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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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5
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2answers
1k views

Why Low Frequency called Approximation and High Frequency Detail?

While we are decomposing a signal using Wavelets into levels why do we call our high frequency components as Detail and Low Frequency Components as Approximation ?
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1answer
803 views

1-D Wavelet Toolbox in Matlab

I'm so happy that i managed to come at this level to understand Wavelet transform to some extent with the help of Stackexchange fellows, Initially i had so many difficulties as i had no concept of ...
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2answers
10k views

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 ...
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1answer
3k views

Understanding this Haar Wavelet Example

I'm trying to understand Wavelet Transform , I've done well enough to understand Continuous Wavelet Transform which was easy enough, where we simply stretch the wavelet and match it with the original ...
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3answers
10k 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, ...
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1answer
921 views

wavelet analysis normalized to have unit energy

I am analyzing some time series of sea surface water temperature and am using wavelet analysis to do so. I am computing the continuous wavelet transform and then removing some specific frequencies and ...
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1answer
2k views

wavelet denoising routine for environmental data series

I have a time series of water temperature, e.g. y = 1+(30-10).*rand(1,365); I have previously used the wavelet denoising routine in the wavelet toolbox by matlab ...
2
votes
1answer
266 views

Multidimensionnal wavelet admissibility criteria

I've read there are two admissibility criteria for wavelets, both of which are designed to preserve total power of the signal (source: http://en.wikipedia.org/wiki/Wavelet#Mother_wavelet, as well as ...
5
votes
1answer
246 views

What are the uses of those three types of wavelet transformations?

In my studies of wavelets, there appear to be 3 different families of them: The Continuous wavelet transform The Discrete wavelet transform The Redundant wavelet transform They are all based on the ...
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0answers
404 views

Wavelets and cryptography [closed]

What papers/articles/books are considered good for getting started with wavelets' application to cryptography? I'm primarily interested in irregular grid wavelets, but regular grid will do for ...
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1answer
3k 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 ...
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3answers
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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, ...
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1answer
1k views

Using Discrete Wavelet Transform in the time-frequency domain

I am creating an application that works like the Shazam service. In short, my goal is to create an audio pattern matching service. However, I would like to use DWT and not the short time Fourier ...
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3answers
7k views

Adding noise to an ECG signal

I am doing a project on ECG arrythmia analysis using matlab. I have designed notch filter for removing 50 Hz noise but don't know how to add a 50 Hz powerline interference noise to a clean ECG signal?...
6
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1answer
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} (\...
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2answers
514 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 ...
2
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1answer
558 views

How to remove/reduce noise by using the Morlet wavelet?

I'm trying to use Morlet wavelet to reduce noise in my signal. I found formula for Morlet wavelet $$\Psi(x) = \frac{1}{\sqrt{\pi\cdot \textrm{bandwidth}}} \cdot \exp\left(i \cdot 2\pi \cdot \textrm{...
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4answers
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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, ...
2
votes
1answer
410 views

Pitch detection algorithm for minsample size

I am looking for a pitch detection algorithm that uses the least number of samples. I don't care about the processing time. I hope to use this on audio signals. I have tried using the one at the ...
2
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1answer
1k views

Signal matching: How to quantify the difference between two signals of varying frequency

I have two waves, and I would like to quantify the difference between them. They are exponential sine waves where the frequency decreases with time. I'm interested in the difference in decay ...
7
votes
1answer
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 ...
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1answer
152 views

wavelet analysis/ dimension reduction

How wavelet analysis works as a dimension reduction techniques? The approximations coefficients at higher level of decomposition are the fewer retained coefficients from the originial ?Is it correct?
7
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1answer
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 ...
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1answer
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 ...
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2answers
3k views

Generating wavelet using amplitude spectra

Equation (4) of a recent paper (An improved peak-frequency-shift method for Q estimation) shows how to generate a wavelet using a zero-phase Ricker wavelet. $|B_1(f)| = |B_0(f)|\exp(-\pi t f / Q)$ ...
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1answer
249 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: ...
12
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1answer
2k 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 ...
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3answers
944 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 ...
7
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1answer
154 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", which is ...
3
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1answer
296 views

T wave analyis and extraction using discrete wavelets

I'm doing a project in T-wave extraction from ECG signal. Initially I completed the preprocessing steps like noise removal and baseline drift cancellation. Then I need to extract T wave using discrete ...
8
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1answer
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 ...
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2answers
351 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 ...
9
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2answers
1k views

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 ...
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6answers
5k views

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. My question is: What is it about certain wavelets that make them preferable when compressing images? Are ...
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1answer
5k 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) ...
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4answers
4k 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 ...