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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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43 votes
6 answers
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What properties make certain wavelets "better" than others in image compression?

I am trying to teach myself more about image compression using the wavelet transform method. What is it about certain wavelets that make them preferable when compressing images? Are they easier to ...
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30 votes
4 answers
6k views

Which time-frequency coefficients does the Wavelet transform compute?

The Fast Fourier Transform takes $\mathcal O(N \log N)$ operations, while the Fast Wavelet Transform takes $\mathcal O(N)$. But what, specifically, does the FWT compute? Although they are often ...
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25 votes
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Bag of Tricks for Denoising Signals While Maintaining Sharp Transitions

I know this is signal dependent, but when facing a new noisy signal what is your bag of tricks for trying to denoise a signal while maintaining sharp transitions (e.g. so any sort of simple averaging, ...
John Robertson's user avatar
24 votes
3 answers
44k 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: $ \...
DeusXMachina's user avatar
23 votes
2 answers
12k 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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22 votes
2 answers
7k views

What's the difference between the Gabor and Morlet wavelets?

The Gabor wavelet is a kind of the Gaussian modulated sinusoidal wave (source)   Gabor wavelets are formed from two components, a complex sinusoidal carrier and a Gaussian envelope. (source) ...
endolith's user avatar
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18 votes
2 answers
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Using continuous verses discrete wavelet transform in digital applications

I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or ...
John Robertson's user avatar
16 votes
1 answer
4k views

Why Wavelet developed when we already had Short-time Fourier transform

If we already had Short-time Fourier transform for better analysis of a signal than Discrete Fourier Transform, then what was the need that leads to development of Wavelet Transform ?
Sufiyan Ghori's user avatar
16 votes
3 answers
21k views

How can I plot frequency vs magnitude of wavelet transform?

I am running Morlet continuous wavelet transform. I have got wscalogram of signal and now I want to plot freq-magnitude like the following picture., but I don't ...
SAH's user avatar
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15 votes
3 answers
13k views

Reading the Wavelet transform plot

I am having trouble understanding on how to read the plot plotted by a wavelet transform, here is my simple Matlab code, ...
Sufiyan Ghori's user avatar
15 votes
3 answers
6k views

When can we write Heisenberg uncertainty Principle as a equality?

We know that Heisenberg uncertainty Principle states that $$\Delta f \Delta t \geq \frac{1}{4 \pi}.$$ But (in many case for Morlet wavelet) I have seen that they changed the inequality to an equality....
SAH's user avatar
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15 votes
2 answers
20k views

Discrete Wavelet Transform - Visualizing Relation between Decomposed Detail Coefficients and Signal

I'm trying to directly visualize the relation between discrete wavelet transform (DWT) detail coefficients and the original signal/its reconstruction. The goal is to show their relation in an ...
geekoverdose's user avatar
14 votes
1 answer
16k views

Comparison between Fourier transform, short-time Fourier transform and wavelets

What is the difference between the Fourier transform, short-time Fourier transform and wavelets?
student's user avatar
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14 votes
1 answer
3k views

What does the normalization step of the Haar wavelet transform represent?

When you perform the Haar wavelet transform, you take the sums and differences, then at each stage, you multiply the entire signal by $\small\sqrt2$. When taking the inverse transform, you multiply ...
bobobobo's user avatar
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14 votes
3 answers
5k views

STFT and DWT (Wavelets)

STFT can be successfully used on sound data (with a .wav soundfile for example) in order to do some frequency-domain modifications (example : noise removal). With ...
Basj's user avatar
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13 votes
1 answer
2k 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 ...
user76284's user avatar
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12 votes
1 answer
7k 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?
OverLordGoldDragon's user avatar
12 votes
3 answers
1k views

How do I get started with Wavelets

Our current project requires us to do some analysis using Wavelet Transform. Can anybody suggest me a practical book, preferably with MATLAB or C examples. I am currently reading some tutorials, but ...
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12 votes
3 answers
4k views

Slow Down Music Playing While Maintaining Frequency

Playing a piece of music audio at a slower speed would lower its pitch (frequency). Is there a tool and theory to slow down the song playing while keep the frequency the same? I suppose one can do ...
Hans's user avatar
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12 votes
1 answer
3k views

Tutorial on 2nd generation wavelets (with lifting)?

For some denoising and deconvolution experiments, I'd like to apply a 2nd generation wavelet transform (using lifting steps) to images. I know that there are several implementations available, but ...
sansuiso's user avatar
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11 votes
4 answers
5k views

What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform?

At a glance, the constant-Q fourier transform and the complex Gabor-Morlet wavelet transform seem the same. Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, ...
endolith's user avatar
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11 votes
2 answers
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Is a wavelet-based correlation measure worth any additional computational overhead?

I have used both correlation and coherence as measures of correlation between signals. I was thinking that a time-frequency approach would give me the best of these worlds. My question is whether ...
jonsca's user avatar
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11 votes
2 answers
436 views

Explanation on Haarlets

Would someone be able to give me some info or a link etc ... regarding haarlets aka Haar wavelet-like features. I'm reading several papers for my master dissertation and several of these papers ...
Olivier_s_j's user avatar
10 votes
2 answers
17k views

Feature extraction/reduction using DWT

For a given time series which is n timestamps in length, we can take Discrete Wavelet Transform (using 'Haar' wavelets), then we get (for an example, in Python) - ...
theharshest's user avatar
10 votes
2 answers
10k views

interpret wavelet scalogram

My knowledge of wavelets is less than epsilon. Bear with me. If I have a signal of two well separated sinusoids (15 and 48 Hz) plus some random noise, I can clearly make out the two in a spectrogram (...
user1641496's user avatar
10 votes
2 answers
307 views

What is the normalization factor for the quincunx lattice wavelet transform, and how do you find it?

On pages 57-60 (preview was available last I checked, images here in case), there is a quincunx lattice transform described. Lattice: ...
bobobobo's user avatar
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9 votes
1 answer
6k views

Scalogram (and related nomenclatures) for DWT?

My understanding of the scalogram is that, for a particular row, the scores of the projection of the input signal with the wavelet at a particular displacement is shown. Across rows, the same thing ...
Spacey's user avatar
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9 votes
1 answer
4k views

Number of Daubechies coefficients

I am wondering about the correlation between input size and number of coefficients given by a discrete wavelet transform. I am using Daubechies wavelets to describe a 1D function and I'm using ...
Gustav Larsson's user avatar
9 votes
1 answer
629 views

What's the similarities and differences between Wigner transform and wavelet transform?

Wigner transform and continuous wavelet transform are both some kind of time-frequency representation of a signal. What are the similarities and differences between them? Could you give some ...
xslittlegrass's user avatar
8 votes
4 answers
3k 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 ...
lemoncake's user avatar
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8 votes
3 answers
10k views

Why does a narrower window in a Fourier transform or STFT give poor frequency resolution?

In theory of FT(Fourier transform) and STFT(Short Time Fourier Transform) it is said that "A wide window gives better frequency resolution but poor time resolution. A narrower window gives good time ...
Nrupatunga's user avatar
8 votes
3 answers
13k views

Difference between a wavelet transform and a wavelet decomposition

I'm confused about the difference between a wavelet transform and a wavelet decomposition is. For example ...
Tom Kealy's user avatar
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8 votes
1 answer
8k views

what is proper setting for Fb,Fc in Complex morlet wavelet (cmor)?

I am using Cmor-Fb-FC wavelet transform in matlab environment. Fb is bandwidth and Fc is center frequency parameters. with trail and error procedure I select Fb-Fc as 5-1, and I've got rational output....
SAH's user avatar
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8 votes
2 answers
1k 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(...
hazrmard's user avatar
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8 votes
2 answers
15k 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 ...
Yash's user avatar
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8 votes
3 answers
1k views

Which mother wavelet for a scalogram?

I'm attempting to create a real-time scalogram (from a 1 dimensional signal) in the style of a spectrogram; Looking through various papers+books; the Gabor wavelet, or complex Morlet seems to be ...
daurnimator's user avatar
8 votes
1 answer
2k views

Apply wavelet transform to analyse EEG signal

I would like to apply The Morlet wavelet transform to analyse my EEG signals. I have many short signals each is only 1 min long. and they all recorded in 30Hz. I have Two questions: In the Morlet ...
Dov's user avatar
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8 votes
1 answer
207 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-...
Br4veSt4rr's user avatar
7 votes
3 answers
4k 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 ...
Wang Yun's user avatar
  • 124
7 votes
2 answers
793 views

Vanishing Moments

I am reading a book titled "Two Dimensional Wavelets and their relatives" by Antoine et al. and it talks about vanishing moments. I have trouble understanding the exact significance of it. Can anybody ...
mkuse's user avatar
  • 395
7 votes
3 answers
25k views

Continuous Wavelet Transform with Scipy.signal: what is parameter "widths" in cwt() function? How do time-frequency?

I search to display a time-frequency signal with an original discrete temporal signal (sampling step = 0.001sec). I use Python and the library Scipy.signal. I use the function ...
ArnoNoo's user avatar
  • 73
7 votes
3 answers
2k views

Convolution of Signal with a Wavelet

I know that the complex wavelet transform is given by $$\int_{-\infty}^{\infty}f(x)\psi^*_{s,u}(x)\,dx$$ where $f$ is the signal, $\psi_{s,u}(x)=\frac{1}{\sqrt{s}}\psi(\frac{x-u}{s})$ is the wavelet. ...
meta_warrior's user avatar
7 votes
2 answers
8k views

Wavelet Transform and STFT

How wavelet transform is different from STFT. I'm not able to understand what is resolution in frequency domain means?
Avinash Baldi's user avatar
7 votes
1 answer
708 views

How to turn Morlet wavelet into second generation wavelet?

I have a very specific application which requires to use the complex Morlet wavelet (or Gabor wavelet, if that's the name you use). I currently use the convolution theorem to compute wavelets ...
PhilMacKay's user avatar
7 votes
1 answer
13k views

What is the scaling function and wavelet function at wavelet analysis?

I'm trying to looking the meaning and functionality about scaling function and wavelet function at wavelet analysis. I have googling already. But I can't find and understand the meaning. What does ...
gmotree's user avatar
  • 651
7 votes
1 answer
172 views

"Normalizing" my D4 wavelet transformation at each step reduces final image quality

Original image: (Images included are .png images, so no additional distortion was added in save/upload for viewing) I have used the D4 transform from page 20 of "Ripples in mathematics", ...
bobobobo's user avatar
  • 945
7 votes
2 answers
633 views

Combining two images

I am working with speckle noise reduction in ultrasound images. I have used wavelet transform for removing the noise by eliminating certain frequencies in order to eliminate any existing noise. Since ...
preethi's user avatar
  • 923
7 votes
1 answer
1k views

Daubechies Wavelet and Matlab

I want to use waverec to evaluate a linear combination of the scaled and shifted wavelet of the form $$ \sum_{i=1}^n\sum_{j=0}^{2^n-1}d_{nj} 2^{-n}\psi_{ij} (\...
warsaga's user avatar
  • 171
7 votes
1 answer
3k views

Discrete (Inverse) Haar (2D) transform implementations

I am interested in implementations of the Haar transform, and its inverse, such that when composed always result in the identity operation. My inputs are discrete ordinals within a given range - and ...
aSteve's user avatar
  • 171
6 votes
1 answer
3k 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?
OverLordGoldDragon's user avatar

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