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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1answer
815 views

What are the main advantages and disadvantages of the lifting scheme?

Can anybody tell me the advantages of the lifting scheme and why it is better then a normal filter bank?
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45 views

DWT initialization from nonuniform samples

Let $D\subset\mathbb R$ be compact, let $f:\mathbb R\to\mathbb R$ be a contintinuous function with support $D$. Let $\phi(x)$ be a well-defined scaling function, in the sense that it generates a ...
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720 views

what is continuous wavelet (cwt) ,wavelet packet (wpt) and stockwell (S-T) computational complexity?

What is computational complexity of continuous wavelet transform cwt ? What is computational complexity of wavelet packet transform ...
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429 views

What the difference between the family of Discrete Wavelet Transform?

When I useed Mathematica,If found many Transforms in the list of Discrete Wavelet Transforms. For example: discrete wavelet transform (DWT) stationary wavelet transform (SWT) lifting wavelet ...
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1answer
233 views

Subsampling property of wavelet transform

One of the properties I have seen for isotropic tight wavelet frames is $$\sum_{i\in\mathbb{Z}} \left|h(2^i\omega)\right|^2 = 1$$ where $h(\omega)$ is the frequency spectrum of the original wavelet. ...
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1answer
56 views

Wavelet Fidelity Filter (video compression)

I have read a specification of Dirac (video compression format). A key element of this format is the use of the discrete wavelet transform. Section 15.6.3 of the specification defines individual ...
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3answers
19k 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 ...
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1answer
567 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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2answers
6k views

Disadvantages of wavelet transform

I have a question related to wavelet transform: we know that while the Fourier transform is good for a spectral analysis or which frequency components occurred in signal, it will not give information ...
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1answer
112 views

possibility of applying ridgelet transformation on signals

After converting a 1D signal to 2D using matlab code, can the ridgelet transform be applied? Is this transformation effective compared to wavelet?
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1answer
187 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 ...
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1answer
160 views

Code for a wavelet based hilbert transform? [closed]

I normally implement the Hilbert transform using the Fourier transform. I have noise related issues I want to solve. Does anybody have an (apodized) implementation of the Hilbert transform handy, ...
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2answers
271 views

Properties of a custom wavelet family for continuous wavelet transform

First of, I'm new to signal processing. I have a signal which is a linear composition of several basis signals, whereas the same basis signal can occur several times, that is translated, but not ...
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2answers
5k views

Is R suitable for digital signal processing

While asking a question about representing large time series in R I was discouraged from using R for digital signal processing. I understand that R is geared towards statistics. However, a signal is ...
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42 views

Example of radial frequency functions that give scale shiftability

Simoncelli's "Shiftable multi-scale transforms" paper talks about shiftability of the parameters of a wavelet transform, in particular translation, rotation and scale. The first two are used in his ...
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125 views

Are wavelets for audio spectrograms available as a simple FIR filter?

I have read that "Debauchies Wavelet is simply a short FIR" so i am searching for a single FIR that i can make into a filterbank, a precise "bandpass filter" that detects narrow frequencies, i.e. 1Hz ...
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1answer
34 views

Measures that can be used to truncate linear series of functions

Say we have the following (wavelet) series representation at some location and scale in a signal: $$ f = \sum_{k=1}^{K} c_k \psi_k$$ where $c_k$ is the coefficient, in order of magnitude ($|c_k| >...
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1k views

stationary vs. undecimated wavelet transform

I have a little bit confused on the difference between stationary wavelet transform and un-decimated wavelet transform. So, can anyone tell me, if there is a difference between them?
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3answers
4k views

What are the spike removal techniques in matlab without using filters

output from wavelet filter using daubechies 4 wavelet. Using wavelet filter this is the output obtained. The problem is elimination of the spikes at 0.023,0.043,0.063 and so on. Please note: no ...
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1answer
905 views

Downsampling in DWT algorithm

I was working on wavelet signal decomposition and got confused with the downsampling part of Discrete Wavelet Transform algorithm. If we consider a signal $\{a_0[0], ... ,a_0[N-1]\}$ of length N and ...
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1answer
386 views

Discrete wavelet transform

I am unable to understand the discrete wavelet transform on images. I followed Robi Polikar's tutorial and got a brief idea about the theory. But I'm unable to understand w.r.t images. Using Matlab's ...
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3answers
742 views

Intuition behind the Continuous Wavelet Transform?

I was thinking sometime back about how to explain the Continuous Wavelet Transform ELI5. So this is what I came across. The correlation of two exact signals is 1. So if I have an input signal $f(x)$ ...
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122 views

This is an expression for the computation of kurtosis.

However, I don't understand what the subscript '4x' or the parameter (0,0) stand for. Could anyone explain ?
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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 ...
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2answers
705 views

Can a wavelet transform give time dependent phase of sinusoids in signal

I have a signal which contains sinusoidal components that oscillate at different frequencies. I think the phase of the sinusoids is changing with time. I could do a Fourier transform on small chunks ...
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1answer
642 views

Daubechies wavelet transform

i have N samples obtained by sampling a signal with lot of frequency contents. How will i apply daubechies wavelet transform to obtain the frequency and its location? i need to write a program which ...
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1answer
149 views

Implementing wavelet transform for finding transients in the power supply

I am new to the concept of wavelet transforms. Can somebody please help me in understanding this ? and also how to implement it in c. Is Short term Fourier transform more efficient than Wavelet ...
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1answer
335 views

Optimized 2D wavelet transform using FFT

I'm currenty aiming to optimize my fast wavelet transform (FWT) algorithm for 2D signals (images). It works as follows: one iteration of 1D FWT does convolution of 1D input data with a selected 1D ...
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464 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 ...
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42 views

Is this a valid thresholding approach?

I am using a wavelet transform and am testing the following approach to thresholding: All coeffients (whatever their value) after the first N are set to 0 So if my timeseries window is 128 ...
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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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189 views

relationship between number of wavelet decomposition level and noise level

I am studying wavelet theory by myself and hope to use wavelet to denoise images. I write one matlab program to watch denoised image. ...
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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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1answer
104 views

Opposite of wavelet transform?

Wavelet transform gives good time resolution for high-frequency events and good frequency resolution for low-frequency events. => I want to have complete opposite of wavelet transform, where I get ...
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1answer
94 views

Time-Frquency Resolution issues

While Im studying wavelet transform, I have this questions in my mind which can't find it's answer: I understand that when we take longer time windows and take the fourier transform we would suffer ...
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53 views

How accurate is Wavelet packet decomposition for emg signals with frequencies from 10 to 40 Hz?

I have an electromyographic signal sampled at a frequency between 10 and 40 Hz in a time window of 300ms. Is wavelet packet decomposition adequate in order to perform features extraction for ...
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529 views

Selecting the number of cycles for wavelet transform

I'm trying some wavelet analysis of EEG signals, using the phase lock measures from [1], specifically the S-PLV measure. In order to calculate that we perform a wavelet transform on the signals and ...
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2k views

How to use wavelet decomposition for feature extraction (of fMRI images)?

I have a dataset consisting of fMRI images (from mice) which are divided into 4 groups (different drug dose levels applied). Each fMRI image is 4D, that means each voxel is a time series. For each ...
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3answers
11k 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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4answers
592 views

Similarity between two Signals: cycle by cycle

I need to find the similarity between two signals, i.e., measured signal and the reference signal(e.g. a simple sinusoidal signal). What I mean by similarity is, if there is any decentralized glitch ...
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404 views

Generating Wavelet family matrixes

We have unnormalized Haar matrix which, is for example, H4=[1 1 1 1;1 1 -1 -1;1 -1 0 0;0 0 1 -1] After normalizing it, we use for haar transform. I know how to ...
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1answer
144 views

Why not stop with the first level decomposition in wavelet?

Typically, We do wavelet decomposition with the last one level. But I wonder, why do decomposition withh the last one level? In the other word, why not stop with the first decomposition level?
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173 views

Singularity Detection from 2D Wavelet Modulus Plot

I was wondering if I could get some tips/resources on how to pick out the singularity from my 2D Continuous Wavelet Transform Coefficient Plot (scalogram) using the Gaussian Derivative as the mother-...
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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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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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2answers
670 views

Compare between JPEG and JPEG2000

JPEG image compression is Fourier based DCT while modern image compression technique like JPEG2000 is based on more multi-scale technique like Wavelets.I want to know how Fourier and Wavelets are ...
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1answer
96 views

How does a wavelet help in image compression?

I understand how the discrete cosine transform is used in image compression in standards like JPEG. However, the concept of wavelets is a mystery to me. I do know that wavelets are functions that have ...
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1answer
34 views

How to cover all spectrum in wavelet when it which is behalved?

As I know , wavelet decomposition behave with halve. I mean that a way like this HH HL LH LL. But I wonder, how to corver the all spectrum when it was halved? I think if it want to all cover spectrum ...
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17 views

What is meant by “complete set” in the context of affine wavelets?

In the book by Sayood on compression, he says "if the set is complete, it is called affine wavelets". I want to know what is meant by completeness of wavelets.
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Matrix expansion into bases

I have an image (that is a matrix), let's say of dimensions NxN. I then want to expand this matrix into M basis matrices (for the moment I'm still unsure how many M of these basis matrices I should ...

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