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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30 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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28 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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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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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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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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52 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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46 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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27 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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34 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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285 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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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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73 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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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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56 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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16 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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63 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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Does wavelet decomposition introduce autocorrelation?

When decomposing a 1D signal with a wavelet transform into various detail levels, should I be observing autocorrelation structure in each detail that doesn't actually exist in the original signal, but ...
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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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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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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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69 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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38 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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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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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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293 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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59 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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91 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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311 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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40 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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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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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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165 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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117 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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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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96 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 ...
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40 views

What's the maximum allowable amplitude modulation frequency for a given carrier frequency?

I'm currently studying wavelets and had an interesting thought experiment: If you were to calculate the wavelet transform of a signal using a wavelet of a fixed frequency, you would get time varying ...
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29 views

What does it mean for a Wavelet transform to commute with translations?

Referencing this article here https://arxiv.org/pdf/1203.1513.pdf It states "A wavelet transform commutes with translations, and is therefore not translation invariant". Now I understand why it is a ...
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scalogram for huge data

I have a huge data for which I want to apply wavelet and plot scalogram. the below code works for small data. However, I have a huge signal, for which I am not able to plot scalogram. Can anyone ...
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101 views

Please help me understand this paper about Discrete Wavelet Transform!

I am trying to understand this paper says. I have found this paragraph to be vague: (a) Preprocessing Stage. The first step in this stage was to apply the Discrete Wavelet Transform (DWT). This ...
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Continuous Wavelet Filter Bank Frequencies

I have followed instructions on how to create a single Morlet wavelet, and can change the centre frequency of the wavelet. My question now, is I would very much like to create a filter bank. How do ...
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150 views

How to calculate Continuous Wavelet Transform (CWT) for specific frequency range in Python?

My first question what is a scale and how to convert it into a frequency? Secondly, I want to get CWT of a signal, but I want to have the option to choose the frequency range to work on. I found ...
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Wavelet Transform Implementation Method

I have been watching the wonderful youtube videos here: https://www.youtube.com/watch?v=4TTpwIZrUAo&list=PLn0OLiymPak2G__qvavn3T8k7R8ssKxVr&index=3 detailing morlet wavelets and fit ...
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215 views

Using Wavelet Transform on a 1D signal while updating the values

I'm working on a NN that uses Wavlet Transformed signals (with different wavelets and levels) and combines them with an additional Statistical Features input (input_4) to provide one step ahead ...
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Can coefficients of a DWT be computed using least squares approximation?

I assume that it can be computed given function values for each sample as a vector and wavelet values for each scale and translation packed in a matrix. Can anyone clarify the matrix construction and ...
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132 views

Extract approximation and detail coefficients

I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)?
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Take a wavelet function as a transfer funtion

Is there anyone having the experience of taking the wavelet funtion as a transfer function? That is: if we have $\psi_{m,n}(x)=a^{-m/2}\psi(a^{-m}x-nb)$, $\psi_{m,n}$ is the dilated and shifted ...
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99 views

For discrete wavelet transforms, is redundancy needed to ensure perfect reconstruction?

So I was using pywt and I noticed that in the padding mode documentation they explain the following: DWT performed for these extension modes is slightly ...