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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questions
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17 views
interpreting wavelet transform of brain siganls
I have created wavelet transform of my signal using the following code:
...
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0answers
15 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?
2
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2answers
123 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....
2
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1answer
29 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 ...
2
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3answers
48 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
19 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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17 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 ...
1
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1answer
39 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
32 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
40 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.
$$
WBC(a_1,a_2)=...
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1answer
17 views
Define frequencies present in the time-frequency spectrum using scipy.signal.cwt
I have a very basic question, but I didn't find a definite answer elsewhere.
When we use scipy.signal.cwt we specify only one parameter ...
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0answers
8 views
Error in check.datum(x1) : biwavelet package R
I am using CWT through biwavelet package to generate results of the Continuous Wavelet Spectrum of a time series. I have 443 observations of the time series. I want ...
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1answer
35 views
Understanding the units of wavelet time & frequency resolution
While using a continuous wavelet transform for my research project, I came up with some questions.
Having a set of equations for a Morlet wavelet,
$\psi(t)=\sqrt{\frac{2}{\pi}}e^{-t^2/2}e^{i6t}$
$\...
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2answers
35 views
Is it possible that the value of a continuous mother wavelet at origin is zero, i.e. $\psi(t=0)=0$?
According to Fourier transform, a continuous wavelet could be written as
$$
\psi(t)=\frac{1}{2\pi}\int\hat\psi(k)\text{e}^{-ikt}\text{d}k
$$
From the equation above, we know that $\psi(t=0)$ is
$$
\...
1
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1answer
41 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
48 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.
...
0
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1answer
38 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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0answers
12 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
41 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
42 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 ...
0
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1answer
56 views
How do I implement a footstep recognition algorithm? One that recognizes the start and end points of each footstep?
I have some time series data captured from a person's footsteps/strides (specifically, a person on rollerblades). It came from an IMU sensor placed on a person's boot. Each data point captures ...
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0answers
19 views
Wavelet, scaling, detail, and smooth/approximation coefficients
I was reading through the documentation for the R wavelets package and doing a little experimentation and noticed that the modwt ...
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0answers
86 views
PyWavelets SWT versus MODWT
I'm just learning about wavelets and the PyWavelets package. I saw a reference to MODWT, which led me to the SO post here and then to this Python package: https://github.com/pistonly/modwtpy
What ...
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1answer
32 views
wavelet_transform
I have a signal
$$Y=f(t),$$
which I want to show the anomalies, using the wavelets transform.
I don't know if I use the CWT or the DWT and which mother wavelet could I use?
2
votes
1answer
165 views
Scalograms in python
I am reading this paper to learning basic concepts of dsp and I want to reproduce the following scalogram of a test signal (fig 4.2 of the paper):
It has been produced from the discretization of the ...
1
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1answer
72 views
3D (time, scale, amplitude) plot in Continuous Wavelet Transform
I will be extremely grateful if someone could please answer this basic question.
How can one plot a 3D (translation, scale, amplitude) plot from the Continuous wavelet transform (CWT) coefficients?
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1answer
26 views
How does signal scaling affects stationary wavelet?
I'm currently working on some signals recorded with different sensors with different adc resolutions. I wonder how this different resolutions affect signal's stationary wavelet. Does it just changes ...
0
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1answer
57 views
Are the Daubechies 4 wavelet function and scaling function dimensionless?
If the dimension of the independent variable $x$ of $f(x)$ is length, i.e. $[x]=L$, then what is the dimension of Daubechies 4 (hereafter D4) wavelet and scaling function?
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50 views
Regarding custom wavelets and their validity
I've recently started working with wavelets, and want to focus primarily on Discrete Wavelet Transform. For experimental purposes, I use the PyWavelets library in Python. In one of my tests, I tried ...
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0answers
16 views
Stockwell S-Transform and multitapering
I want to estimate just the spectral amplitudes at different time points using S-transform given a noisy signal. Would I benefit (in terms of noise reduction) from an approach used in multi taper ...
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0answers
28 views
Pros/Cons to using Spectral and Diffusive Graph Wavelets
As I understand, there are two major methods of constructing wavelets on graphs. Spectral wavelets, from David K Hammond et. al, and diffusive wavelets from Coifman and Maggioni. I can't quite parse ...
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0answers
36 views
Check vanishing moment property of db4 wavelets
I am reading the book "a primer on wavelets and their scientific applications" by James S. Walker. In chapter 3, Property I on page 46 says that if a signal $f$ is linear, then the $k$-level ...
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1answer
52 views
energy normalization across different scales in case of discrete wavelet transform
In case of continuous wavelet transform (CWT), the wavelets are generated from the mother wavelet by scaling and translation. To achieve energy normalization and to ensure that all wavelets have the ...
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32 views
Why the inverse discrete fourier transform of the Ricker pulse isn't the same as the Ricker pulse in time domain?
Question
I'm trying to use Python's scipy library to compute the IDFT of the Ricker wavelet function and compare it with the analytical time-domain version of the same function. When I compare the ...
1
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1answer
43 views
Why discrete wavelet transforms use sampling rate 2 and need signal length to be a power of 2?
I know Fourier transforms but new to wavelet transforms. I can understand Haar transform needs signal length a power of 2, since the filters have 2 taps and down-sampling and up-sampling in the ...
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0answers
21 views
Plot frequency tiling wavelets/curvelets
Is there a convinient way to plot the frequency tiling of for wavelets/curvelets? For example the input would be the number of scales $j$ and the output would be something like this:
Preferably in ...
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2answers
351 views
How is wavelet time & frequency resolution computed?
Mallat gives analytic wavelet time & frequency widths/uncertainties as
$$
\begin{align}
\sigma_{ts}^2 &= \int_{-\infty}^{\infty} (t - u)^2 |\psi_{u, s}(t)|^2 dt
= s^2 \sigma_t^...
1
vote
1answer
80 views
Energy normalization across wavelet subbands
According to the following reference: A Really Friendly Guide to Wavelets, © C. Valens, 1999
Equation 3, the wavelets are generated from the mother wavelet by scaling and translation. S is the scaling ...
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2answers
62 views
Coefficient meaning in DWT
I understand that approximate and detail coefficient represent the different signal bands. But what do the values mean and how are they used?
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0answers
20 views
How to compute inner product of Wavelet transform convoluted with signal
I have two datasets $X_1$ and $X_2$ in a sparse wavelet basis, and I have two filters $f_1$ and $f_2$. I’d like to compute the inner product of the convolutions $$\langle X_1 \star f_1, X_2 \star f_2\...
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2answers
97 views
Is there a systematic method for converting an even length FIR filter to odd length?
I'm currently implementing a discrete wavelet transform (DWT) as a cascaded QMF filter bank (pictured below). I've put together a convolution function that attempts to filter an input signal in a non-...
0
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1answer
88 views
Is it possible to define Fourier or wavelet transforms on DNA sequences?
I am wondering how and if it is possible to define a Fourier transform or Wavelet transform on DNA sequences which are basically arrays with the values $\{T,C,G,A\}$ in them.
I have found a paper ...
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0answers
30 views
How to take wavelet transform of sparse input data
I have a sparse dataset indexed by nanoseconds. Storing the dataset in a discrete fashion would take too much memory. I'd like to take a wavelet transform and I'd like it to be relatively fast. The ...
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2answers
1k views
Synchrosqueezing Wavelet Transform explanation?
How does Synchrosqueezing Wavelet Transform work, intuitively? What does the "synchrosqueezed" part do, and how is it different from simply the (continuous) Wavelet Transform?
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1answer
34 views
Does the Fast Wavelet Transform produce the same coefficient as the Discrete Wavelet Transform?
Does the Fast Wavelet Transform(FWT) produce the same coefficients as the Discrete Wavelet Transform(DWT) if configured for the same depths? Or is the the FWT just an approximation of the DWT?
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2answers
67 views
What mother wavelet should be chosen as an alternative to the STFT?
The Short Time Fourier Transform (STFT) is used to identify time localized frequency content of a signal. The STFT operates by chunking an input signal into blocks and performing FFT on the block, and ...
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2answers
91 views
One integral inverse CWT
MATLAB's icwt docs state inversion to be done by a single integral:
$$
f(t) = 2 \Re e\left\{
\frac{1}{C_{\psi, \delta}} \int_0^\infty \left< f(t), \psi(t) \right> \frac{da}{a} \tag{1}
\...
2
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1answer
54 views
What should the time-shift be when implementing a continuous wavelet transform on a computer?
I'm currently researching implementation methods of the Continuous Wavelet Transform(CWT). On paper, the CWT produces infinitely many outputs on a finite signal since the scaling and shifting ...
1
vote
1answer
56 views
Where is the mother wavelet defined in the Fast Wavelet Transform?
Referring to the Fast Wavelet Transform, this transform is implemented as a QMF filter bank. This algorithm consists of high/low pass filtering and subsampling. However, a wavelet transform is ...
1
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1answer
27 views
Why are the Continuous Wavelet Transforms of the same signal drastically different?
I'm currently studying wavelets and am running into confusion with regards to CWT coefficients. Ideally, I want a CWT algorithm that produces outputs similar to that of a STFT - i.e. produces ...
