OverLordGoldDragon
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How does modulation frequency appear in the modulation spectra?
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This problem is precisely what synchrosqueezing wavelet transform was invented for, and indeed maps it with great precision. I'm still developing it, and first pre-release is expected today or ...

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Unclear time-to-frequency integration step
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Matt isn't wrong, but there's a more satisfactory answer; it is convolution theorem: $$ \begin{align} \int_{-\infty}^{\infty}f(t)\psi^*(t-b)dt &= \frac{1}{2\pi}\int_{-\infty}^{\infty} F(\omega) \...

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Does Zero Padding Distort the Spectrum of a Signal?
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DFT vs DTFT, Fourier Transform The problem appears rooted in viewing DFT as a 'special case' of the continuous Fourier Transform, and of its input as some signal with legitimate frequency contents. ...

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How to train a FCNN with Spectrogram images?
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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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Joint Time-Frequency Scattering structure & implementation?
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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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Why is CWT implemented with FFT convolution?
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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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Wavelet Scattering time-warp equivariance
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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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How to remove heartbeat signal from blood pressure signal?
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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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FFT of a Time series data
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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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Explain the Process of Spectral Pooling and Spectral Activation in the Context of CNN in Frequency Domain
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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
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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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EEG peaks do not get identified at the correct frequencies
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EEG representations are typically log-transformed to offset $1/f$ power scaling, and baseline-normalized, which can drastically change the final output. Since you use a specific implementation, the ...

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What is the consensus about what is a signal?
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This question is very broad (if not ill-defined) and subject to a long article, or a book - but I'll take a shot. In broadest sense, a "signal" is anything which can be observed and ...

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Minimum discernible frequency in power spectral analysis
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If the goal is to map out a range of low frequencies, then CWT is preferred over STFT, as it zooms logarithmically and will provide far more detail (examples). If the goal is a few specific ...

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Are signals modeled either digitally or analogously or can signals modeled as both?
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Any signal can be modeled, but not necessarily uniquely. Any finite duration (i.e. real-world) signal is not bandlimited unless we assume it is - meaning, it has infinite valid representations. This ...

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Do mel-spectrograms of two audios have linear property?
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No. Mel-spectrogram is the projection of spectrogram, $|\text{STFT}|$ or $|\text{STFT}|^2$, onto mel basis. Linearity is lost at modulus: $|\text{STFT}(x_0)| + |\text{STFT}(x_1)| \neq |\text{STFT}(...

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Python- FM Modulation
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Input to sine should be phase, not frequency The * t is only to apply to fc per 1 Corrected: Code import numpy as np import matplotlib.pyplot as plt #%% Generate ####################################...

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What does the intensity values on wavelet transform mean? Amplitude or power?
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Its absolute value is amplitude. Squared is power. But if it's a plot you've come across, it's not possible to tell without units, as it could be log-transformed (decibels), which nullifies the ...

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One integral inverse CWT
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The formula is premised on the wavelet being analytic, or being nonzero only over non-negative frequencies: ${\hat\psi} (\omega < 0) = 0$. (Note all wavelets also have ${\hat \psi (0)}=0$ per the ...

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When joining two signals of different frequencies how do I find the phase shift that makes the join smooth?
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To ensure smooth continuity we generate $$ x_0 = \cos(\omega_0 t), \ t_0 \leq t < t_1 \\ x_1 = \cos(\omega_1 t + t_1 \cdot (\omega_0 / \omega_1)), \ t_1 \leq t < t_2 \\ $$ where $\omega_0 t$ is ...

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One integral inverse CWT
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Revisiting this question for a more definitive/intuitive answer. I've added reasoning here that shows real wavelets are a fair game for one integral reconstruction - along conditions on the entire ...

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Extracting EEG Bands from raw EEG signal to match with the Bands calculated on the sensor level
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Proper STFT isn't simply putting a window on data and taking its FFT; I wouldn't recommend reinventing it unless knowing exactly what you're doing. There's open source implementations: librosa, ...

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CWT Disapointing Frequency Separation
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The wavelet is too time localized. Also pywt and scipy implems are flawed. On your signal w/ ssqueezepy: Laurent is correct that CWT isn't always superior. import numpy as np from ssqueezepy import ...

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How to calculate the instantaneous frequency for one specfic signal?
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Synchrosqueezing with ssqueezepy. from ssqueezepy import TestSignals, ssq_cwt from ssqueezepy.visuals import plot, imshow x = TestSignals(N=2048).lchirp()[0] Tx, _, ssq_freqs, *_ = ssq_cwt(x) plot(x,...

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One-sided waveforms in both time and frequency?
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Disclaimer: I understand the question as "is there an $x(t)$ that's $x(t<0)=0$ with $X(\omega < 0) = 0$". I present some ideas rather than proofs. Approach 1 I'll answer in terms of ...

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Define frequencies present in the time-frequency spectrum using scipy.signal.cwt
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The center frequency at scale=1 is w, which defaults to 5. Then for any other scale (cwt's width) the frequency is w / scale, i.e. w / widths. However, PyWavelets' cwt is flawed, and scipy's even more ...

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Finding Frequencies from Log Indexed FFT
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This is a question on fitting an exponential through two points, like That depends on the parent function, which could take on form of: $$ f(x) = ab^x \tag{1} $$ or $$ f(x) = a b_0^x + c \tag{2} $$ ...

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Theoretical considerations for Using Finite Arrays to Represent Samples of Signals of Infinite Length
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The accepted answer is wrong. There's always discretization error in the sense that any number is representable to finite number of decimal points, but no one cares about that (in context of ...

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References of deep learning and ai for dsp researchers
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For understanding conv nets, I recommend works on scattering theory which provide the best explanation of their success I know of, with interpretability and mathematical rigor: Lecture Paper A ...

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