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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Step-by-Step calculation of stationary wavelet transform gives shifted results?
Good morning,
I am doing an SWT by hand to understand it better, and have a couple of questions. Maybe someone here has experience with this?
I am using the book "Conceptual Wavelets" by Fugal, ...
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24 views
How to tell, which coefficient corresponds to which frequency while computing wavelet transform?
I am applying wavelet transform on functional Near Infrared Spectroscopy (fNIRS) signal.
My aim is to get the info that which coefficient corresponds to which frequency in the signal. Is it possible ...
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100 views
Scaling a wavelet in continuous wavelet transform
The mexican hat wavelet, obtained from the second derivative of a Gaussian, has a functional form of
$$ \frac{2}{\sqrt{3 \sqrt{\pi} \sigma \ }} \left(1-\frac{t^2}{\sigma^2} \right) e^{-t^2/(2\sigma^...
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27 views
How to create different Time frequency images from a data
I'm new to Python.
I have a time series in a CSV file that has about 5000 rows and 3 columns.
I have split the data into training and testing in ratio 70:30 respectively.
However, I have a problem ...
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1answer
33 views
Refinement equation and orthogonal wavelets basis
I have a wavelet function space defined by,
$ \phi(x) = \sqrt(2) \sum_n h_{\phi}(n) \phi(2x-n) $ .
given the Fourier transform of the function is:
$\hat{\phi}(\omega) = \frac{1}{\sqrt(2)} \hat{h}...
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19 views
Applying Wavelet on energy disaggregation as denoising technique to remove uncertainties
I would like to apply Wavelet in MATLAB as a denoising technique on Non-Intrusive load Monitoring data. The data was captured by sensors on each appliance and one sensor on the smart meter (Normally ...
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1answer
46 views
Difference between “scaled white noise ” vs. “unscaled white noise”
I have been searching Matlab user-guide for Wavelets. In their graphical user interface for denoising, there is an option for "unscaled white noise" and "scaled white noise" for the noise structure. ...
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54 views
Fourier Transform of the full Morlet wavelet
In 2014 someone asked here the Fourier transform of the Morlet wavelet; link below:
Fourier Transform of Morlet wavelet Function?
However, it was the approximated Morlet wavelet not written with the ...
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165 views
Relationship between wavelet shape and wavelet filters
MATLAB has a library of wavelet functions, showing their "continuous forms" as well as the the decomposition and reconstruction filters.
In decimated wavelet transform the filter size remains the ...
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164 views
Plotting a scalogram of a signal's Continuous Wavelet Transform (CWT) in python
So I've been learning about wavelets for a few weeks because I'd like to use them in a research project I'm working on and I've been trying to grasp the general ideas behind them.I've been struggling ...
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27 views
Wavelets: Reconstruction Filters for 2 Level Decomposition
I am trying to understand the reconstruction part after discrete wavelet decomposition and how do we get approximations and details at various levels. Most textbooks show the complete reconstruction ...
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31 views
Number of datapoints after decimation in discrete wavelet wavelet analysis
I am following an example provided by MATLAB on 1-D wavelet decomposition (DWT). The number of datapoints is 10000. If we do a level 3 decomposition following a similar example provided by MATLAB ...
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24 views
CWT coefficients as features for ML algorithms
I use CWT coefficients as features in ML algorithms and then I did the feature selection using the chi-square test but recently I figured out that the chi-square test can only be applied for ...
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50 views
Stuck with plotting wavelet transform in Python
I want to plot the frequency composition of a sampled signal data versus time by using surf or any 3D plot. Normally time resolution of FFT is zero so I want to use wavelet transform where I want to ...
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1answer
55 views
Meaning of wavelet and scaling coefficients
What is the meaning of wavelet coefficients and scaling coefficients? E.g. for a sequence I obtained the following wavelet coeffients.
How am I supposed to interpret them? I used ...
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1answer
15 views
Clarification regarding discrete wavelet transform
One of the books on "Conceptual Wavelets" by Fugal explains some major differences between the undecimated discrete wavelet transform (UDWT) vs. discrete wavelet transform (DWT). In UDWT the scale of ...
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13 views
What wavelet should i use to analyze harmonic function?
If i have the following signal:
$$
s(t) = cos\left [ t\cdot \left (\frac{a}{2}t+b \right ) \right ]
$$
What is the best family of wavelet to analize the signal, and what is its scale range?
Do i ...
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33 views
At what stage do we compute the approximations and details while performing a DWT?
$$
\int_{-\infty}^{+\infty}{f(t)\psi_{j,k}^\ast(t)dt}\ \textrm{with}\ \psi_{j,k}(t)\ =\ a_0^{-j/2}\psi(a_0^{-j}t\ -\ b_0k)
$$
If this is the expression for the wavelet transform, how does this lead to ...
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1answer
109 views
Scaling Function in Wavelet Analysis
I was watching a YouTube tutorial on wavelets https://www.youtube.com/watch?v=wgRgodvU_Ms, where the presenter showed that if we multiply a Gaussian with a sine wave (and follow some other conditions),...
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21 views
how can we calculate Mathieu wavelet filter coefficients from its design equation? a detailed explanation will be highly appreciated
Elliptic-Cylindrical Wavelets: The Mathieu Wavelets
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1answer
66 views
Discrete wavelet transform disadvantages
I read in a paper that the discrete wavelet transform (DWT) has two disadvantages
The first one is the shift variance property due to the downsampling process. Could you please help me understanding ...
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31 views
Why my Time-Frequency plot is time reversed?
I'm trying to build my own code implementation for Continuous Wavelet Fourier Transform. But when I compare the time-frequency plot created with my function with time-frequency plot created with the ...
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1answer
35 views
Can anybody recommend a good source for material of Gaussian and Complex Gaussian wavelet? [closed]
Can anybody recommend a good source for material of Gaussian and Complex Gaussian wavelet?
Please share the link if possible.
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563 views
Python tool for time-frequency analysis
I am trying to perform time-frequency analyses using the PyWavelets (pywt) toolkit for python. My ultimate goal is to perform time-frequency analyses for EEG signals but I am starting with something ...
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12 views
What are the Red-Black Wavelets transformation for color (RGB) images?
I am looking for Red-Black Wavelet transform implementation on internet but I am unable to find it. Or How wavelets can be used for Images. Please help if you know how wavelets can be used for images.
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120 views
Any experiences for plotting a stationary wavelet transform?
I am experimenting with wavelets for my thesis and am currently working with the stationary WT pywavelets provides.
There are very nice plots for CWTs, but does anyone know a technique for producing ...
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6 views
Scaling factor in lifting scheme wavelet transform
I have a small question
why the scaling factor coefficients K1 and K2 are interchanged in the inverse process in lifting scheme wavelet transform.
thank you in advance
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60 views
Difference in the meaning of kernel, filter, and dictionary atoms
While reading literature on wavelets, I have encountered keywords filters and dictionary atoms and their exact meaning is confusing for me. Basically, one can use them interchangeably and I won't see ...
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20 views
Wavelet synthesis boundary conditions
I am interested in discrete wavelet decomposition using the D4 wavelet and am having issues understanding how the boundaries are handled during the synthesis step. Say I want to use a smooth boundary ...
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1answer
76 views
Non-Linear, Non-Stationary spectral analysis methods! When and where?
I have been reading about non-linear non-stationary signal analysis methods and it seems to do this type of analysis the go-to method is the Empirical Mode Decomposition (EMD), then Hilbert Transform (...
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17 views
Does the set of Hermitian Wavelets include fractional derivatives?
According to Wikipedia, Hermitian wavelets, "The $n^{{\textrm {th}}}$ Hermitian wavelet is defined as the $n^{{\textrm {th}}}$ derivative of a Gaussian distribution."
Are the wavelets defined by ...
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31 views
Morse / Morlet wavelet relationship?
Does anybody know what the relationship between Morse and (complex) Morlet wavelets are? I'm looking at images in papers about the Morse, and it looks like a Morlet to me. Is the Morse a ...
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can I combine 2 raster with wavelet transform in R? [closed]
I Have same problem, i will combine 2 raster data with wavelet fusion
r1<-brick("mask data/r1_mask_black.tif")
r2<-brick("mask data/r2_mask_black.tif")
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13 views
Expectation of power spectrum for nonorthogonal wavelets
I'm working through "A Practical Guide to Wavelet Analysis" by Torrence and Compo, and I am confused about section 3d ("Wavelet Power Spectrum").
Let $x_n$ denote the signal, sampled at increments $\...
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1answer
76 views
Data Adaptive technique
I am doing data analysis. I used the wavelet transform and now I am trying the Hilbert–Huang transform (HHT). In the literature, I read that Hilbert–Huang transform (HHT) is an adaptive technique. I ...
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1answer
50 views
Is it possible to extract peak locations in the time domain using help from fourier/wavelet analysis?
The signal I'm studying has fundamental frequencies of 20 and 60 cycles per minute (shown in the Periodogram graph). It is straight forward to extract the peaks in the time domain belonging to the 20 ...
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1answer
171 views
Is there an equivalent of Parseval's theorem for wavelets?
Parseval's theorem can be interpreted as:
... the total energy of a signal can be calculated by summing power-per-sample across time or spectral power across frequency.
For the case of a signal $x(...
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1answer
40 views
Peak Detection on ECG signal
I've been working on a ECG signal collected during exercise through my chest mount heart rate monitor. My goal is to accurately detect the location of the R-wave; R-wave is the narrow peak similar to ...
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3answers
481 views
Why is the high-pass filter result in a discrete wavelet transform (DWT) downsampled?
From Wikipedia's description of the Discrete Wavelet Transform, a signal yields a set of:
approximation coefficients (low-pass: by averaging + downsampling)
detail coefficients (high-pass: convolving ...
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1answer
69 views
CWT Disapointing Frequency Separation
I'm attempting to perform multi-resolution analysis via Continuous-Wavelet Transform (CWT) using Pywavelets. I've heard that CWT is supposed to be superior to STFT due to varying frequency content as ...
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1answer
132 views
What is the correct order of operations for a 2D Haar wavelet decomposition?
The source code of iqdb contains a 2D Haar transform implementation. The author claims to have implemented it according to the paper "Fast Multiresolution Image Querying", which is freely available ...
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315 views
Does it make sense to use a wavelet that is equal to a sine of one period?
Would I get same results with STFT method (short-time Fourier transform) if I try this?
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1answer
44 views
What happens if I zero out the initial terms of the fft output and take inverse fft? [duplicate]
I am new to signal processing domain. When I run fft on data of length 1000, I get 1000 complex numbers. Now, if I want to extract the low frequency information or signal approximation, I take the ...
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10 views
Morlet-based Cross Spectral Density vs Wavelet Transform
I am interested in the frequency distribution and power of neural alpha waves (8-12Hz), and have been using WT to examine them. I am quite new to the techniques involved, however, and have noticed ...
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31 views
Obtaining Continuous Wavelet Transform coefficients from Discrete Wavelet Transform
On an earlier StackExchange question, I read that for a given signal, "From the resulting DWT the corresponding full CWT can be obtained by convolving the DWT with the reproducing kernel of the ...
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1answer
229 views
Discrete Wavelet Transform (DWT) Filter Bank
I have some stumbling block in my thesis writing.
Do we use the same filter pair while implementing DWT filter bank with downsampling of the filter output, or filters do change also from level to ...
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Is the convolution between a decomposition and reconstruction filter a scalar?
I'm very new in a research topic about wavelet filtering and I received an observation by a professor, but I actually cannot understand it, so I ask you to help me.
Suppose to perform a stationary ...
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1answer
146 views
High frequencies disappear when applying discrete wavelet transform
Trying to decompose and reconstruct a signal using a to some extent self-made implementation of DWT for some reason fails. The result looks highpass filtered and/or shifted. I wanted to write the code ...
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47 views
What's the difference between Wavelet transform coherency and Singular Spectrum Analysis
I know that Wavelet transform Coherence is the most common method to find the linkage between two time series, in field of finance.
Can we use Singular Spectrum Analysis to find out the linkage of ...
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2answers
121 views
Down sampling an EEG signal
I have a set of 10 minute EEG signals that were sampled at 400 Hz and have 16 channels which corresponds to a 16x240000 matrix. These EEG signals belong to two different classes. I am trying to ...
