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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308 views

Getting started with wavelet-based real-time anomaly detection for temporal signals using Python

I have an anomaly detection problem I wanted to consider addressing in software (python) with wavelets. I’m new to wavelets as well as the python’s spicy.signal wavelet package, let alone with the ...
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1answer
4k views

Discrete wavelet transform; how to interpret approximation and detail coefficients?

I am trying to understand Wavelet transform. So far I have understood the basic theory of it. But I am not able to get my head around how to interpret both coefficients. I am using PyWavelets ...
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86 views

How i can create ghost on wavelet or seismic trace and then Deghosting that in MATLAB? [closed]

I want to model a seismic trace or wavelet and then create ghost on them, at the end Deghosting in MATLAB. Can anyone help me please?
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555 views

What are the pros and cons of wavelet for filtering compared to conventional filters?

Wavelets have been widely used in denoising or extracting one specific frequency band of a signal nowadays. However, these can also be done through conventional filters (e.g. butterworth, Chebyshev). ...
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2k views

What is the difference between Constant-Q Transform and Wavelet Transform and which is better

i have been seeking for a better Transform than STFT with high overleaping. The Transform should more suitble for the human auditory system. And i learned that there are at least 3 Methods i may use ...
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1k views

What happens when we reconstruct a signal after its Fourier transform is done and some frequencies are altered? [closed]

Since we loose time information when we take a Fourier transform, what happens if we alter a few frequencies from the transform and then reconstruct the signal, do we get the altered frequency at the ...
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231 views

Inverse wavelet transform on wavelet coefficients

I have a data set which consists of Morlet coefficients for 7 channels in 18 bands. When I try to use inverse DWT in Matlab to get the raw data in time, using this code: ...
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606 views

sparsifying an ECG signal using wavelet

I have an ECG signal, and want to sparsify it using wavelet (DWT) in Matlab. In some paper they use Daubechies wavelet (DB4) with 8-tap filters. but i don't know how to extract the wavelet ...
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134 views

Quadtree decomposition of Discrete Wavelet Transform using bio4.4/CDF wavelet

My problem is pretty basic but fundamental. It relates to the way discrete wavelet transform behaves for biorothognal 4.4 or CDF wavelets. When using most wavelets (e.g., CDF 9/7 or bio4.4 or ...
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1answer
123 views

Continuous wavelet transform subsampling at lower frequencies?

I am not completely confident in my understanding of wavelet theory, but since I am currently in the process of creating a CWT scalogram tool, I have to ask: Is there a theorem allowing us to ...
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38 views

What is the meaning of negative second for a Morlet wavelet?

I kind of familiar with wavelet transform (I just used it in code but do not have a deep understanding about it). I've been reading an article and came across this sentence: where 4Fs is the ...
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1answer
105 views

Reduce Signal Size to Compare Them

I have multiple experiments and each of them produce several ($k$ for example) binary signals; some artificial example next: I have a metric to compare experiment results but I need vectors of equal ...
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769 views

2D Wavelet Transform Explanation

I am new to wavelets and for several times I stumbled over these 2D wavelet transformation pictures, but I do not understand how they are created. Can anybody try to explain in his own words how this ...
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2k views

Multilevel partial wavelet reconstruction with PyWavelets

I'm looking for a way to partially reconstruct branches of a wavelet decomposition, such that the sum would recreate the original signal. This could be achieved in MATLAB using: ...
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1answer
137 views

Output of MATLAB's two-dimensional DWT function $\tt dwt2$

This is a conceptual doubt about the two-dimensional DWT. I am trying to understand the decomposition step of a two-dimensional DWT. In the MATLAB explanation, the two-dimensional DWT generates 4 new ...
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78 views

Values (amplitudes) of the CWT and their relationship to waveform amplitudes?

I'm coding up a scalogram in C++. Right now it calculates a single row of the CWT matrix and immediately maps it to a line of pixels. Trouble is my colouring scales with the values of the transform ...
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257 views

Is Wavelet Transform better than FT if I'm only interested in knowing the frequencies and not interested of when did they happen?

I'm still in the first stages of learning about these different transformations. But one thing that came to my mind while learning about them is the question above. I learned that ...
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118 views

Transform coding gain of two channel Haar Wavelet transform (first stage)

Question My interpretation Work I'm attempting to do this in MATLAB. I know that for discrete Random Processes going into an LTI system the autocorrelation function of the output is $R_y[n] =...
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1answer
1k views

What is the relationship between scales and frequency in a Morlet wavelet transform?

I'm using PyWavelets, with a complex Morlet wavelet. Its complex wavelet transform function requires scales as one of its parameters, rather than frequencies. However, I don't understand the ...
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243 views

Complex Morlet coefficient

A complex Morlet wavelet looks like this: $$\psi(t) = C \cdot e^{i \omega t} \cdot e^{-t^2/2}$$ Here $\omega$ is the frequency and $C$ is some normalization constant. The first exponential ...
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61 views

What Is Proper Paper and MATLAB Toolbox Describing and Discussing Wavelet, Ridgelet, Curvelet and Contourlet Transforms in Detail?

Question 1: Does anybody know any paper proper for getting started understanding the concept of Wavelet, Ridgelet, Curvelet and Contourlet transforms and their differences in detail? Question 2: ...
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2answers
540 views

Log vs. linear frequency scales of Fourier and wavelet transforms

I'm trying to understand the difference between the output of a Fourier transform and a wavelet transform. A Fourier transform is done via the following function: $$\hat{f}(\xi) = \int^\infty_{-\...
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755 views

Should I ever pick the continuous wavelet transform over the discrete one? DWT vs CWT vs STFT

Of course I mean in terms of numerical algorithms. I'm reading various papers on the wavelet transform and why it's better than the short-time Fourier one. The reason that's cited more often is that ...
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81 views

Factor $|a|^{-1/2}$ in definition of mother wavelets

The mother wavelet is defined as $$\Psi_{a,\tau}(t) = \lvert a\rvert^{-1/2}\Psi\left(\frac{t-\tau}{a}\right)\tag{1}$$ in which the factor $$ \lvert a\rvert^{-1/2}\tag{2}$$ is supposed to serve ...
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103 views

How to detect the singular value with signal processing technology?

I have a signal like ...
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1answer
1k views

Continuous Wavelet Transform time vector in python

I have a signal sampled at 128 Hz. I used to extract features with the spectrogram function and I decided to upgrade my algorithm and I'm trying to analyze it using Continuous Wavelet Transform (...
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3k views

Audio time stretching, without pitch shifting

This might be a Sound Design question, or a StackOverflow question since I am attempting to do this with Java. I would like to play back a sound at the same pitch, but stretched out in time. My ...
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587 views

Which transform most closely mimics the human auditory system?

The Fourier transform is commonly used for frequency analysis of sounds. However, it has some disadvantages when it comes to analyzing the human perception of sound. For example, its frequency bins ...
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33 views

General form of dilations and translations of wavelet function

In some papers, the dilations and translations of a wavelet function is written as follows: $$\psi_{j,k}=\frac {1}{\sqrt {2^j}} \psi\left({2^{-j}t-k}\right),\quad\text{where $j$ and $k$ are integers}$...
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649 views

Relationship between Wavelet transform and Fourier Power Spectral Density

Is there anyway to obtain the Fourier Power Spectral Density from a wavelet transform of a time series? I am particularly interested in this problem because I was wondering if there is any ...
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199 views

Is MATLAB documentation wrong on when to use discrete versus continuous wavelet transform?

I was reading some of the MATLAB documentation and I get confused when reading the part about When is Continuous Analysis More Appropriate than Discrete Analysis? My knowledge before reading the ...
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4answers
543 views

Why are wavelet transforms (Multi Resolution Analysis) used more in practice for compression rather than Fourier series?

I know that both Fourier and wavelet can be used for compression of signals. The Fourier series guarantees that it gets the closest approximation of the original signal in the least squared sense. ...
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1answer
613 views

Edge map based on a Haar Wavelet Transform

I have been implementing the paper Blur Detection for Digital Images Using Wavelet Transform and was asking myself how the following formula could reconstruct the edges given a Haar Wavelet ...
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153 views

Phase Information at Higher Frequencies in Continuous Wavelet Transform

I'm using the code I found here to compute the wavelet transform of a sine wave with a constant frequency. ...
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1answer
66 views

Does SWT/ISWT require intermediate approximation coefficients to represent/reconstruct the original signal?

Taking into account that Stationary Wavelet Transform (Algorithme à trous) is not an orthogonal transform do we need intermediate approximation coefficients for signal decomposition? For example, in ...
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215 views

Additive white Gaussian noise and undecimated DWT

One of the benefits of DWT is that it is an orthonormal transform. There are statements that the energy of noise component mainly concentrates on the high-frequency (detail) part and distributes ...
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1answer
264 views

Undecimated DWT vs. CWT. In what cases is one preferable over another?

Talking about undecimated DWT let's focus here on SWT algorithm. SWT is said to be: numerically more stable due to Mallat algorithm. And the inverse operation is capable of returning the original ...
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80 views

Does Wavelet Packets (WPT) decompose signal on dyadic scales like DWT?

As far a I understand WPT is a generalization of DWT in a sense that you get a whole binary tree of possible orthogonal decompositions where DWT is only a one branch. And WPT also downsamples a signal ...
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1answer
816 views

Bandpass filter to get EEG frequency bands?

I'm doing a project with an EEG to detect driver drowsiness and learned about EEG frequency bands (alpha, beta, gamma...). As the frequency bands are simple frequency ranges, I wonder if I can use ...
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272 views

What are the known use cases for different wavelet families?

There are numerous wavelet families that differ by a number of parameters (like the number of vanishing moments, symmetry, etc.). What are the known use cases where one particular family is known to ...
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12k views

What Is the Difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat Wavelet?

There are three techniques used in CV that seem very similar to each other, but with subtle differences: Laplacian of Gaussian: $\nabla^2\left[g(x,y,t)\ast f(x,y)\right]$ Difference of Gaussians: $ \...
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421 views

Optimal Level of wavelet decomposition for denoising

If a certain mother wavelet is defined and the optimal threshold shall be defined via Donoho, how can I define the optimal decomposition level to achieve the best denoising results.
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774 views

Implementing Continuous Wavelet Transform

I need to implement the discretized continuous wavelet transform from scratch. Could someone please point me to useful papers and references available online for this?
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74 views

Wavelets in time series predictions

Wavelet transforms are linear in nature. Then how good they are for time series predictions. Can they analyze nonlinear relations in data well??
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237 views

Help understanding constant q output

I'm trying to visualise and understand the output of constant q transform. Based on my experience with FFT and the articles I've read so far, I would expect that each output bin would represent one ...
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1answer
176 views

2D DWT computation order

In 2D the discrete wavelet transform (DWT) of an image using lifting based 5/3 filter, if I perform a row-wise operation first then perform column-wise operation then I will get 4 sub-band LL, LH and ...
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1answer
744 views

Bandpass filter using wavelet transform

I'm working on a speech recognition project. The first step of this project is to find phoneme in the speech signal. To do that, I found this paper that discusses about it. In the paper, wavelets are ...
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1answer
242 views

Haar Wavelets vs STFT for graceful audio quality degradation (newbie question)

I'm playing around with FFT (using Naudio library) and with Wavelets (using TarsosDSP library) trying to get better understanding of both of them. I've noticed that when I zero out FFT/Wavelet ...
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75 views

Energy Preserving Laplacian Pyramid

Both Discrete Wavelet Transform (DWT) and Undecimated DWT possess an important property of energy preservation: on each level $$\sum_i W_i^2 + \sum_j V_j^2 = \sum_k X_k^2$$ where $W$ and $V$ are ...
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274 views

Difference(relation?) between filter banks and wavelet decomposition

I'm implementing multirate system and met concepts of filter banks and polyphase decomposition of filters. While trying to understand them, I've found that they look very similar to wavelet ...