Questions tagged [wavelet]
A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.
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Synchrosqueezing transform
I am using the Synchrosqueezing Wavelet Transform and I want to compare it to classical CWT. For this, I use a signal consisting of a chirp. Strangely, in the SST result, it looks like the chirp has ...
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Invertible Multi-band STFT (one spectrogram, N different time/frequency resolutions)
I'm working on an ML model that edits audio spectrograms which are then inverted. The problem is too many channels (and so too much compute) are dedicated frequencies that don't really matter much to ...
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What is wrong with my Meyer wavelet implementation?
In general, given a mother wavelet $\psi \in L^2(\mathbb{R})$, a wavelet frame is constructed by
$$
\psi_{j,k} (x) := 2^{j/2} \psi(2^jx - k),
$$
for $j,k\in \mathbb{Z}$. Given such a wavelet frame, ...
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Recreating the `dwt` function from Matlab
I am trying to implement DWT (Discrete Wavelet Transform) on a given signal, without using the dwt function in Matlab. My approach was to get the synthesis filter coefficients using,
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Why is my implementation of the Haar wavelet not normalized?
The Haar wavelet system is defined by
$$
\psi_{j,k} (x) = 2^{j/2} \psi(2^jx - k),
$$
where
$$ \psi (x) = \begin{cases}
1, & 0 \leq x < \frac{1}{2} \\
-1, & \frac{1}{2}\leq x\leq 1 \\
...
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Debugging a Haar wavelet transform in the Fourier domain
I'm trying to get a minimum-viable prototype going for a project on sensor fault detection using a scale-zero Haar wavelet (frequency-domain locality is not important). After some Googling, I managed ...
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Detecting and fixing clipped positive waveforms
I have a large number of audio files recorded using custom IOT devices. When analysing the data I noticed that a portion of them seems to have their positive amplitude ramp up, but the negative ...
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Time step (skipping) in CWT function with PyWavelets
I am using cwt function from pywavelet to perform time-frequency decomposition of a large signal (several million samples). The computational requirements for this is huge, sin it performs the ...
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Normalisation of Complex Morlet Wavelet
I am currently writing an essay on Wavelet transforms, and as part of such, I am trying to show that the Morlet wavelet satisfies the standard criteria:
$$
\int^\infty_{-\infty} \psi(t) dt = 0
$$
$$
\...
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Wavelet basis orthonormality
I recently started learning about wavelet transforms, and there's something that is confusing me. My understanding was that most wavelet decompositions are simply a decomposition of a given signal in ...
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Correlation Matrix Problem of Three Decomposition Level of DWT
I'm trying to apply a DWT with 3 composition levels and the following question arose when calculating the composition matrix.
The step I'm trying to follow is:
The DWT coefficientes are obtained from ...
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Wavelet Scattering features extraction
I want ask about the wavelet scattering feature extraction with machine learning -- if it is correct to use it for fault detection in induction machines?
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How to implement scale-dependent Gaussian averaging using Morlet wavelet envelope in Python?
I'm trying to reproduce the scale-dependent Gaussian averaging of a time series as described in this paper: https://arxiv.org/pdf/1706.01126.pdf
The process involves performing a continuous wavelet ...
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Online Noise Reduction on Non-Stationary, Broadband Signals
im capturing ultrasonic waves using an analog MEMS mic and other components on a PCB. My signal is similiar broadband and non-stationary (see 2) and im trying to remove/reduce environmental noise. I ...
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Why window functions can't have both narrow main lobe and low-level side lobes?
Why window functions can't have both narrow main lobe and low-level side lobes?
i got a hint from my mentor that it's quite often expained in books about wavelets...
I thought it could be associated ...
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