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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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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 ...
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1answer
80 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 ...
2
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2answers
620 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
589 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 ...
0
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3answers
2k views

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: ...
1
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1answer
162 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 ...
0
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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: ...
2
votes
1answer
277 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 ...
0
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0answers
238 views

Complex Morlet Wavelet piano sound analysis

my project is monophonic music transcription I am using complex Morlet wavelet but over the 1000 Hz complex Morlet does not give all results right, my code is like that ; ...
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1answer
338 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 ...
0
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1answer
98 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?
0
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2answers
2k views

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 ...
0
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1answer
250 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: ...
-1
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1answer
151 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 ...
1
vote
1answer
626 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
285 views

Undecimated DWT vs. CWT. In what cases is one preferable over another?

Talking about undecimated DWT let's focus here on SWT algorithm. SWT is said to be: numerically more stable due to Mallat algorithm. And the inverse operation is capable of returning the original ...
2
votes
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 ...
0
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1answer
784 views

Inverse of Wavelet Transforms - Background and Noise Removal

Main Problem: How can you inverse Wavelet Transforms (Using the data given by signal.scipy.cwt) I was wondering if anyone understands the ...
2
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1answer
581 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
votes
1answer
3k views

What are the advantages and disadvantages of the Ridgelet transform?

I used the continuous wavelet transform (CWT) to analyze the behavior of a 1-D smooth signal (extracting its modal property, damping and frequency components) in my research. Now someone asked: Why ...
1
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1answer
251 views

Haar Wavelets vs STFT for graceful audio quality degradation (newbie question)

I'm playing around with FFT (using Naudio library) and with Wavelets (using TarsosDSP library) trying to get better understanding of both of them. I've noticed that when I zero out FFT/Wavelet ...
0
votes
1answer
122 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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0answers
620 views

Cross correlation coefficient using MATLAB

Actually I want to calculate the cross correlation coefficient of any signal on comparing with all mother wavelets like Morlet, Daubechies using MATLAB.
1
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1answer
904 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 ...
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 ...
1
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1answer
153 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 ...
0
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1answer
75 views

Wavelets in time series predictions

Wavelet transforms are linear in nature. Then how good they are for time series predictions. Can they analyze nonlinear relations in data well??
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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 ...
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 ...
1
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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 ...
5
votes
1answer
8k views

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 ...
0
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2answers
141 views

Is it required to quantize wavelet coefficients before one derives features from?

I am using wavelet coefficients for feature extraction in classification problem. As the wavelet coefficient values are real, positive and negative, is it required to quantize them before feature ...
4
votes
1answer
107 views

Expanding piecewise polynomial using Daubechies wavelet

What is the best Daubechies wavelet (i.e. the number of vanishing moment) to expand a signal $\boldsymbol{x} \in \mathbb{R}^n$? $\boldsymbol{x}$ consists of $m$ pieces of polynomial with $d$ degree. ...
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1answer
264 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 ...
2
votes
2answers
643 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_{-\...
1
vote
1answer
850 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 ...
1
vote
2answers
140 views

Compression Ratio in ECG compression using Wavelet Decomposition

I have compressed and reconstructed an ECG signal using wavelet coefficients. In the compression part, many of wavelet coefficients are set to zero. For example, if in original ECG $5000$ wavelet ...
4
votes
2answers
83 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
107 views
2
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2answers
208 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 ...
-1
votes
2answers
214 views

Is there any difference between the 2D continuous and discrete Gabor filter when it comes to MATLAB implementation

I want to know the difference between the 2D continuous and discrete Gabor filter when it comes to Matlab implementation. I found many files related to 2D Gabor filter on Mathworks File Exchange but I ...
12
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1answer
642 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 ...
1
vote
4answers
592 views

Why are wavelet transforms (Multi Resolution Analysis) used more in practice for compression rather than Fourier series?

I know that both Fourier and wavelet can be used for compression of signals. The Fourier series guarantees that it gets the closest approximation of the original signal in the least squared sense. ...
1
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0answers
708 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 ...
0
votes
2answers
358 views

Whether convolution followed by down sampling equals wavelet decomposition

I know that wavelet decomposition equals convolution followed by down sampling by two.I tried to test this on mat lab on haar wavelet. I write the below code and compared with the default wavedec ...
2
votes
1answer
665 views

Edge map based on a Haar Wavelet Transform

I have been implementing the paper Blur Detection for Digital Images Using Wavelet Transform and was asking myself how the following formula could reconstruct the edges given a Haar Wavelet ...
1
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1answer
160 views

Phase Information at Higher Frequencies in Continuous Wavelet Transform

I'm using the code I found here to compute the wavelet transform of a sine wave with a constant frequency. ...
1
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2answers
228 views

Additive white Gaussian noise 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 ...
1
vote
1answer
69 views

Does SWT/ISWT require intermediate approximation coefficients to represent/reconstruct the original signal?

Taking into account that Stationary Wavelet Transform (Algorithme à trous) is not an orthogonal transform do we need intermediate approximation coefficients for signal decomposition? For example, in ...
1
vote
1answer
82 views

Does Wavelet Packets (WPT) decompose signal on dyadic scales like DWT?

As far a I understand WPT is a generalization of DWT in a sense that you get a whole binary tree of possible orthogonal decompositions where DWT is only a one branch. And WPT also downsamples a signal ...