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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27
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4answers
5k 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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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, ...
10
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3answers
3k 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 ...
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2answers
4k 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 ...
1
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1answer
85 views

PyWavelets CWT: normalization? Vs Scipy?

Related. The equation being implemented normalizes by sqrt(1 / scale): $$ C_{a, b} = \frac{1}{\sqrt{a}} \sum_k s(k)\left( \int_{-\infty}^{k+1} \overline{\psi \left(\...
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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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2answers
21k 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: $ \...
9
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1answer
4k 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 ...
1
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1answer
269 views

What is the correct order of operations for a 2D Haar wavelet decomposition?

The source code of iqdb contains a 2D Haar transform implementation. The author claims to have implemented it according to the paper "Fast Multiresolution Image Querying", which is freely available ...
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1answer
53 views

PyWavelets CWT implementation

I seek to understand PyWavelets' implementation of the Continuous Wavelet Transform, and how it compares to the more 'basic' version I've coded and provided here. In particular: How is integrated ...
1
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1answer
242 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 ...
0
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1answer
614 views

2D DWT Image Issue

In the literature, I see that a 2D signal can be transformed by first doing a 1D transformation on each row of the matrix followed by the same procedure on each column. It seems that $k^{th}$ level ...
22
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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, ...
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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 ...
4
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1answer
3k views

inquiries for writing continuous wavelet transform codes manually

I want to write continuous wavelet transform codes manually by matlab. And I want to use complex morlet function. Here are some background: Continuous wavelet transform definition: $C(S,T;f(t),\psi (...
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0answers
277 views

Hints and helps to implement an accurate wavelet packet transfrom

I want to implement a Time-Freqency analysis by wavelet packets. I don't know what level and sampling rate should I use. I've tried different value for level(3,4,5,6,). but I couldn't get an accurate ...
7
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1answer
539 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 ...
2
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0answers
68 views

Does a “chirp”-like generalization of the Gabor or Morlet wavelets definitions exist in the lit somewhere?

I have asked this at the Math SE also. Predicating this on the definition of the continuous Fourier Transform preferred by most electrical engineers: $$ X(f) \triangleq \mathscr{F} \Big\{ x(t) \Big\}...
3
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2answers
270 views

Additive White Gaussian Noise (AWGN) 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 ...
2
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1answer
915 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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2answers
1k views

Fourier Transform of Morlet wavelet Function?

One definition of the Morlet wavelet function is given by: $$\frac{1}{\sqrt{\pi f_b}}e^{\frac{-t^2}{f_b}}e^{j2\pi f_c t}$$ The Fourier transform of this equation is: $e^{-\pi^2 f_b(f-f_c)^2}$ (is it ...
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6answers
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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. My question is: What is it about certain wavelets that make them preferable when compressing images? Are ...
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, ...
9
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1answer
14k 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?
15
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2answers
12k 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 ...
16
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1answer
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 ?
10
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2answers
390 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 ...
15
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3answers
20k 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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1answer
818 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 ...
7
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1answer
13k 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) - ...
18
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1answer
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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) ...
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 ...
4
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2answers
4k views

infomation about Stockwell Transform

I need some information about Stockwell transform (also known as the S-transform): How can I implement it in MATLAB? *Does it give you the damping ratio $\zeta$ of a signal like the complex Morlet ...
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3answers
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Comparison between 2 images in Frequency domain

As you can see there are 2 images from the Tom and Jerry cartoon program. In the 1st image both Tom and Jerry are present. But in the 2nd one,only Tom is present.Now,we can clearly see this ...
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2answers
564 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 ...
3
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2answers
2k views

Morlet wavelet time and frequency resolution

I want to calculate Morlet time and frequency resolution. the Morlet wavelet function is define as : $\psi(t)=\frac{1}{\sqrt{\pi f_b}}e^{j2\pi f_c}e^{-t^2/f_b}$ Note: I know the answers, but I don't ...
3
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1answer
185 views

Noise rejection / feature extraction

I'm hoping someone could point me in the direction of some signal processing methods to clean up my data. I'm collecting physiological data from human muscle (lower leg; gastrocnemius) during walking/...
3
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1answer
691 views

Complex Morlet function and DWT

I have an application that I must use a complex Morlet wavelet function (cmorfb-fc), I can run CWT (continuous wavelet transform)...
2
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3answers
4k views

Why is a wavelet transform implemented as a filter bank?

The mother wavelet function $\psi(t)$ must satisfy the following: $$\int\limits_{-\infty}^{+\infty} \frac{|\psi(\omega)|^2}{\omega} d \omega < +\infty,$$ $$\psi ( \omega ) \bigg|_{ \omega =0} =0,...
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2answers
2k views

Shift invariant in wavelet

I always hear that wavelet transform is not shift invariant, and that there are other types of wavelet, like stationary wavelet and double density dual-tree wavelet transform, that are shift invariant....
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0answers
757 views

How can I identify the damping of the modes in a signal by Cmor wavelet method?

I read several papers which proposed a method to identify modal parameters. such as natural frequency and damping ratio.I've tried to implement those methods by Matlab.but I couldn't get the result.It ...
8
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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 ...
2
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0answers
545 views

Shifting of Shift-Invariant Wavelet Transforms

Main Question: Why would iterative wavelet/inverse-wavelet transforms cause a shift along the x-axis for undecimated (shift-invariant) wavelet transforms? I am attempting to remove backgrounds from ...
2
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1answer
198 views

How to implement a $j$-level $M$-band wavelet transform of an image?

I want to implement an $M$-band (or multi-band) wavelet transform, to be used for feature extraction on images. Is there a built-in Matlab function available? Do I have to implement is using filter ...
2
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1answer
1k 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 ...
0
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1answer
3k views

How to calculate CWT shannon entropy?

I am trying to calculate shannon entropy of CWT. I am not sure if I am doing it right. Assume that $W(a_i,t), i=1;2;...;M$ is a set of wavelet coefficients. The ...
0
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1answer
43 views

What are the differences between the DWT and the MODWT?

What are the differences between the DWT (Discrete Wavelet Transform), which is the most classical algorithm and the Maximum Overlap Discrete Wavelet Trasnform (MODWT)? Both these algorithm are ...
2
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2answers
797 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). ...
2
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2answers
476 views

How to extract features of individual spikes in non-negative signal?

I have data of non-negative (in the sense there's no signal below baseline) spiking waveforms, which are in the form of a 1D array of numbers: Spikes that cross some threshold are considered real ...
2
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1answer
299 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 ...