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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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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4answers
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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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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 ?
16
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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) ...
15
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3answers
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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, ...
14
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3answers
18k 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 ...
12
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3answers
924 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 ...
12
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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 ...
12
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3answers
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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....
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 ...
12
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1answer
603 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 ...
12
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3answers
4k 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 ...
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3answers
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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 ...
10
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2answers
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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3answers
3k 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, ...
10
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2answers
349 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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1answer
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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 ...
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 ...
9
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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 ...
9
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1answer
244 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: ...
8
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3answers
925 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 ...
8
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1answer
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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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3answers
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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 ...
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3answers
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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 ...
7
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1answer
11k 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) - ...
7
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1answer
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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....
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2answers
500 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 ...
7
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2answers
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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 (...
7
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1answer
498 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 ...
7
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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 ...
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 ...
7
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1answer
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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 ...
7
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1answer
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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 ...
6
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1answer
12k 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?
6
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1answer
615 views

Data fusion using 2d discrete wavelet transform (DWT)

I am working on a project that employs a linear array sensor that provides data from the same object at two different energies. Collected in time, I end up with two images (16-bit sensor values, MxM ...
6
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2answers
453 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 ...
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} (\...
6
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1answer
998 views

Issues with the smoothing operator in coherence estimation using the complex Morlet (Gabor) wavelet

The goal I wish to compute the coherence estimate using the continuous wavelet transform (CWT) of a real-valued signal with the complex Morlet (a.k.a. Gabor) wavelet. I compute the cwt of the signal ...
6
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0answers
222 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 ...
5
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2answers
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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 ?
5
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4answers
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Why does the high frequency component of an image contain more noise?

I am working with wavelet transforms. When we apply a discrete wavelet transform to an image, it decomposes into four components named the approximation component, thevertical component, the ...
5
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2answers
529 views

Implementing Wavelet Transform using Equations

I want to implement Wavelet Transform from the scratch, that mean breaking the wavelet transform into its equations to implement in any Programming language. Matlab Comes with built-in functions to ...
5
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2answers
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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. $|B_1(f)| = |B_0(f)|\exp(-\pi t f / Q)$ ...
5
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1answer
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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 ...
5
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2answers
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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 ...
5
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1answer
245 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 ...
5
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1answer
1k views

Haar series approximation of a function?

I'm trying to code the Haar wavelet approximation of a function. I'm a complete newbie. Edit Below is a pseudo-code of my algorithm for $f: [0,10] \to \mathbb R$, $f(x)=x$. I picked it here and ...
5
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1answer
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 ...
4
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2answers
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 ...