes "similarity" of chunks that are otherwise "alike" but have large Euclidean distance in terms of raw waveforms ... View answer 0 votes JTFS overview provided in this post. Computational structure JTFS breaks the tree structure by convolving along frequency, exploiting the joint time-frequency geometry:$$ \begin{align} S_{(J, J_{fr})}... View answer Accepted answer 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 ... View answer Accepted answer 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 ... View answer 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 ... View answer 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$... View answer 0 votes Time-warp-frequency equivariance (multiplicative) The argument is simple: CWT center frequencies are distributed exponentially. Adjacent coefficients are hence related multiplicatively in frequency: ... View answer 0 votes Algorithms aside, a scalogram is proven to be strongly invertible - perfectly for recovering instantaneous frequency and amplitude; see "Invertibility". Besides Griffin-Lim and alike, since ... View answer Accepted answer 4 votes Scattering overview provided in this answer. Computational structure Fig 4, Deep Scattering Spectrum In steps: (First order begins)$x$convolves with$\psi1_i$-->$W1_i$Modulus,$W1_i \...

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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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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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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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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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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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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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2 votes

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

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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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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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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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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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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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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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