# 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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### 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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### 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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### 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, ...
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### 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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### 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 ...
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### 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 ...
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### 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-...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### Wavelet Transform and STFT

How wavelet transform is different from STFT. I'm not able to understand what is resolution in frequency domain means?
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### 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 ...
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### 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 ...
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### "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", ...
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### 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 ...
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### 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} (\...
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### 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 ...
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