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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Implementation boundary-corrected wavelets on the unit interval

I was wondering if there is a 'ready-to-use' implementation available of the (boundary-corrected) wavelets constructed in Cohen, Albert, Ingrid Daubechies, and Pierre Vial. "Wavelets on the ...
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45 views

Near Real Time Algorithm For Approximating Fundamental Frequency

I'd like to analyse the notes being played on a cello C2(65.4Hz) to C6(1046.5Hz) recorded on a PC and thus a likely sampling rate of 44.1kHz. If I can get that to behave then I'd like to be able to ...
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1answer
26 views

Choosing a good low pass filter in the wavelet scattering transform

What's the impact of a specific filter $\phi$ when building the wavelet scattering transform? I mean, if I compute the MFCC choosing different windows, (Hamming, Blackman, etc.), the behaviour ...
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43 views

Time support for wavelets in scattering transform

In 1 they say that the energy of $\psi_\lambda(t)$ is concentrated in an interval of length $2\pi Q/\lambda$. I understand the inverse proportionality between the frequency band $\lambda/Q$ and the ...
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1answer
35 views

Building the low pass filter in the wavelet scattering transform

In 1, analyzing the equivalence between MFCC and wavelet transform, the scaled wavelets are truncated for $\lambda < 2\pi Q/T$ to fit the time spread of the wavelets within the length $T$ of the ...
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574 views

Advantage of STFT over wavelet transform

I have learned about STFT and wavelet transform recently, and wavelet transform seems better than STFT in my opinion. So, I wonder if there is any advantage of using STFT than WT, and if so, what are ...
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1answer
51 views

Understanding stability in frame theory. Wavelets

I'm trying to grasp some understanding of the concept of stability in the context of the frame theory. The definition of frame in ref1 states that a sequence of functions $\{ \phi_n \}_{n \in \Gamma}$ ...
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Calculate and plot CDF 5/3 wavelet phi and psi functions

For a FOSS project I've to work with the CDF 5/3 wavelet. And while I understand the implementation by lifting scheme and my code works well, I want to understand the math theory behind wavelets in ...
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How to do appcoef and detcoef using pyWavelets?

I am new to signal processing and currently doing a school project in wavelet transform using Python. I want to extract all details and approximations (Example: cA2, cA1, cD2, cD1), pywt could return ...
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How can we divide our long-time domain signal into equal segments and then apply Wavelet transform?

I have a time-domain signal and the samples size is 80000. I want to divide these samples into equal sizes of segments and want to apply wavelet transform to them. How I can do this step. please guide ...
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Multilevel DWT wavedec - How to get each coefficient (approximations and details) in the same length as the original signal?

I am doing a school project referring to the research paper https://www.tandfonline.com/doi/abs/10.1080/0952813X.2013.813976?journalCode=teta20 The overall concept of the research is as the following ...
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113 views

Image / Video Upscaling (Super Resolution) Algorithm Explanation (Image and Video Upscaling from Local Self Examples)

So, I'm trying to implement the classical algorithm described in this paper Image and Video Upscaling from Local Self-Examples and this presentation to serve as a baseline for comparison with AI/NN-...
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Level dependent threshold in wavelet coefficients to compress an image

What's the way to choose a threshold in a certain level decomposition? I found about S-median threshold but at this point I'm not working with noise so I think implementing this wounldn't make sense
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1answer
45 views

Should i use window with hop_size in Wavelet Transform or Discrete Wavelet Transform?

I have a signal (audio - voice) with 1 second of duration with sample rate of 50000 Hz. It is big signal and I wish extract some features and apply pattern recognition or classification. My question ...
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45 views

Joint Time-Frequency Scattering structure & implementation?

How does JTFS differ from wavelet time scattering in its computation graph, and how does FDTS discriminability work, at a lower level? How is it implemented in practice, and how can one visualize ...
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1answer
87 views

Joint Time-Frequency Scattering explanation?

How does JTFS work, intuitively? What are its motivations, and how's it differ from the Wavelet (time) Scattering transform? Can it be visualized?
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1answer
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Wavelet Scattering time-warp equivariance

Is scattering equivariant to multiplicative time warps? Defined as $$ x(t) \rightarrow x(\tau(t)t),\ \text{sup}|\tau'(t)| < 1 $$ This post claims it holds approximately - what are the arguments, ...
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1answer
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Inverting a scalogram

A scalogram is said to discard phase information with modulus; is it still possible to recover the signal to some extent? Algorithms like Griffin-Lim can invert within an error, but what's the ...
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174 views

Wavelet Scattering properties & implementation?

What are the properties of the scattering transform, besides shift invariance and warp stability? How is it implemented in practice, and how can one visualize its computational graph?
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1answer
297 views

Wavelet Scattering explanation?

How does Wavelet Scattering work, intuitively? What are its motivations, and how's it differ from the (continuous) Wavelet Transform? Can it be visualized?
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2answers
58 views

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

Translational invariance is a property that the continuous wavelet transform (CWT) has but the discrete wavelet transform (DWT) does not have. It says that a shift of the signal, i.e. $x(t)\rightarrow ...
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1answer
52 views

How to plot the shape of a 2D wavelet?

I often see images like this: where on the left it depicts 2D wavelets and on the right curvelets for different scales and locations. How can I visualize different 2D wavelets/curvelets in such a way ...
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How to effectively stationarise non-periodic wave signals?

I am pre-processing a non-periodic signal for further implementation of autoregressive modelling on the signal. The signal is shown in the following figure. However, when I applied the Augmented ...
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Question about pywt.wavedec() validation

I am trying to validate and understand Wavelet decomposition using pywt.wavedec(). Here are the steps I took: (1) For a 3 level decomposition, I added a sine component with the following frequency for ...
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1answer
73 views

What exactly is meant by "translation invariant dictionaries/wavelets"?

I'm trying to wrap my head around the notion of translation invariance in terms of dictionaries/wavelets. For example in Lecture Notes, Page 41 its written that one starts with a family of atoms/...
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Estimating significance in time-frequency spectrograms

I want to investigate the common input of two EMG signals using a wavelet-based approach. To this end, I chose the continuous wavelet transform to approach my research question. In addition, I would ...
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Inverse discrete wavelet transfrom

I am trying to understand the formula of the inverse wavelet transform. Although I have looked at many papers none of them fully define the summations that appear and this is creating a lot of ...
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1answer
147 views

How to alleviate the edging effect of the Hilbert transform?

I am trying to use Hilbert transform to extract the envelope of a residual signal. After implementing the Hilbert transform, I find that envelope jumps very high at its boundaries. May I ask the ...
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3answers
298 views

Continuous Wavelet Transform vs Discrete Wavelet Transform

The discrete wavelet transform is applied in many areas, such as signal compression, since it is easy to compute. I notice that, However, the continuous wavelet transform (CWT) is also applied to ...
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2answers
87 views

Manual DWT vs Python pywt

I am trying to understand Discrete Wavelet Transform. I am trying to do it manually to understand all the steps well. Taking as an example the wavelet function 'sym2' knowing that its low decompostion ...
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2answers
53 views

Discrete Wavelet Transform (DWT) and wavelet family

I have just started reading about wavelets for a data compression problem that I want to perform. I am reading about Discrete Wavelet Transform (DWT) but I can't understand where the wavelet family ...
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24 views

Alternatives to Meyer Windows as Curvelets?

I am looking for alternative to Meyer window functions (Section 4.1) from which one can define a curvelet system. Are there any similar window functions which would be as easy to implement?
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2answers
194 views

How does the scale of a wavelet relate to the Fourier frequency (or period) under CWT?

I noticed that there are many ways to relate the scale factor of wavelets to some characteristic frequency, such as the peak frequency, the central instantaneous frequency, and so on(plz see section 2....
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1answer
47 views

how does wavelet transform detect pulses from a signal

I am learning wavelet transform, below image is an example I have that uses haar wavelet for decomposing the simple haar wavelet like signal. i know that the coefficients at each level are results of ...
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3answers
68 views

What does the intensity values on wavelet transform mean? Amplitude or power?

So when applying wavelet transform, we get a 2d plot. Each point in that 2d plot has a color, showing intensity of something. But I cannot understand if it is an amplitude or power?
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1answer
47 views

What scheme of padding should I choose if my 1D data satisfy the periodical boundary condition under CWT?

By CWT, I mean the continuous wavelet transform. The usual padding schemes are zero padding, periodic padding, and decay padding. If I adopt the periodic padding, can I avoid the edge effects for the ...
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19 views

Understanding why we have low-pass/high-pass filters in MRA

I am new to Multiresolution analysis and I can't figure out and find something mathematically convincing of why in multiresolution decomposion the filters are low and high pass. I.e. in the ...
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1answer
56 views

Is single integral inverse CWT possible with real-valued wavelets?

Where the CWT in the title refers to the continuous wavelet transform. Torrence1998 proposed a reconstruction formula as shown below Obviously, Eq.(11) is a single integral. However, Torrence1998 ...
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1answer
49 views

Compared with the real-valued continuous wavelet, what are the advantages of the complex-valued continuous wavelets?

I noticed that there are two types of wavelet functions, i.e. the real-valued, such as the Mexican hat wavelet, and the complex-valued, such as the Morlet wavelet. How was the complex-valued wavelet ...
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1answer
54 views

How to understand the statistical noise level of wavelet bicoherence?

Wavelet bicoherence was given by Van Milligen1995, which used to analyze turbulence. And the normalized squared wavelet bicoherence (usually called wavelet bicoherence) is shown below. $$ WBC(a_1,a_2)=...
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1answer
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Define frequencies present in the time-frequency spectrum using scipy.signal.cwt

I have a very basic question, but I didn't find a definite answer elsewhere. When we use scipy.signal.cwt we specify only one parameter ...
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Error in check.datum(x1) : biwavelet package R

I am using CWT through biwavelet package to generate results of the Continuous Wavelet Spectrum of a time series. I have 443 observations of the time series. I want ...
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1answer
50 views

Understanding the units of wavelet time & frequency resolution

While using a continuous wavelet transform for my research project, I came up with some questions. Having a set of equations for a Morlet wavelet, $\psi(t)=\sqrt{\frac{2}{\pi}}e^{-t^2/2}e^{i6t}$ $\...
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50 views

Is it possible that the value of a continuous mother wavelet at origin is zero, i.e. $\psi(t=0)=0$?

According to Fourier transform, a continuous wavelet could be written as $$ \psi(t)=\frac{1}{2\pi}\int\hat\psi(k)\text{e}^{-ikt}\text{d}k $$ From the equation above, we know that $\psi(t=0)$ is $$ \...
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1answer
63 views

Why does each node in the wavelet scattering transform split into multiple paths?

Why does each node in the wavelet scattering transform split into multiple paths as in this figure from https://arxiv.org/abs/1304.6763? I understand roughly what’s happening along a single path, but ...
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1answer
109 views

How to filter out noise from non-stationary signal

I have this non-stationary signal. the mean is roughly constant but the second moment (autocorrelation) does not depend only on the time lag $tau$. Correct me if I am wrong in the above statement. ...
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1answer
45 views

Detecting and removing interferences from a signal

I am using MATLAB in order to denoise and remove interferences on a signal. I used wdenoise to denoise my signal which works by setting a threshold (for example ...
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14 views

Smoothing contours for contour analysis for character recognition

I am making a character recognition library using contour analysis. Contours are sequencies of complex numbers X + j*Y (in fact in contour analysis they are defined ...
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1answer
79 views

Scaling Function and Wavelet Function

I don't understand the meaning of scaling function when I used CWT/DWT. For me, I understand that the wavelet function (mother wavelet) is the function that we used to decompose our signal in ...
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1answer
178 views

Difference between Gabor filtering and Discrete Wavelet Transform

Both Gabor filtering and discrete wavelet transform (DWT) analyze the image in both spatial and frequency domains, unlike Fourier transform which analyzes the image only in the frequency domain. What ...

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