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 ...

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) \... View answer Accepted answer 1 votes 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. ... View answer 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 ... 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})}...

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 ...

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

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 ...

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 ...

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) ...

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 ...

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, ...

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 ...

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 ...

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 ...

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 ...

No. Mel-spectrogram is the projection of spectrogram, $|\text{STFT}|$ or $|\text{STFT}|^2$, onto mel basis. Linearity is lost at modulus: $|\text{STFT}(x_0)| + |\text{STFT}(x_1)| \neq |\text{STFT}(... View answer Accepted answer 0 votes Input to sine should be phase, not frequency The * t is only to apply to fc per 1 Corrected: Code import numpy as np import matplotlib.pyplot as plt #%% Generate ####################################... View answer 0 votes Its absolute value is amplitude. Squared is power. But if it's a plot you've come across, it's not possible to tell without units, as it could be log-transformed (decibels), which nullifies the ... View answer 0 votes The formula is premised on the wavelet being analytic, or being nonzero only over non-negative frequencies:${\hat\psi} (\omega < 0) = 0$. (Note all wavelets also have${\hat \psi (0)}=0$per the ... View answer 0 votes 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 ... View answer 0 votes 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 ... View answer 0 votes 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, ... View answer 0 votes 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 ... View answer Accepted answer 0 votes Synchrosqueezing with ssqueezepy. from ssqueezepy import TestSignals, ssq_cwt from ssqueezepy.visuals import plot, imshow x = TestSignals(N=2048).lchirp() Tx, _, ssq_freqs, *_ = ssq_cwt(x) plot(x,... View answer 0 votes 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 ...

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 ...

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 $$f(x) = a b_0^x + c \tag{2}$$ ...