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Question: <p>The mother wavelet function $\psi(t)$ must satisfy the following:</p>
<p>$$\int\limits_{-\infty}^{+\infty} \frac{|\psi(\omega)|^2}{\omega} d \omega < +\infty,$$
$$\psi ( \omega ) \bigg|_{ \omega =0} =0,$$
and
$$ \int\limits_{-\infty}^{+\infty} \psi(t) \ dt = 0$$</p>
<p>To serve as the wavelet basi... | https://dsp.stackexchange.com/questions/25408/why-is-a-wavelet-transform-implemented-as-a-filter-bank |
Question: <p>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 carrying out discrete convolutions of the wavelet at different scaling factors, one can perform this transform. No... | https://dsp.stackexchange.com/questions/53106/discrete-wavelet-transform-specifics-of-filter-bank |
Question: <p>When I useed <em>Mathematica</em>,If found many Transforms in the list of Discrete Wavelet Transforms.</p>
<p>For example:</p>
<ol>
<li>discrete wavelet transform (DWT)</li>
<li>stationary wavelet transform (SWT)</li>
<li>lifting wavelet transform (LWT)</li>
<li>discrete wavelet packet transform (DWPT) <... | https://dsp.stackexchange.com/questions/30870/what-the-difference-between-the-family-of-discrete-wavelet-transform |
Question: <p>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 discrete wavelets. In all reality everything on a computer is discrete of course, so it seems obvious that... | https://dsp.stackexchange.com/questions/8009/using-continuous-verses-discrete-wavelet-transform-in-digital-applications |
Question: <p>I'm trying some wavelet analysis of EEG signals, using the phase lock measures
from <a href="http://brainimaging.waisman.wisc.edu/~lutz/LeVanQuyen_et_all_JNM_2001.pdf" rel="nofollow">[1]</a>, specifically the S-PLV measure.</p>
<p>In order to calculate that we perform a wavelet transform on the signals an... | https://dsp.stackexchange.com/questions/18722/selecting-the-number-of-cycles-for-wavelet-transform |
Question: <p>Suppose I have a wave with $20 \textrm{ kHz}$, $100 \textrm{ kHz}$ and $300 \textrm{ kHz}$. Sampling frequency used is $1000 \textrm{ kHz}$. I apply the discrete wavelet transform on the wave like <code>dwt(wave,'db2')</code>. I will get one level of approximation and detail coefficients. According to the ... | https://dsp.stackexchange.com/questions/30871/wavelet-transform-in-matlab |
Question: <p>How can power or energy be computed from Continuous Wavelet Transform? Is it just <span class="math-container">$\sum |\text{CWT}(x)|^2$</span>, or are there other considerations, particularly if interested in a subset of frequencies?
Do the results interpret differently from what's computed from DFT?</p>
... | https://dsp.stackexchange.com/questions/86181/power-energy-from-continuous-wavelet-transform |
Question: <p>According to <a href="https://dsp.stackexchange.com/questions/13527/spectral-structure-of-sinusoidal-model">my previous question</a>, I have changed the generate command to: </p>
<pre><code>y=generate1(100,1000,1);
</code></pre>
<p>and got the following picture:</p>
<p><img src="https://i.sstatic.net/2K... | https://dsp.stackexchange.com/questions/13535/get-spectral-picture-from-a-wavelet-transform |
Question: <p>What is "modified frequency slice wavelet transform"? It was written in an article but It's not been described on the web.</p>
Answer: | https://dsp.stackexchange.com/questions/85519/what-is-modified-frequency-slice-wavelet-transform |
Question: <p>I want to estimate the Power spectral density using Discrete wavelet transform and a Morlet Wavelet. Bellow you can find the function I am using. Any comments or suggestions on wether or not the following code is correct?</p>
<pre><code>import pycwt as wavelet
mother_wave_dict = {
'gaussian': wavelet... | https://dsp.stackexchange.com/questions/84522/estimate-power-spectral-density-using-discrete-wavelet-transform-form-pycwt |
Question: <p>I have been implementing the paper <a href="https://www.cs.cmu.edu/~htong/pdf/ICME04_tong.pdf" rel="nofollow noreferrer">Blur Detection for Digital Images Using Wavelet Transform</a> and was asking myself how the following formula could reconstruct the edges given a Haar Wavelet transformed image :</p>
<... | https://dsp.stackexchange.com/questions/38183/edge-map-based-on-a-haar-wavelet-transform |
Question: <p>I would like to apply The Morlet wavelet transform to analyse my EEG signals. I have many short signals each is only 1 min long. and they all recorded in 30Hz.
I have Two questions:</p>
<ol>
<li>In the Morlet wavelet, What is the best scale (alpha) to use in my case ?</li>
<li>About the edge effect: How ... | https://dsp.stackexchange.com/questions/970/apply-wavelet-transform-to-analyse-eeg-signal |
Question: <p>One pertinent attribute is <em>normalization</em>, which measures performance in describing signal spectral amplitude and energy, like <a href="https://dsp.stackexchange.com/a/70643/50076">here</a>. Others are robustness to noise, time vs frequency resolution. Anything else? And are there examples of each ... | https://dsp.stackexchange.com/questions/70669/how-to-test-wavelet-transforms |
Question: <p>Is there anyway to obtain the Fourier Power Spectral Density from a <a href="http://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf" rel="nofollow noreferrer">wavelet transform</a> of a time series?</p>
<p>I am particularly interested in this problem because I was wondering if there is any possibi... | https://dsp.stackexchange.com/questions/38543/relationship-between-wavelet-transform-and-fourier-power-spectral-density |
Question: <p>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 scaled. These basis signals look very similar to wavelets. I'm thinking of using a continuous wavelet transform ... | https://dsp.stackexchange.com/questions/23971/properties-of-a-custom-wavelet-family-for-continuous-wavelet-transform |
Question: <p>what is '<code>parm</code>' means when you set the name of wavelet function in <code>cwtft</code> or <code>icwtft</code>. <code>wave = {wname,[7.6]}</code>. also can I change Fb and Fc when I use '<code>morl</code>' function in <code>cwtft</code> or <code>icwtft</code> transform? and If not, then how can I... | https://dsp.stackexchange.com/questions/10593/inverse-continuous-wavelet-transform-and-parm-in-cwtft |
Question: <p>I have recently created a <a href="https://dsp.stackexchange.com/a/83477/62730">real-time STFT</a> with 50% overlap.</p>
<p><a href="https://i.sstatic.net/WwjV1.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/WwjV1.gif" alt="enter image description here" /></a></p>
<p>I wanted to know if thi... | https://dsp.stackexchange.com/questions/83480/is-online-continuous-wavelet-transform-possible |
Question: <p>I have looked at several packages to do continuous wavelet transform (cwt), and the usable wavelet families that are available are always symmetric. Is there a reason for that? The kind of signals I am studying can be highly asymmetric sometimes, so I would like to do cwt with asymmetric wavelets.</p>
Ans... | https://dsp.stackexchange.com/questions/89420/is-there-a-reason-why-wavelet-in-continuous-wavelet-transform-are-symmetric |
Question: <p>I am learning wavelet transform, below image is an example I have that uses haar wavelet for decomposing the simple haar wavelet like signal.</p>
<p>i know that the coefficients at each level are results of the convolution of the signal and the wavelet, the magnitude represents the similarities between the... | https://dsp.stackexchange.com/questions/76327/how-does-wavelet-transform-detect-pulses-from-a-signal |
Question: <p>One of the properties I have seen for isotropic tight wavelet frames is</p>
<p>$$\sum_{i\in\mathbb{Z}} \left|h(2^i\omega)\right|^2 = 1$$</p>
<p>where $h(\omega)$ is the frequency spectrum of the original wavelet. See page 8 in <a href="http://bigwww.epfl.ch/preprints/unser1202p.pdf" rel="nofollow">A unif... | https://dsp.stackexchange.com/questions/30551/subsampling-property-of-wavelet-transform |
Question: <p>Yesterday I asked about how to extract 2D DFT matrix for a vectorized image. Today my question is how can I extract 2D DWT matrix for a vectorized image.
Fourier transform have this property that rows of the image are transformed first, than columns are transformed. Is there a similiar property for discre... | https://dsp.stackexchange.com/questions/59389/discrete-wavelet-transform-matrix-for-vectorized-image |
Question: <p>I've been reading this article: <a href="http://aix1.uottawa.ca/~jkhoury/haar.htm" rel="nofollow">http://aix1.uottawa.ca/~jkhoury/haar.htm</a> which explains the Haar Wavelet Transform. </p>
<p>At a certain point, the author says:</p>
<blockquote>
<p>... Since the transformation matrix $W$ is the produ... | https://dsp.stackexchange.com/questions/34687/obtaining-normalized-matrix-for-the-haar-wavelet-transform |
Question: <p>Both Gabor filtering and discrete wavelet transform (DWT) analyze the image in both spatial and frequency domains, unlike Fourier transform which analyzes the image only in the frequency domain. What is the difference between DWT and Gabor filtering?</p>
Answer: <p><em>Per se</em>, a Gabor filter in ima... | https://dsp.stackexchange.com/questions/74389/difference-between-gabor-filtering-and-discrete-wavelet-transform |
Question: <p>I want to use the <a href="https://en.wikipedia.org/wiki/Continuous_wavelet_transform" rel="nofollow noreferrer">continuous wavelet transform</a> (CWT) to modify the amplitude of a signal in the frequency domain (in a specific frequency band) and then reconstruct the signal. I want to do it by scaling the ... | https://dsp.stackexchange.com/questions/67037/reconstruct-a-signal-via-continuous-wavelet-transform-cwt |
Question: <p>I recently stumbled upon a bothering fact when using the <code>pywavelet</code> library in Python. When we use the default <code>"symmetric"</code> padding, the inverse wavelet transform is not the adjoint of the wavelet transform (and it's not the mathematical inverse of the wavelet transform, "only in on... | https://dsp.stackexchange.com/questions/55840/is-there-a-reason-why-with-symmetric-padding-the-inverse-wavelet-transform-is-n |
Question: <p>I am trying to use the discrete wavelet transform for signal processing (time series data from a plant). I would like to use a mother wavelet that is not in Matlab. Mallat and Zhong 1992 described a nonorthogonal quadratic spline wavelet I would like to use. They name some coefficients and impulse response... | https://dsp.stackexchange.com/questions/67473/how-do-i-implement-a-nonorthogonal-quadratic-spline-wavelet-into-discrete-wavele |
Question: <p>Wigner transform and continuous wavelet transform are both some kind of time-frequency representation of a signal.</p>
<p>What are the similarities and differences between them? Could you give some comparison between them? Let's restrict ourselves in 1D signal at the moment.</p>
Answer: <p>There is a nice... | https://dsp.stackexchange.com/questions/11425/whats-the-similarities-and-differences-between-wigner-transform-and-wavelet-tra |
Question: <p>Sorry in advance if my question is too dumb.
I'm going through the book of Mallat, and from what I understand, the approximation/wavelet coefficients <span class="math-container">$a_j[n] = <f, \phi_{j,n}>$</span> and <span class="math-container">$d_j[n] = <f, \psi_{j,n}>$</span> can either be c... | https://dsp.stackexchange.com/questions/82121/difference-between-discrete-wavelet-transform-and-convolution |
Question: <p><strong>Main Problem: How can you inverse Wavelet Transforms</strong></p>
<p><strong>(Using the data given by <code>signal.scipy.cwt</code>)</strong></p>
<p>I was wondering if anyone understands the <code>scipy.signal.cwt()</code> function well enough to use it to remove backgrounds and noise from data.
I ... | https://dsp.stackexchange.com/questions/14058/inverse-of-wavelet-transforms-background-and-noise-removal |
Question: <p>I'm working on a project to hide simple string inside a 255x255 image using Wavelet transform. The problem is that, </p>
<p>When i used <code>Haar</code> Wavelet the result is successful,
This is what I've done,</p>
<ul>
<li>Decompose the image into its approximation and details(Vertical,Horizontal,Diogn... | https://dsp.stackexchange.com/questions/8202/steganography-using-wavelet-transform-not-every-wavelet-recovering-the-hidden |
Question: <p>I'm trying to detect the presence of a sinusoid in 1/f noise conditions using the STFT and the DWT with Haar wavelets. I find this interesting phenomenon that I'm not able to explain (see plot at <a href="https://i.sstatic.net/x3UQ9.png" rel="nofollow noreferrer">1</a>)</p>
<p>My sampling rate is 1200 Hz ... | https://dsp.stackexchange.com/questions/8469/question-about-the-haar-wavelet-transform |
Question: <p>I am implementing a continuous wavelet transform and its inverse using morlet wavelets. When I compute the inverse, the resulting signal is off by some constant factor (but otherwise correct). Depending on which frequencies of wavelet I use for the transforms, the resulting signal is off by a different con... | https://dsp.stackexchange.com/questions/83724/inverse-continuous-wavelet-transform-off-by-constant-factors |
Question: <p>Suppose that a signal is decomposed by using discrete wavelet transform (DWT) and transmitted. Is it possible for receiver to find which type of wavelet is applied in transmitter side ?</p>
<p>I mean, if the signal is decomposed by Haar or DB and then reconstructed. Is it have any way to know the type of ... | https://dsp.stackexchange.com/questions/15761/estimate-the-type-of-wavelet-transform-in-receiver-side |
Question: <p>When you perform the Haar wavelet transform, you take the sums and differences, then at each stage, you multiply the entire signal by $\small\sqrt2$.</p>
<p>When taking the inverse transform, you multiply the signal by $\frac{1}{\sqrt2}$ for each iteration.</p>
<p>What does this "normalization" really re... | https://dsp.stackexchange.com/questions/1739/what-does-the-normalization-step-of-the-haar-wavelet-transform-represent |
Question: <p>so the <a href="https://en.wikipedia.org/wiki/Generalized_lifting" rel="nofollow noreferrer">lifting</a> scheme is basically an alternative to performing the discrete wavelet transform with several advantages. </p>
<p>But here are three questions which I did not find an answer to:</p>
<ol>
<li>is it poss... | https://dsp.stackexchange.com/questions/68149/wavelet-packet-transform-and-lifting-scheme |
Question: <p>I understand tha the wavelet transform is about computing the coefficients to assign to scaled and translated versions of the chosen mother wavelet. The coefficients measure the correlation between the signal and shifted/scaled wavelet. That said, I know that the CWT is used to compute the scalogram while ... | https://dsp.stackexchange.com/questions/93387/wavelet-transform-scalogram-detail-and-approximation-coefficients |
Question: <p>In case of continuous wavelet transform (CWT), the wavelets are generated from the mother wavelet by scaling and translation. To achieve energy normalization and to ensure that all wavelets have the same energy regardless of their scales, each wavelet is divided by the square root of the the scale S. In ca... | https://dsp.stackexchange.com/questions/72314/energy-normalization-across-different-scales-in-case-of-discrete-wavelet-transfo |
Question: <p>I want to write continuous wavelet transform codes manually by matlab. And I want to use complex morlet function. Here are some background:<br>
Continuous wavelet transform definition: $C(S,T;f(t),\psi (t))=\frac{1}{\sqrt{S}}\int_{S}^{b}f(t)\psi^{\ast }(\frac{t-T}{S})$<br>
S is scale vector.for example <c... | https://dsp.stackexchange.com/questions/11576/inquiries-for-writing-continuous-wavelet-transform-codes-manually |
Question: <p>I am using CMOR(complex morlet) wavelet in Fourier space in order to reconstruct my signal and also estimate damping and frequencies of the embedded modes. there are two main parameters in cmor. the Fb and Fc. bandwidth and center frequency, with increasing the Fb i get better result for frequency estimati... | https://dsp.stackexchange.com/questions/10884/heisenberg-uncertainly-principle-and-wavelet-transform |
Question: <p>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 Daubechies higher order wavelets) the size of the returned approximation and detail matrices is not a power of two.... | https://dsp.stackexchange.com/questions/43224/quadtree-decomposition-of-discrete-wavelet-transform-using-bio4-4-cdf-wavelet |
Question: <p>Referencing this article here <a href="https://arxiv.org/pdf/1203.1513.pdf" rel="nofollow noreferrer">https://arxiv.org/pdf/1203.1513.pdf</a></p>
<p>It states "A wavelet transform commutes with translations, and is therefore not translation invariant". Now I understand why it is a problem that the result ... | https://dsp.stackexchange.com/questions/56696/what-does-it-mean-for-a-wavelet-transform-to-commute-with-translations |
Question: <p>I have a pressure vs time data of a noise on which I wish to perform discrete wavelet transform.
I have divided my frequency range into 1/3rd Octave Bands and have calculated sound pressure level at each band.</p>
<p>I am very much confused on how to perform a discrete wavelet transform in 1/3rd Octave Fre... | https://dsp.stackexchange.com/questions/68913/plotting-a-time-frequency-contour-colormesh-plot-of-a-discrete-wavelet-transform |
Question: <p>how to apply wavelet transform method to extract alpha waveform( higher and lower band frequency known) from a given known signal ?</p>
Answer: <p>The mother wavelet is a bandpass filter. This means we have to apply the CWT(in this case), calculate the correspondence between scales and frequencies, zero o... | https://dsp.stackexchange.com/questions/20310/use-wavelet-transform-to-extract-a-waveform-of-certain-frequency |
Question: <p>I was wondering if anyone may know of any method for the construction of a 3D wavelet transform in matrix form? I've been able to build matrices to perform 1D & 2D transforms. Yet, am finding very little resources regarding the 3D case in the literature.</p>
Answer: <p>In general, if you want to const... | https://dsp.stackexchange.com/questions/88885/3d-wavelet-transform-in-the-form-of-a-matrix |
Question: <p>I'm working on my own implementation of the discrete Haar wavelet transform, I understand the wavelet theory and how to construct the Haar matrix of size N to perform the transform, but obviously there is a problem using the Haar matrix in application - it's simply too big.</p>
<p>I am working on an appli... | https://dsp.stackexchange.com/questions/12619/discrete-haar-wavelet-transform-fast-and-efficient-method |
Question: <p>I am in need of an open source library for computing Fast wavelet transforms (FWT) and Inverse fast wavelet transforms (IFWT) - this is to be part of a bigger code I am currently writing. </p>
<p>The things I am looking for in the library:</p>
<p>1) Contains a good variety of wavelet families (Daub,Haar,... | https://dsp.stackexchange.com/questions/10268/any-open-source-fast-wavelet-transform-libraries |
Question: <p>After being away from DSP for a long time, I am trying to familiarize myself with wavelet transform. Here is what I (think) have understood so far:</p>
<ul>
<li>Wavelet transform provides you high time resolution at higher frequencies and high frequency resolution at lower frequencies.</li>
<li>DWT can be... | https://dsp.stackexchange.com/questions/27671/getting-frequency-content-at-different-times-from-discrete-wavelet-transform-coe |
Question: <p>I have a sparse dataset indexed by nanoseconds. Storing the dataset in a discrete fashion would take too much memory. I'd like to take a wavelet transform and I'd like it to be relatively fast. The dataset has about 100,000 dirac deltas in it.</p>
<p>Is this possible?</p>
<p>Thanks!
James</p>
Answer: | https://dsp.stackexchange.com/questions/71606/how-to-take-wavelet-transform-of-sparse-input-data |
Question: <p>This question came up in the context of the <a href="https://github.com/OverLordGoldDragon/ssqueezepy/issues/6" rel="nofollow noreferrer"><code>ssqueezepy</code></a> library. As a basic experiment I did compute the synchrosqueezed wavelet transform of three basic signals:</p>
<ol>
<li>A sine of 440 Hz.</li... | https://dsp.stackexchange.com/questions/71855/why-does-a-synchrosqueezed-wavelet-transform-show-oscillating-behavior |
Question: <p>My basic question is, "What is the standard way to post-process/smooth a continuous wavelet transform result to measure the wavelet's activation at a specific frequency?"</p>
<p>When using wavelets for isolating a signal at a specific frequency, a continuous wavelet transform (CWT) may give the d... | https://dsp.stackexchange.com/questions/83266/standard-method-of-smoothing-amplitude-envelope-of-continuous-wavelet-transfor |
Question: <p>I will be extremely grateful if someone could please answer this basic question.</p>
<p>How can one plot a 3D (translation, scale, amplitude) plot from the Continuous wavelet transform (CWT) coefficients?</p>
<p>The CWT coefficient is a M X N matrix. Which of the axis corresponds to the translation, scale... | https://dsp.stackexchange.com/questions/73928/3d-time-scale-amplitude-plot-in-continuous-wavelet-transform |
Question: <p>I have implemented the Continuous Wavelet Transform using the pycwt library(<a href="https://github.com/regeirk/pycwt/blob/master/pycwt/wavelet.py" rel="nofollow noreferrer">https://github.com/regeirk/pycwt/blob/master/pycwt/wavelet.py</a>) and its inverse using Morlet wavelets, however, upon calculating t... | https://dsp.stackexchange.com/questions/86439/inverse-continuous-wavelet-transform-off-by-constant-factor-in-the-y-axis |
Question: <p>I'm currenty aiming to optimize my fast wavelet transform (FWT) algorithm for 2D signals (images). It works as follows:</p>
<ul>
<li>one iteration of 1D FWT does convolution of 1D input data with a selected 1D filter (lengths from 2 to approx. 60) and downsamples the result</li>
<li>algorithm for 2D trans... | https://dsp.stackexchange.com/questions/28051/optimized-2d-wavelet-transform-using-fft |
Question: <p>I don't understand the mapping time-scale plane to the time-frequency plane in synchrosqueezed wavelet transform, i.e. $(3)$. You can find the paper <a href="https://services.math.duke.edu/~jianfeng/paper/synsquez.pdf" rel="nofollow">here</a>.</p>
<p>For the given signal of $x(t)$ and mother wavelet of $\... | https://dsp.stackexchange.com/questions/31309/how-to-map-cwt-to-synchrosqueezed-wavelet-transform |
Question: <p>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 of the signal and the phase of the sinusoids from that, but is there a better way to do this with a wavelet ... | https://dsp.stackexchange.com/questions/18476/can-a-wavelet-transform-give-time-dependent-phase-of-sinusoids-in-signal |
Question: <p>let us suppose that we have following signal values,which consists by deterministic components and random noise(white noise)</p>
<pre><code>56.69
75.24
13.77
8.56
-12.88
-65.34
-45.33
-48.78
-22.23
54.12
83.77
11.84
2.31
39.59
-32.09
-88.86
5.45
50.24
-37.39
-35.69
38.62
7.06
-30.01
22.36
60.71
30.96
5... | https://dsp.stackexchange.com/questions/15178/use-wavelet-transform-to-extract-frequencies-from-given-signal |
Question: <p>I have some stumbling block in my thesis writing.</p>
<p>Do we use the same filter pair while implementing DWT filter bank with downsampling of the filter output, or filters do change also from level to level?
Though on the Wiki page and in the book "Biosignal and Medical Image Processing, 3rd edition" by... | https://dsp.stackexchange.com/questions/58209/discrete-wavelet-transform-dwt-filter-bank |
Question: <p>I am reading </p>
<p><a href="http://users.rowan.edu/~polikar/WAVELETS/WTpart3.html" rel="nofollow noreferrer">The Wavelet Tutorial</a></p>
<p>Part III
MULTIRESOLUTION ANALYSIS
&
THE CONTINUOUS WAVELET TRANSFORM</p>
<p>by
Robi Polikar </p>
<p>The author explains about the following fig and says;</p... | https://dsp.stackexchange.com/questions/9319/trying-to-understand-wavelet-transform-frequncy-time-diagram |
Question: <p>I am using 5 channels [ fz , cz , c3 , c4 , pz] to detect drowsiness of driver
My First Question is, what is the right input to get feature power band ( Theta , alpha , gamma , beta ) to wavelet transform ? ( these 5 channels or 1 channel or what ? )
My Second Question is, Is it right to classify data bas... | https://dsp.stackexchange.com/questions/49272/wavelet-transform-and-fft-using-to-extract-feature-power-bands-with-eeg-signals |
Question: <p>I'm using the code I found <a href="https://dsp.stackexchange.com/a/12880/26474">here</a> to compute the wavelet transform of a sine wave with a constant frequency. </p>
<pre><code>#!/usr/bin/python2
from pylab import *
import matplotlib.pyplot as plt
import numpy as np
import scipy
x = np.linspace(0, 1... | https://dsp.stackexchange.com/questions/38055/phase-information-at-higher-frequencies-in-continuous-wavelet-transform |
Question: <p>So far, I used STFT a.k.a windowed fourier transform for convert signal to time-frequency domain.</p>
<p>In general, the parameter I can tune is window size, where smaller window size lead lower frequency resolution but higher time resolution. And vice versa. The resulted spectogram is consistent.</p>
<p>I... | https://dsp.stackexchange.com/questions/95008/spectogram-short-time-fourier-transform-vs-time-frequency-wavelet-transform |
Question: <p>In Continuous Wavelet Transform (CWT) To achieve energy normalization and to ensure that all wavelets have the same energy regardless of their scales, each wavelet is divided by the square root of the the scale S.</p>
Answer: | https://dsp.stackexchange.com/questions/87188/in-continous-wavelet-transform-all-wavelets-must-have-the-same-energy-regardles |
Question: <p>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:</p>
<p>$$\hat{f}(\xi) = \int^\infty_{-\infty}\ f(t)\ e^{-2\pi i t \xi}\ dt$$</p>
<p>Whereas a wavelet transform is going to use this:</p>
<p>... | https://dsp.stackexchange.com/questions/41259/log-vs-linear-frequency-scales-of-fourier-and-wavelet-transforms |
Question: <p>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 (pywt.cwt) in python.
this function has only 2 outputs: coefficient and frequency, while spectrogram returns t... | https://dsp.stackexchange.com/questions/40502/continuous-wavelet-transform-time-vector-in-python |
Question: <p>I am porting <a href="https://github.com/ebrevdo/synchrosqueezing" rel="nofollow noreferrer">Synchrosqueezing</a> to <a href="https://github.com/OverLordGoldDragon/ssqueezepy" rel="nofollow noreferrer">Python</a>, and came across an implementation difference on CWT between mine and <a href="https://github.... | https://dsp.stackexchange.com/questions/66889/difference-between-these-two-continuous-wavelet-transforms |
Question: <p>For one stage discrete wavelet transform (DWT), if we have a signal with 1000 samples occupying the frequency range from zero to 500 Hz, the output of the low-pass filter is a signal with frequency range 0-250 Hz, and the output of the high-pass filter is a signal with frequency range 250-500 Hz. Downsampl... | https://dsp.stackexchange.com/questions/82508/the-downsampling-step-with-discrete-wavelet-transform |
Question: <p>I have a noisy sparse signal containing number of frequency components.
Is there any method to uniformly denoise this signal.
in other words, a method that estimated and eliminates the noise power across all the frequencies in the band and not only on the borders like in wavelet denoising?</p>
<p>The follo... | https://dsp.stackexchange.com/questions/54897/signal-denoising-uniformly-in-frequency-domain |
Question: <p>I would like to use time averaging technique for denoising vibration signal, using the below function, how do we choose the appropriate parameters D and N for optimal denoising !</p>
<pre><code>% sigav.m - signal averaging
%
% y = sigav(D, N, x)
%
% D = length of each period
% N = number of periods
% x =... | https://dsp.stackexchange.com/questions/72762/time-averaging-denoising-signal |
Question: <p>I'm starting hydraulic experiments, where I'd have to measure velocity in an unsteady flow with a device called Acoustic Doppler Velocimeter. In DSP terms, I'd have a nonstationary signal in a shape of waves (In the figure below, the instantaneous velocity (cm/s) as function of time (s) in one point, the p... | https://dsp.stackexchange.com/questions/50664/denoising-a-signal |
Question: <p>im trying to denoise a signal to which i added AWGN. Here is what ive done so far:</p>
<pre><code>import numpy as np
import matplotlib.pyplot as plt
from scipy import signal
"""Creating a cosine and adding AWGN to it. Then denoising it.
"""
# Create cosing and cosine with noi... | https://dsp.stackexchange.com/questions/87273/denoising-signal-with-butterworth-filter |
Question: <p>I'm new to DSP due to a research project related with audio classification. We are designing a DL-based pipeline to determinate which kind of vessel appears in underwater recordings.</p>
<p>Thing is that I've seen that it would be good (and given how many papers refer and focus on the denoising process, al... | https://dsp.stackexchange.com/questions/96644/implications-of-adding-gaussian-noise-after-denoising-original-signal |
Question: <p>The example that I've seen on state estimation involves deriving the ABCD matrix of a physical system (i.e. falling object) and tracking that object.</p>
<p>I would like to use Kalman Filter for signal denoising applications (specifically EEG signal). How could I apply KF in this situation since ABCD matr... | https://dsp.stackexchange.com/questions/17333/how-do-you-apply-kalman-filter-to-track-a-signal |
Question: <p>I have a program which takes in data from an oscilloscope, and due to reflections in the medium, we will get random signals at random intervals. The two grey windows at the right bottom show the original data (below red line), and after FFT forward and backward (above red line). </p>
<p>The data set is or... | https://dsp.stackexchange.com/questions/11485/denoise-a-randomly-occuring-signal |
Question: <p>I have the clean version of the signal.<br>
I can obtain the environmental noise.
I want to apply an effective denoising technique on a noisy signal (i.e., clean plus environmental noise).</p>
<p>Some observations:</p>
<ul>
<li>The noise to signal ratio is extremely low.</li>
<li>The noise is spread acro... | https://dsp.stackexchange.com/questions/47815/denoise-techniques-when-clean-signal-and-pure-noise-are-available |
Question: <p>When I read papers on image denoising, I always encounter sparse representation. For image denoising, we try to separate image signal from noise. It is assumed that signal is correlated and noise is uncorrelated. Sparse representation represents one signal as a linear combination of a small number of dicti... | https://dsp.stackexchange.com/questions/30557/sparse-representation-for-image-denoising |
Question: <p>I have a <strong>complex</strong> observable series <span class="math-container">$Y(t)$</span> which is the result of summing two <strong>complex</strong> r.v <span class="math-container">$X(t)$</span> (unobservable) and a <span class="math-container">$\epsilon(t)$</span> (unobservable).</p>
<p><span clas... | https://dsp.stackexchange.com/questions/53269/denoising-a-signal-using-eigendecomposition |
Question: <p>I am learning Wiener filtering for 2D images by myself. From one book, it reads</p>
<p><em>It should be noted that the study of the more general problem of signal denoising dates
back to at least Norbert Wiener in the 1940s. The celebrated Wiener filter provides the optimal solution to the recovery of Gau... | https://dsp.stackexchange.com/questions/27890/what-is-a-gaussian-signal |
Question: <p>Say I have a noisy signal in which I want to denoise.</p>
<p>There's two methods I'm considering</p>
<ol>
<li>FFT denoising, where I take the FFT of the signal and then threshold somewhere, attenuate all the frequencies below this threshold, and then take the IFFT.</li>
<li>Low pass filtering, which in the... | https://dsp.stackexchange.com/questions/82676/fft-denoising-vs-low-pass-filter |
Question: <p><strong>Distributed Acoustic Sensing (DAS)</strong></p>
<p>I have an iDAS (intelligent distributed acoustic sensing) dataset obtain from an undersea optical fibre. iDAS data have a 2D dimensional representation. On the one axis we have the channel axis, i.e. the point on the cable from which we measure the... | https://dsp.stackexchange.com/questions/85371/bibliographic-references-on-denoising-distributed-acoustic-data-with-deep-learni |
Question: <p>I currently am trying to portray PSNR's ability to measure noise in an image. The PSNR is said to be high (around 40 dB) if there is a low amount of noise in the 2D signal.</p>
<p>In my experiment I have fairly noisy image (artificially added) and through 6 iterations I add more and more denoising strength... | https://dsp.stackexchange.com/questions/89794/psnr-decreases-while-denoising |
Question: <p>I am using matlab wavelet toolbox to denoise physiological signals, I am plotting the denoised signal on top of the original noisy signal and making sure spikes were not removed as a measure of effectiveness as well as plotting the FFT of the two signals (original and denoised).</p>
<p>Is this a correct wa... | https://dsp.stackexchange.com/questions/69076/best-way-to-measure-effectiveness-of-discrete-wavelet-denoising |
Question: <p>So I work in this domain of biophysics that has to do with a light-based detection for measuring small movement of molecules (nanometer and piconewton scale) via a Quadrant Photodiode. This signal contains lots of information but is riddled with noise. One of the challenges is denoising this signal and whi... | https://dsp.stackexchange.com/questions/84570/a-self-supervised-learning-technique-to-denoise-my-specific-signal |
Question: <p>I am reading this <a href="https://paris.cs.illinois.edu/pubs/liu-interspeech2014.pdf" rel="nofollow noreferrer">paper</a> for signal denoising. In the paper, the authors says</p>
<blockquote>
<p>The core concept in this paper is to compute a regression between a noisy signal frame and a clean signal frame... | https://dsp.stackexchange.com/questions/83023/understand-short-time-fourier-transform |
Question: <p>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 about at which time it happens. That's why the wavelet transform is suitable for the time-frequency analys... | https://dsp.stackexchange.com/questions/15148/disadvantages-of-wavelet-transform |
Question: <p>This is a cross posting from the crossvalidated stack exchange as I thought this may be a better forum to ask.</p>
<p>I have a dataset consisting of respiratory time series signals of different lengths obtained from different groups of patients. I want to either classify or cluster the patients using these... | https://dsp.stackexchange.com/questions/71917/help-with-denoising-signal-and-periodogram-analysis-resources |
Question: <p>The highest voted answer to <a href="https://dsp.stackexchange.com/questions/3066/bag-of-tricks-for-denoising-signals-while-maintaining-sharp-transitions">this question</a> suggests that to denoise a signal while preserving sharp transitions one should </p>
<blockquote>
<p>minimize the objective functio... | https://dsp.stackexchange.com/questions/3465/solving-convex-optimization-problem-used-for-high-quality-denoising |
Question: <p>I know this is maybe a very basic question but I am doing this as a hobby and I can't find a solution to this problem.
Basically I am trying to remove some noise from data I am reading from an accelerometer. This is what I want to achieve (<a href="http://eeweb.poly.edu/iselesni/lecture_notes/TVDmm/TVDmm.p... | https://dsp.stackexchange.com/questions/14968/using-total-variation-denoising-to-clean-accelerometer-data |
Question: <p>im capturing ultrasonic waves using an analog MEMS mic and other components on a PCB. My signal is similiar broadband and non-stationary (see <a href="https://innovatus-pub.github.io/abstractpublications_archive/2020/paper1_pdf.pdf" rel="nofollow noreferrer">2</a>) and im trying to remove/reduce environmen... | https://dsp.stackexchange.com/questions/91556/online-noise-reduction-on-non-stationary-broadband-signals |
Question: <p>I have been researching effective algorithms for denoising biomedical signals (non-stationary) that can be implemented in real time either using FPGA or DSP. I can across many suggestions for algorithms and effectiveness but found DWT to be the one that can denoise most of the noises I am interested in (po... | https://dsp.stackexchange.com/questions/68400/can-discrete-wavelet-transform-for-denoising-purposes-be-implemented-in-real-tim |
Question: <p>I recently started working on sleep study.</p>
<p>For my research I download sleep EEG data from physionet. The EEG data has 100 Hz sampling rate and was recorded from 2 bipolar EEG site.</p>
<p>When I start the preprocessing stage, I encounter a simple problem:</p>
<p>How would I know if my signal has... | https://dsp.stackexchange.com/questions/45527/how-do-i-know-if-my-eeg-signal-need-denoising |
Question: <p>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, i.e. convolving with a gaussian, is out). I often find myself facing this question and don't feel like I k... | https://dsp.stackexchange.com/questions/3066/bag-of-tricks-for-denoising-signals-while-maintaining-sharp-transitions |
Question: <p>I would like to apply Wavelet in <strong>MATLAB</strong> as a denoising technique on Non-Intrusive load Monitoring data. The data was captured by sensors on each appliance and one sensor on the smart meter (Normally called Aggregated Data). The dataset contains the following:</p>
<ol>
<li>timestamp</li>
<... | https://dsp.stackexchange.com/questions/62904/applying-wavelet-on-energy-disaggregation-as-denoising-technique-to-remove-uncer |
Question: <p>I have 2 ADC channels of constant voltage measurement with small amount of high frequency noise only and no low frequency oscillations. The final signal should be the simple sum of those and denoised with the moving average in the end. Does the moving average denoising of each separate channel before final... | https://dsp.stackexchange.com/questions/24360/denoising-approach-for-a-combination-of-several-adc-voltage-channles |
Question: <p>When I apply differerent thresholding, wavelet denosing functions to non stationary time series which has been detrended via Loess regression and demean it. I expect that when this processed series are submited to denoising / thresholding will result in a clean series with smaller values than the submited ... | https://dsp.stackexchange.com/questions/25519/denoising-thresholding-via-wavelets |
Question: <p>I have data captured by a wireless sensor that is noisy. It randomly jumps in value frequently, and I want to know what this signal will look like without these jumps. I am looking for an elegant signal processing technique to do this, if one exists. Below is the time-series signal:</p>
<p><a href="https:/... | https://dsp.stackexchange.com/questions/93113/how-can-i-denoise-this-signal |
Question: <p><strong>Statement of the problem:</strong></p>
<p>I used a MEMS sensor to detect break signals in a concrete beam. The sensor was attached to a L-form steel plate, which was glued on the concrete surface. The sensor was connected to a preamplifier through BNC cable. To achieve a better SNR of the signal, t... | https://dsp.stackexchange.com/questions/96061/denoising-a-digitalized-electric-signal-with-spikes-probabaly-due-to-emi |
Question: <p>I have a signal and its derivative simultaneously measured, both including additive noise. The measurement is completed before the analysis, so it can be looked ahead. Now I want to reconstruct a less noisy version of the signal. I'm looking for pointers to algorithms I should look into.</p>
<p>Kalman fil... | https://dsp.stackexchange.com/questions/52150/estimating-a-signal-given-a-noisy-measurement-of-the-signal-and-its-derivative |
Question: <p>I'm trying to do some example elementary denoising of the audio signal. Let's say input is speech with constant traffic background noise.</p>
<ul>
<li>First I calculated block-based overlap-add Fourier transform (size 512) and continued in the frequency domain with the signal <code>in[n]</code>.</li>
<li>T... | https://dsp.stackexchange.com/questions/87096/basic-audio-denoising-in-the-frequency-domain-using-minimum-statistics |
Question: <p>I have an image that looks like <a href="https://drive.google.com/file/d/0B1X1jFSEgpjJNmMzZTZ6QkdSOTg/view?usp=sharing**" rel="nofollow noreferrer">this</a> (it might appear low res in a browser because it is 16 MB). This image was taken with a scanning electron microscope, but because the equipment is out... | https://dsp.stackexchange.com/questions/42110/what-techniques-are-used-for-signal-image-denoising-example-image-provided |
Question: <p>I have a time series of water temperature, e.g.</p>
<pre><code>y = 1+(30-10).*rand(1,365);
</code></pre>
<p>I have previously used the wavelet denoising routine in the wavelet toolbox by matlab to remove unwanted noise from a signal, e.g.</p>
<pre><code>[s_denoised, ~, ~] = wden(y, 'minimaxi', 's', 'sln... | https://dsp.stackexchange.com/questions/7817/wavelet-denoising-routine-for-environmental-data-series |
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