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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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2answers
2k views

How to implement a filter associated to a specific wavelet

I am working on ECG signals, to eventually extract features in order to detect an arrhythmia and classify it. I am using Discrete Wavelet Transform with biorthogonal wavelet bior6.8 During my research,...
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2answers
422 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 ...
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3answers
158 views

Denoise Techniques When Clean Signal and Pure Noise Are Available

I have the clean version of the signal. I can obtain the environmental noise. I want to apply an effective denoising technique on a noisy signal (i.e., clean plus environmental noise). Some ...
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1answer
86 views

What the entropy equations mean?

In wavelet packet image compression, different types of entropy methods can be used, like Shannon and log-energy. Shannon entropy uses this equation $\mathrm{ent}= -\sum (x^2 \times \log(x^2))$, ...
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199 views

Log energy and Shannon entropy?

For best tree decomposition using wavelet packets, i have tried both Shannon and log energy entropy functions. I noticed that log energy leads to images with higher PSNR values. Could you please help ...
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0answers
70 views

Selection of transforms, windows, wavelets for current signal analysis

I am new to this topic but I already read about the propperties of different signal analysis methods. I am stuck with the obvious advantages of FFT, STFT and Wavelet transforms but can't find good ...
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1answer
12k views

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 ...
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1answer
131 views

Wavelets and bank filters

The wavelet transform has a problem as it gives poor time resolution for low frequencies and poor frequency resolution for high frequencies according to uncertainty conditions. This appears well ...
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1answer
134 views

Question about normalization before estimate the spectrum

I work with a Electrophysiologist Team and i have seen something who interrogate me (i'm a noobs in DSP). They acquires a signal into a brain structure (an LFP to be precise) : in a first time they ...
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1answer
873 views

Making sense of Haar transform and inverse Haar transform

Yesterday, my teacher taught us about the Haar transform (for pictures). We had to implement it in Python and when I finished I was wondering: what was the point? I can't explain the purpose of what I'...
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1answer
80 views

Integer Wavelet with Only Positive coefficients

Is there any Integer Wavelet Transform which produce only positive coefficients? Currently i'm using Haar wavelet but it produces both positive and negative coefficients.
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1answer
28 views

Are there analogues to orthogonal transformations in non-orientable surfaces?

I am working on extremely large, symmetric matrices of counts, and attempting to identify patterns/shapes within them. Wavelets are a popular tool in image processing, and have some nice statistical ...
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0answers
131 views

Perfect reconstruction of 2 channel filter bank

I am studying Perfect reconstruction of 2 channel filter bank for using Biorthogonal Spline wavelet for decomposing ECG signal. I am using Wavelets and Filter Banks By Gilbert Strang, Truong Nguyen to ...
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1answer
83 views

Dimensional analysis in the Morlet wavelet

I'm a complete beginner on signal processing, so please forgive the basicness of this question - but I'm very confused by this. Regarding the Morlet wavelet, Wikipedia says: The wavelet is defined ...
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1answer
320 views

Programming the IDWT for image processing

I want to program the 2D inverse discrete wavelet transform (only 1 level) in the case of image processing. In the matlab website there's this diagram: now, I want to program the IDWT with haar ...
2
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1answer
655 views

Real-time wavelet decomposition and reconstruction for ECG feature extraction

I need to locate R-peaks in an ECG signal. I'm using wavelets to extract QRS complexes: First, I decompose the signal using a maximal overlap discrete wavelet transform with the Symlet 4 wavelet. This ...
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1answer
40 views

How left out down-sampling in 3D-DWT just on the Z direction

I am working on image processing by a 3D wavelet transform. I have a problem with the classification size of the wavelet coefficients. As you know, when we apply 3D_DWT on the image (for example: ...
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1answer
299 views

Why do wavelets integrate to 0 and how do they match a signal?

I have been reading about the Wavelet transform recently and its relationship to the Fourier transform. From what I understand the wavelet transform represents signal data with many short-lived ...
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1answer
175 views

Computational burden of EMD/Huang-Hilbert vs wavelet

I am working on an online application of signal processing and pattern recognition. It involves sampling the signal at 2 MS/s, extracting features and classifying. My classifier has pretty good ...
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1answer
357 views

Getting started with wavelet-based real-time anomaly detection for temporal signals using Python

I have an anomaly detection problem I wanted to consider addressing in software (python) with wavelets. I’m new to wavelets as well as the python’s spicy.signal wavelet package, let alone with the ...
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1answer
5k views

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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1answer
104 views

How i can create ghost on wavelet or seismic trace and then Deghosting that in MATLAB? [closed]

I want to model a seismic trace or wavelet and then create ghost on them, at the end Deghosting in MATLAB. Can anyone help me please?
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2answers
664 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). ...
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1answer
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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 ...
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2answers
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What happens when we reconstruct a signal after its Fourier transform is done and some frequencies are altered? [closed]

Since we loose time information when we take a Fourier transform, what happens if we alter a few frequencies from the transform and then reconstruct the signal, do we get the altered frequency at the ...
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1answer
265 views

Inverse wavelet transform on wavelet coefficients

I have a data set which consists of Morlet coefficients for 7 channels in 18 bands. When I try to use inverse DWT in Matlab to get the raw data in time, using this code: ...
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1answer
652 views

sparsifying an ECG signal using wavelet

I have an ECG signal, and want to sparsify it using wavelet (DWT) in Matlab. In some paper they use Daubechies wavelet (DB4) with 8-tap filters. but i don't know how to extract the wavelet ...
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1answer
164 views

Quadtree decomposition of Discrete Wavelet Transform using bio4.4/CDF wavelet

My problem is pretty basic but fundamental. It relates to the way discrete wavelet transform behaves for biorothognal 4.4 or CDF wavelets. When using most wavelets (e.g., CDF 9/7 or bio4.4 or ...
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1answer
138 views

Continuous wavelet transform subsampling at lower frequencies?

I am not completely confident in my understanding of wavelet theory, but since I am currently in the process of creating a CWT scalogram tool, I have to ask: Is there a theorem allowing us to ...
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1answer
43 views

What is the meaning of negative second for a Morlet wavelet?

I kind of familiar with wavelet transform (I just used it in code but do not have a deep understanding about it). I've been reading an article and came across this sentence: where 4Fs is the ...
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1answer
115 views

Reduce Signal Size to Compare Them

I have multiple experiments and each of them produce several ($k$ for example) binary signals; some artificial example next: I have a metric to compare experiment results but I need vectors of equal ...
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1answer
972 views

2D Wavelet Transform Explanation

I am new to wavelets and for several times I stumbled over these 2D wavelet transformation pictures, but I do not understand how they are created. Can anybody try to explain in his own words how this ...
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3answers
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Multilevel partial wavelet reconstruction with PyWavelets

I'm looking for a way to partially reconstruct branches of a wavelet decomposition, such that the sum would recreate the original signal. This could be achieved in MATLAB using: ...
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1answer
170 views

Output of MATLAB's two-dimensional DWT function $\tt dwt2$

This is a conceptual doubt about the two-dimensional DWT. I am trying to understand the decomposition step of a two-dimensional DWT. In the MATLAB explanation, the two-dimensional DWT generates 4 new ...
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0answers
78 views

Values (amplitudes) of the CWT and their relationship to waveform amplitudes?

I'm coding up a scalogram in C++. Right now it calculates a single row of the CWT matrix and immediately maps it to a line of pixels. Trouble is my colouring scales with the values of the transform ...
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1answer
291 views

Is Wavelet Transform better than FT if I'm only interested in knowing the frequencies and not interested of when did they happen?

I'm still in the first stages of learning about these different transformations. But one thing that came to my mind while learning about them is the question above. I learned that ...
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1answer
124 views

Transform coding gain of two channel Haar Wavelet transform (first stage)

Question My interpretation Work I'm attempting to do this in MATLAB. I know that for discrete Random Processes going into an LTI system the autocorrelation function of the output is $R_y[n] =...
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1answer
1k views

What is the relationship between scales and frequency in a Morlet wavelet transform?

I'm using PyWavelets, with a complex Morlet wavelet. Its complex wavelet transform function requires scales as one of its parameters, rather than frequencies. However, I don't understand the ...
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1answer
275 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 ...
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1answer
64 views

What Is Proper Paper and MATLAB Toolbox Describing and Discussing Wavelet, Ridgelet, Curvelet and Contourlet Transforms in Detail?

Question 1: Does anybody know any paper proper for getting started understanding the concept of Wavelet, Ridgelet, Curvelet and Contourlet transforms and their differences in detail? Question 2: ...
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2answers
686 views

Log vs. linear frequency scales of Fourier and wavelet transforms

I'm trying to understand the difference between the output of a Fourier transform and a wavelet transform. A Fourier transform is done via the following function: $$\hat{f}(\xi) = \int^\infty_{-\...
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1answer
890 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 ...
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2answers
84 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 ...
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1answer
114 views

How to detect the singular value with signal processing technology?

I have a signal like ...
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1answer
2k views

Continuous Wavelet Transform time vector in python

I have a signal sampled at 128 Hz. I used to extract features with the spectrogram function and I decided to upgrade my algorithm and I'm trying to analyze it using Continuous Wavelet Transform (...
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2answers
3k 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 ...
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1answer
679 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 ...
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3answers
33 views

General form of dilations and translations of wavelet function

In some papers, the dilations and translations of a wavelet function is written as follows: $$\psi_{j,k}=\frac {1}{\sqrt {2^j}} \psi\left({2^{-j}t-k}\right),\quad\text{where $j$ and $k$ are integers}$...
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0answers
757 views

Relationship between Wavelet transform and Fourier Power Spectral Density

Is there anyway to obtain the Fourier Power Spectral Density from a wavelet transform of a time series? I am particularly interested in this problem because I was wondering if there is any ...
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2answers
211 views

Is MATLAB documentation wrong on when to use discrete versus continuous wavelet transform?

I was reading some of the MATLAB documentation and I get confused when reading the part about When is Continuous Analysis More Appropriate than Discrete Analysis? My knowledge before reading the ...