# 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.

440 questions
Filter by
Sorted by
Tagged with
22 views

### Can coefficients of a DWT be computed using least squares approximation?

I assume that it can be computed given function values for each sample as a vector and wavelet values for each scale and translation packed in a matrix. Can anyone clarify the matrix construction and ...
153 views

### Extract approximation and detail coefficients

I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)?
20 views

### Take a wavelet function as a transfer funtion

Is there anyone having the experience of taking the wavelet funtion as a transfer function? That is: if we have $\psi_{m,n}(x)=a^{-m/2}\psi(a^{-m}x-nb)$, $\psi_{m,n}$ is the dilated and shifted ...
103 views

### For discrete wavelet transforms, is redundancy needed to ensure perfect reconstruction?

So I was using pywt and I noticed that in the padding mode documentation they explain the following: DWT performed for these extension modes is slightly ...
135 views

### CWT matlab function [closed]

i'm trying to apply the cwt function from matlab in the first graph and from the different articles that i've read i should get something that shows different peaks to determine the location of damage,...
59 views

### Is there a reason why with symmetric padding, the inverse wavelet transform is not the adjoint of the wavelet transform?

I recently stumbled upon a bothering fact when using the pywavelet library in Python. When we use the default "symmetric" ...
47 views

### Daubechies Wavelets in mulitresolutional analysis decomposition

I have an understanding problem with Daubechies wavelets. When I use a multiresolutional analysis, I want to approximate the given input Signal $f\in L^2(\mathbb{R})$ on the subspaces $V_i$. By ...
40 views

### What are the constraints in design of discrete orthogonal wavelets?

Can anyone point me to literature that explains a quote from here : Why is a wavelet transform implemented as a filter bank? So not all wavelets can be implemeted perfectly (invertible) with ...
534 views

### Filter ECG signal with Wavelet and Python

I have to filter the signal of an ECG with the wavelet method with Python. The data is in a txt file. I can create my dataframe with pandas, display that with seaborn, but can not find a way to apply ...
67 views

### Calculating the Mean Square Error (MSE) in Wavelet Denoising

I´m currently reading the paper (to be more precise: it´s a chapter from the book "Shearlets, Multiscale Analysis of Multivariate Data" by Kutyniok and Labate) "Image Processing Using Shearlets" by G....
11 views

### Why packet wavelet transform for frequency analysis gets non-informative results for some frequencies and phase?

I wrote the following code in Julia for packet wavelet transform. It uses Haar transform (I've chosen low-pass filter to keep average value of the signal). As usual, it works recursively filtering ...
68 views

### Wavelet is a small wave, what is problem with using sin(x) of one cycle?

As far as I know a $\sin(x)$ which is one cycle long can be made into a wavelet and then we can use its dilated and translated versions to represent another function, effectively a wavelet transform. ...
114 views

### Constrained LASSO Problem - ${L}_{1}$ Regularized Least Squares with Linear Equality Constraints

I have an optimization question. I want to solve the following problem: $$\arg\min_S\frac{1}{2}\|s-c\|_2^2 +\lambda\|\Phi s\|_1 \mbox{ s.t. } As = 0$$ in which $\Phi$ is the wavelet transform ...
19 views

### Which algorithms can efficiently identify rectangular regions in noisy greyscale image?

I have a large number (~50000) of square greyscale images, about 180x180 pixels. I need to efficiently scan them for containing significant block like regions. See the following pictures where I have ...
231 views

### Multifractal analysis of an image using wavelets

I want to measure the fractal character of images using a wavelet approach (if possible) in python. (E.g., maybe things like roughness, anisotropy, or just the fractal dimension - perhaps just ...
283 views

### Wavelet Transform and STFT

How wavelet transform is different from STFT. I'm not able to understand what is resolution in frequency domain means?
354 views

### Why does decimation make a system time variant?

On Wikipedia I read this : "The Discrete Wavelet Transform, often used in modern signal processing, is time variant because it makes use of the decimation operation." Why does decimation makes system ...
51 views

### Threshold both detail and analysis coefficients?

Suppose I perform a discrete wavelet transform on some noisy signal $x$ and obtain ${a_1, d_1, d_2, \ldots, d_n}$ where $a_1$ is the set of analysis coefficients and $\{d_j\}$ are the detail ...
82 views

### Discrete Wavelet Transform: Specifics of Filter Bank

So I have been given to understand that the discrete wavelet transform is able to provide both time and frequency resolution in ways that classic Fourier and even short time Fourier cannot. By ...
35 views

### Why is the sound field intensity due to $K$ point sources given by $I(p,\omega) = \sum_{k=1}^K \sigma_k^2(\omega) \delta(p - p_k)$?

I am trying to understand the following piece of text. I am not used to dealing with sound intensity and power so I'm not familiar with the derivation of the formula $(*)$ below. Statement: 1. We ...
162 views

### Connecting DWT matrix operations to Daubechies D4 scaling $\left(\phi(x)\right)$ and wavelet $\left(\psi(x)\right)$ functions by plotting

I'd like to duplicate the plot in the Wikipedia entry for Daubechies D4 scaling and wavelet functions: I don't have Matlab or Mathematica, and my question is not about hacking the curve, but rather ...
67 views

### Can I have some feedback on this research paper on vibration diagnostics?

I have submitted this paper "Detecting a Valve Spring Failure of a Piston Compressor with the Help of the Vibration Monitoring" to figshare.com. I would like to get some feedback on the methodology ...
373 views

112 views

### Reproducing paper results about a wavelet transformation using python [closed]

I have been reading this PhD theis about wavelets and I am trying to reproduce some of the results but I don't know the specific code to use to generate similar results. The original time series ...
52 views

232 views

### Wavelet central frequency

What is the definition of the central frequency of a Wavelet and the bandwidth of a Wavelet? How do they affect the resultant waveform of the wavelet? Thanks.
93 views

### Can I apply CWT on a digital signal?

First, I am so sorry for my dumb and stupid question, I am very beginner with signals. Say that I have an ultrasonic sensor cabled to an ADC (Analog to Digital Converter). The ADC converts the analog ...
22 views

### why is my inbuilt function is not matching with the db5 CA and CD coefficients generated by my code

I am working on wavelet decomposition.As read by the theory i have implemented wavelet decomposition in MATLAB. CA and CD for wavelet decomposition of db1 matches with the inbuilt function but not ...
127 views

### Alternative function for Matlab Stationary Wavelet Transformation

I'm currently working on a project of mine where I have to use stationary wavelet transformation. I found a perfect way to do the transformation using wavelet toolbox of the Matlab. But since it is ...
145 views

### How to define the scales in a biorthogonal, dyadic Discrete Wavelet Transform in Python

I am sorry if this has been discussed before but I could not find any answer. I am trying to implement an algorithm that I found in a paper which asks for a biorthogonal, dyadic DWT with scales 1 and ...
73 views

### wavelet reconstruction

I am doing mtech project now. Actually I am working on discrete wavelet transform.I have done till wavelet decomposition. I have been stuck in reconstructing the signal back to original .please help ...
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,...
417 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 ...
142 views

### Denoise techniques when clean signal and pure noise is 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 ...
In wavelet packet image compression, different types of entropy methods can be used, like Shannon and log-energy. Shannon entropy uses this equation $\mathrm{ent}= -\sum (x^2 \times \log(x^2))$, ...