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wavelet transform | Why is a wavelet transform implemented as a filter bank? | https://dsp.stackexchange.com/questions/25408/why-is-a-wavelet-transform-implemented-as-a-filter-bank | <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 basis for wave... | <p>First of all the basic idea of wavelet transforms lies in multi-resolution analysis. What this means is that the signal is looked at from different scales.</p>
<p>It is probably easier to understand this with images (which are 2D signals). The idea of multi-resolution is like zooming in and out of a reference signal... | 234 |
wavelet transform | Discrete Wavelet Transform: Specifics of Filter Bank | https://dsp.stackexchange.com/questions/53106/discrete-wavelet-transform-specifics-of-filter-bank | <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. Now, I have ... | <p>The paper by H. Caglar and A. Akansu show that other known wavelet families can also be designed by using Bernstein polynomial approximation. Their examples in H. Caglar and A.N. Akansu, A Generalized Parametric PR-QMF Design Technique Based on Bernstein Polynomial Approximation, IEEE TRANSACTIONS ON SIGNAL PROCESSI... | 235 |
wavelet transform | What the difference between the family of Discrete Wavelet Transform？ | https://dsp.stackexchange.com/questions/30870/what-the-difference-between-the-family-of-discrete-wavelet-transform | <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) </li>
<li>s... | 236 | |
wavelet transform | Using continuous verses discrete wavelet transform in digital applications | https://dsp.stackexchange.com/questions/8009/using-continuous-verses-discrete-wavelet-transform-in-digital-applications | <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 discrete ... | <p>As Mohammad stated already the terms Continuous Wavelet Transforms (CWT) and Discrete Wavelet Transforms (DWT) are a little bit misleading. They relate approximately as (Continuous) Fourier Transform (the math. integral transform) to DFT (Discrete Fourier Transform).</p>
<p>In order to understand the details it is ... | 237 |
wavelet transform | Selecting the number of cycles for wavelet transform | https://dsp.stackexchange.com/questions/18722/selecting-the-number-of-cycles-for-wavelet-transform | <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 and
one of t... | 238 | |
wavelet transform | Wavelet transform in MATLAB | https://dsp.stackexchange.com/questions/30871/wavelet-transform-in-matlab | <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 basics, th... | <p>What you might be forgetting is that <code>dwt</code> does downsampling. After filtering (low-pass or high-pass), the filtered signal is subsampled. In order to keep the number of samples. So aliasing may occur, depending on the quality of the filters.</p>
<p>And <code>db2</code> is a quite poor filter. So if you <... | 239 |
wavelet transform | Power/Energy from Continuous Wavelet Transform | https://dsp.stackexchange.com/questions/86181/power-energy-from-continuous-wavelet-transform | <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>
| <p>CWT power is tricky. We must distinguish between <strong>energy of transform</strong> and <strong>energy of signal</strong>, and the two can be very different. As energy is the more fundamental and less conceptually intricate quantity, I develop this answer for energy, then relate to power. Answer applies to CWT <st... | 240 |
wavelet transform | Get spectral picture from a wavelet transform | https://dsp.stackexchange.com/questions/13535/get-spectral-picture-from-a-wavelet-transform | <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/2KsED.png" a... | <p>Try this one:</p>
<pre><code>m=cwt(y,1:100,'sym2','plot');
colormap(pink)
</code></pre>
<p>Result (btw, I cannot reproduce your curve in time domain with the function <code>generate1</code>):</p>
<p><img src="https://i.sstatic.net/OQDSs.jpg" alt="enter image description here"></p>
<p>Low scale values compress th... | 241 |
wavelet transform | What is "modified frequency slice wavelet transform"? | https://dsp.stackexchange.com/questions/85519/what-is-modified-frequency-slice-wavelet-transform | <p>What is "modified frequency slice wavelet transform"? It was written in an article but It's not been described on the web.</p>
| 242 | |
wavelet transform | Estimate Power spectral density using Discrete wavelet transform form pycwt | https://dsp.stackexchange.com/questions/84522/estimate-power-spectral-density-using-discrete-wavelet-transform-form-pycwt | <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.DOG(),
... | 243 | |
wavelet transform | Edge map based on a Haar Wavelet Transform | https://dsp.stackexchange.com/questions/38183/edge-map-based-on-a-haar-wavelet-transform | <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>
<p>$$ \sqrt... | <p>One single level of a standard separable 2-channel wavelet transform, denoted by $i$, uses a low-pass $l$ and a high-pass $h$ filters (followed by downsampling). Traditionally, one applies $l$ and $g$ on the rows of the image, putting the downsampled low-passed coefficients on a left-half, and the downsampled high-... | 244 |
wavelet transform | Apply wavelet transform to analyse EEG signal | https://dsp.stackexchange.com/questions/970/apply-wavelet-transform-to-analyse-eeg-signal | <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 can I know... | <p>I'm not sure whether you're talking about Discrete Wavelet Transform (DWT) or Continuous Wavelet Transform (CWT). Both can be used on discrete signals similarly to DFT and DTFT, I'm not sure if anyone calls it the Discrete Time Wavelet Transform instead. In any case, the <a href="http://www.ece.rice.edu/~yyue/resear... | 245 |
wavelet transform | How to test wavelet transforms? | https://dsp.stackexchange.com/questions/70669/how-to-test-wavelet-transforms | <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 being comp... | <p>There are many options to test a wavelet transform, or compare them.</p>
<p>You can first compare them on their most basic properties. One can check whether it is invertible, orthogonal, biorthogonal, critical or redundant (and the oversampling ratio), separable or not, (close-to) invariant to transformations of the... | 246 |
wavelet transform | Relationship between Wavelet transform and Fourier Power Spectral Density | https://dsp.stackexchange.com/questions/38543/relationship-between-wavelet-transform-and-fourier-power-spectral-density | <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 possibility to ob... | 247 | |
wavelet transform | Properties of a custom wavelet family for continuous wavelet transform | https://dsp.stackexchange.com/questions/23971/properties-of-a-custom-wavelet-family-for-continuous-wavelet-transform | <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 to get the... | <p>Your question is quite central to the development of wavelet theory. </p>
<p>Indeed, the word wavelet has an early history. It is coined in "<a href="http://dx.doi.org/10.1190/1.1441816" rel="nofollow">The form and nature of seismic waves and the structure of seismograms</a>", Norman Ricker, 1940, Geophysics. Here,... | 248 |
wavelet transform | inverse continuous wavelet transform and [Parm] in cwtft | https://dsp.stackexchange.com/questions/10593/inverse-continuous-wavelet-transform-and-parm-in-cwtft | <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 reconstru... | <p><code>cwtft</code> and <code>icwtft</code> use Fourier transform of wavelet function to reconstruct the signal. The ‘<code>morl</code>’ in <code>wname</code> is analytic morlet function. So it’s exactly <strong>complex morlet</strong> and will give you phase and magnitude information about signal. The ‘<code>parm</c... | 249 |
wavelet transform | Is online Continuous Wavelet Transform possible? | https://dsp.stackexchange.com/questions/83480/is-online-continuous-wavelet-transform-possible | <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 this window-b... | <p>Whether it's "real-time" depends on sampling rate. What's true is that most implementations fall short for realistic <span class="math-container">$f_s$</span>.</p>
<p>I am currently working on CWT that will be faster than any other I know of, best case by several times. Though, it may be a while until it's... | 250 |
wavelet transform | Is there a reason why wavelet in continuous wavelet transform are symmetric? | https://dsp.stackexchange.com/questions/89420/is-there-a-reason-why-wavelet-in-continuous-wavelet-transform-are-symmetric | <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>
| <p>Continuous wavelets do not need to be symmetric. Due to their high redundancy, mathematical conditions for a function to be an admissible wavelet are quite mild. In a nutshell, integrability, zero-mean and fast decay in the frequency domain are "enough".</p>
<p>Issues arise when one wants non-redundant cri... | 251 |
wavelet transform | how does wavelet transform detect pulses from a signal | https://dsp.stackexchange.com/questions/76327/how-does-wavelet-transform-detect-pulses-from-a-signal | <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 them.</p>
<p>... | <p>At level 1, the discrete Haar wavelet transform reduces to a 2-tap discrete derivative, downsampled by a factor of two. This downsampling is the main reason for the wavelet shift-variance, and for missed "pulses" or discontinuities. For instance, if your signal is:</p>
<p><span class="math-container">$$ [... | 252 |
wavelet transform | Subsampling property of wavelet transform | https://dsp.stackexchange.com/questions/30551/subsampling-property-of-wavelet-transform | <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 unifying param... | <p>I am not completely confident with the full theory of wavelet frames, however I will share some pointers and my beliefs, do not take any of the following for a truth. The property you show is (partly) a characterization of an orthogonal system. In Hernandez & Weiss, A first course on wavelets, 1996, you find Th... | 253 |
wavelet transform | discrete wavelet transform matrix for vectorized image | https://dsp.stackexchange.com/questions/59389/discrete-wavelet-transform-matrix-for-vectorized-image | <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 discrete wavelet... | <p>For only one level on both direction, the classical DWT schemes are applied separately (rows then columns, or colums then rows). </p>
<p>For more levels, there exist two schemes:</p>
<ul>
<li>one interleaving decompositions: row, col, row, col, etc. (also called non-separable/square/non-standard/isotropic/Mallat),... | 254 |
wavelet transform | Obtaining normalized matrix for the Haar Wavelet Transform | https://dsp.stackexchange.com/questions/34687/obtaining-normalized-matrix-for-the-haar-wavelet-transform | <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 product of thre... | <p>After a few quick calculations, it seems to me that the trouble comes from poor notations for the root in your reference. If you read, in the final normalized matrix, $\sqrt{8/64}$ and $\sqrt{2/4}$ instead of $\sqrt{8}/64$ and $\sqrt{2}/4$ (along with the $\pm$ signs), then the final result is correct.</p>
<p>The... | 255 |
wavelet transform | Difference between Gabor filtering and Discrete Wavelet Transform | https://dsp.stackexchange.com/questions/74389/difference-between-gabor-filtering-and-discrete-wavelet-transform | <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>
| <p><em>Per se</em>, a Gabor filter in image processing is one linear filter at a certain scale and 2D frequency used for orientation filtering and texture analysis.</p>
<p>It would be easier to compare Gabor representations and discrete wavelet transforms. Both are related to a linear decomposition of possibility mul... | 256 |
wavelet transform | Reconstruct a signal via continuous wavelet transform (CWT) | https://dsp.stackexchange.com/questions/67037/reconstruct-a-signal-via-continuous-wavelet-transform-cwt | <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 wavelet co... | 257 | |
wavelet transform | Is there a reason why with symmetric padding, the inverse wavelet transform is not the adjoint of the wavelet transform? | https://dsp.stackexchange.com/questions/55840/is-there-a-reason-why-with-symmetric-padding-the-inverse-wavelet-transform-is-n | <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 one directio... | <p>Actually the redundancy perfectly explains why the adjoint property is not verified. The reconstruction operator is not orthogonal anymore and therefore the inverse is not necessarily its adjoint.</p>
<p>You can compute the adjoint efficiently according to <a href="https://arxiv.org/pdf/1707.02018.pdf" rel="nofollo... | 258 |
wavelet transform | How do I implement a nonorthogonal quadratic spline wavelet into discrete wavelet transform? | https://dsp.stackexchange.com/questions/67473/how-do-i-implement-a-nonorthogonal-quadratic-spline-wavelet-into-discrete-wavele | <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 responses, but I'm... | <p>I would think it is available in the Matlab codes from the <a href="https://statweb.stanford.edu/~wavelab/" rel="nofollow noreferrer">Wavelab</a> toolbox. It hosts codes for papers and books. Especially, there is a directory <code>\Wavelab\Books\WaveTour\</code> for Stéphane Mallat's book: <a href="https://www.elsev... | 259 |
wavelet transform | What's the similarities and differences between Wigner transform and wavelet transform? | https://dsp.stackexchange.com/questions/11425/whats-the-similarities-and-differences-between-wigner-transform-and-wavelet-tra | <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>
| <p>There is a nice tutorial: <a href="http://tftb.nongnu.org/tutorial.pdf" rel="nofollow noreferrer">Time-Frequency Toolbox For Use with MATLAB</a> tthat compares many transformations, notably continuous wavelet transform and Wigner and its avatars.</p>
<p>Basically, the CWT belongs to atomic linear representations (a ... | 260 |
wavelet transform | Difference between Discrete Wavelet Transform and convolution | https://dsp.stackexchange.com/questions/82121/difference-between-discrete-wavelet-transform-and-convolution | <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 computed by... | 261 | |
wavelet transform | Inverse of Wavelet Transforms - Background and Noise Removal | https://dsp.stackexchange.com/questions/14058/inverse-of-wavelet-transforms-background-and-noise-removal | <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 have seen ... | <p>I ended up finding a package which provides an inverse wavelet transform function called <code>mlpy</code>. The function is <code>mlpy.wavelet.uwt</code>. This is the snippet which may interest people if they are trying to do noise or background removal:</p>
<pre><code># Make 2**n amount of data
new_y, bool_y = w... | 262 |
wavelet transform | Steganography using wavelet transform — not every wavelet recovering the hidden message efficiently | https://dsp.stackexchange.com/questions/8202/steganography-using-wavelet-transform-not-every-wavelet-recovering-the-hidden | <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,Diognal)</li>
<... | 263 | |
wavelet transform | Question about the Haar Wavelet transform | https://dsp.stackexchange.com/questions/8469/question-about-the-haar-wavelet-transform | <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 and the gr... | <p>The FFT is much better at detecting a sinusoid than a DWT. The FFT is approximating a periodic signal with a series of periodic signals. The coefficients of the FFT will be maximum in the frequency bins (could be a single bin with sufficient resolution) where the component of the FFT series best matches the period... | 264 |
wavelet transform | Inverse Continuous Wavelet Transform off by constant factors | https://dsp.stackexchange.com/questions/83724/inverse-continuous-wavelet-transform-off-by-constant-factors | <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 constant fact... | 265 | |
wavelet transform | Estimate the type of wavelet transform in receiver side | https://dsp.stackexchange.com/questions/15761/estimate-the-type-of-wavelet-transform-in-receiver-side | <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 wavelet (l... | 266 | |
wavelet transform | What does the normalization step of the Haar wavelet transform represent? | https://dsp.stackexchange.com/questions/1739/what-does-the-normalization-step-of-the-haar-wavelet-transform-represent | <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 represent?</... | <p>As I understand it, the normalization is because the Haar wavelet conserves energy of the signal. In that, when you take signal from one domain to another, you aren't supposed to <em>add</em> energy to it, (although conceivably you might lose energy).</p>
<p>The normalization is just a way to ensure that the energy... | 267 |
wavelet transform | wavelet packet transform and lifting scheme? | https://dsp.stackexchange.com/questions/68149/wavelet-packet-transform-and-lifting-scheme | <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 possible to us... | <p>A lifting scheme is a method for splitting a sequence of discrete samples into downsampled subsequences, so that you can predict a subsequence from the other, and update the former later, using possibly nonlinear predict and update operators. <strong>This corresponds to a generalization of one level of discrete wave... | 268 |
wavelet transform | Wavelet transform, scalogram, detail and approximation coefficients | https://dsp.stackexchange.com/questions/93387/wavelet-transform-scalogram-detail-and-approximation-coefficients | <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 the DWT is... | 269 | |
wavelet transform | energy normalization across different scales in case of discrete wavelet transform | https://dsp.stackexchange.com/questions/72314/energy-normalization-across-different-scales-in-case-of-discrete-wavelet-transfo | <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 case of disc... | <p><strong>It's just the same like in CWT:</strong></p>
<p>multiply with one over square-root of the scale.</p>
<p><strong>Here is why</strong></p>
<p>The energy is defined as:</p>
<pre><code>E = Sum(abs(x0(t))^2)
</code></pre>
<p>see <a href="https://en.wikipedia.org/wiki/Energy_(signal_processing)" rel="nofollow no... | 270 |
wavelet transform | inquiries for writing continuous wavelet transform codes manually | https://dsp.stackexchange.com/questions/11576/inquiries-for-writing-continuous-wavelet-transform-codes-manually | <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 <code>1:60;<... | <p>Here is the Python code that I use for CWT. You'll need a short 16bit mono 44.1Khz <code>test.wav</code> soundfile as input. </p>
<p>In order to compute the CWT, we need to compute the convolution between the input <code>x[n]</code> and the morlet wavelet. An efficient way to do this is to do <code>ifft(x_ft * morl... | 271 |
wavelet transform | Heisenberg Uncertainly Principle and wavelet transform | https://dsp.stackexchange.com/questions/10884/heisenberg-uncertainly-principle-and-wavelet-transform | <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 estimation, but i ... | <p>The HUP follows directly from the properties of the Fourier Transform, because time and frequency are orthogonal bases in which we can expand the co-efficient sequence of our signal. </p>
<p>In fact all pairs of orthonormal bases will have some kind of Uncertainty Principle associated with them.</p>
<p>In traditio... | 272 |
wavelet transform | Quadtree decomposition of Discrete Wavelet Transform using bio4.4/CDF wavelet | https://dsp.stackexchange.com/questions/43224/quadtree-decomposition-of-discrete-wavelet-transform-using-bio4-4-cdf-wavelet | <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. For my ap... | <p>First, for compression, it is neither advised to truncate the data nor to the nearest 2th power. First, for compression, it is generally better to expand the original image. After all, this in in use for <a href="https://dsp.stackexchange.com/a/35343/15892">JPEG DCT padding</a>. Second, you can expand the image to ... | 273 |
wavelet transform | What does it mean for a Wavelet transform to commute with translations? | https://dsp.stackexchange.com/questions/56696/what-does-it-mean-for-a-wavelet-transform-to-commute-with-translations | <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 is not tra... | <p>We can start from what is "shift invarient":</p>
<p>Transform G is shift invariant if - <span class="math-container">$$\forall x:\sigma^nG(x) = G(x)$$</span>
<span class="math-container">$\sigma^n$</span> being shift by n. Examples for transforms that are invarient to shifts are histogram and the amplitude of Fouri... | 274 |
wavelet transform | Plotting a Time Frequency contour/colormesh plot of a Discrete Wavelet Transform | https://dsp.stackexchange.com/questions/68913/plotting-a-time-frequency-contour-colormesh-plot-of-a-discrete-wavelet-transform | <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 Frequency Ban... | <p>With wavelets, that rely on scaling, you can expect time-scale, more than time-frequency. Obtained 2D images of scalograms from continuous wavelets is relatively easy. Most of them are not exactly invertible.</p>
<p>Exactly invertible discretized wavelets come in different shapes. To preserVe images with equal-sized... | 275 |
wavelet transform | Use wavelet transform to extract a waveform of certain frequency | https://dsp.stackexchange.com/questions/20310/use-wavelet-transform-to-extract-a-waveform-of-certain-frequency | <p>how to apply wavelet transform method to extract alpha waveform( higher and lower band frequency known) from a given known signal ?</p>
| <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 out everything outside the known frequency band for the alpha wave and invert the transform. </p>
<pre><code>data = Import["your_sample_eeg_data"];
ListLineP... | 276 |
wavelet transform | 3D wavelet transform in the form of a matrix? | https://dsp.stackexchange.com/questions/88885/3d-wavelet-transform-in-the-form-of-a-matrix | <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>
| <p>In general, if you want to construct the matrix form of a linear operator, you can always apply the operator to the sequence of basis vectors. The result for each basis vector is the corresponding column of the matrix.</p>
<p>For example, let <span class="math-container">$f(\mathbf{x}) : \mathbb{C}^N \rightarrow \ma... | 277 |
wavelet transform | discrete Haar wavelet transform, fast and efficient method? | https://dsp.stackexchange.com/questions/12619/discrete-haar-wavelet-transform-fast-and-efficient-method | <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 application tha... | <p>The Haar wavelet is actually a part of the Daubechies wavelet, for the case D=2. There's some example code <a href="https://en.wikipedia.org/wiki/Daubechies_wavelet" rel="nofollow">on wikipedia</a> that shows the Daubachies transform.</p>
<p>The Haar transform is just a low pass filter combined with a high pass fil... | 278 |
wavelet transform | Any Open Source Fast Wavelet transform libraries? | https://dsp.stackexchange.com/questions/10268/any-open-source-fast-wavelet-transform-libraries | <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, Coif etc.... | <p>you can have a look at the LTFAT's wavelet module
<a href="http://ltfat.sourceforge.net/doc/wavelets/index.php" rel="noreferrer">http://ltfat.sourceforge.net/doc/wavelets/index.php</a></p>
<p>it runs in Matlab/Octave with backend written in C. It has fairly large database of wavelet filters and new ones can be adde... | 279 |
wavelet transform | Getting frequency content at different times from discrete wavelet transform coeffs | https://dsp.stackexchange.com/questions/27671/getting-frequency-content-at-different-times-from-discrete-wavelet-transform-coe | <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 calculate... | <p><strong>Question 1</strong>: I think you want to investigate <a href="http://www.mathworks.com/help/wavelet/ref/centfrq.html" rel="nofollow noreferrer">centfreq</a> & <a href="http://www.mathworks.com/help/wavelet/ref/scal2frq.html" rel="nofollow noreferrer">scal2freq</a> (Scale to frequency):</p>
<blockquote>... | 280 |
wavelet transform | How to take wavelet transform of sparse input data | https://dsp.stackexchange.com/questions/71606/how-to-take-wavelet-transform-of-sparse-input-data | <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>
| 281 | |
wavelet transform | Why does a synchrosqueezed wavelet transform show oscillating behavior? | https://dsp.stackexchange.com/questions/71855/why-does-a-synchrosqueezed-wavelet-transform-show-oscillating-behavior | <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>
<li>A si... | <p>This was interesting to figure out. The key lies in the phase transform, and how CWT interacts with own derivative upon insufficient component separation. Relevant are, and I'll be answering, the following:</p>
<ol>
<li>What causes the wavy pattern?</li>
<li>Is the wavy pattern truly a <em>sine</em>, or a lookalike?... | 282 |
wavelet transform | Standard method of smoothing (amplitude envelope) of continuous wavelet transform | https://dsp.stackexchange.com/questions/83266/standard-method-of-smoothing-amplitude-envelope-of-continuous-wavelet-transfor | <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 desired res... | 283 | |
wavelet transform | 3D (time, scale, amplitude) plot in Continuous Wavelet Transform | https://dsp.stackexchange.com/questions/73928/3d-time-scale-amplitude-plot-in-continuous-wavelet-transform | <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 and Magni... | <p>It suffices to use the translation and scale as <span class="math-container">$(X,Y)$</span> axes, and build some elevation map from the absolute values of the CWT (or the phase, the real or imaginary parts). A simple example in Matlab is:</p>
<pre><code>load mtlb
scal = abs(cwt(mtlb,'bump',Fs));
mesh(scal)
axis tigh... | 284 |
wavelet transform | Inverse continuous wavelet transform off by constant factor in the y axis | https://dsp.stackexchange.com/questions/86439/inverse-continuous-wavelet-transform-off-by-constant-factor-in-the-y-axis | <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 the inverse... | <p><code>.sum(axis=0)</code> is the <a href="https://dsp.stackexchange.com/a/76239/50076">one-integral inverse</a>, and depends on the forward transform. Check against the list of conditions outlined there. Here's a <a href="https://github.com/OverLordGoldDragon/ssqueezepy/blob/master/ssqueezepy/_cwt.py" rel="nofollow ... | 285 |
wavelet transform | Optimized 2D wavelet transform using FFT | https://dsp.stackexchange.com/questions/28051/optimized-2d-wavelet-transform-using-fft | <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 transform does ... | <p>I'm still not convinced you are spending your time optimally. Probably you would get better gains doing other optimizations. Already 10-15 taps are considered very long wavelet filters for most applications that I have seen. But nevermind that I will try and answer your question.</p>
<hr>
<p>You can do two differe... | 286 |
wavelet transform | How to Map CWT to Synchrosqueezed wavelet transform? | https://dsp.stackexchange.com/questions/31309/how-to-map-cwt-to-synchrosqueezed-wavelet-transform | <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 $\psi$, the ... | <p>Let me explain the intuition briefly. The authors of the paper you've cited assume that the signal $x(t)$ can be written in the form
\begin{align*}
x(t) &= \sum_{k=1}^K a_k(t) \exp(2\pi\mathrm{i} \phi_k(t)),
\end{align*}
where the $a_k$ denote <em>instantaneous amplitudes</em>, the $\phi_k$ denote <em>instantan... | 287 |
wavelet transform | Can a wavelet transform give time dependent phase of sinusoids in signal | https://dsp.stackexchange.com/questions/18476/can-a-wavelet-transform-give-time-dependent-phase-of-sinusoids-in-signal | <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 transform?... | <p>It is indeed possible (up to a period), with complex "continuous" wavelet transforms, provide your mother wavelet ooscillate sufficiently. You can look at the scalogram modulus and its phase at the appropriate scales, as illustrated from <a href="http://fr.mathworks.com/help/wavelet/examples/wavelet-coherence.html?r... | 288 |
wavelet transform | use wavelet transform to extract frequencies from given signal | https://dsp.stackexchange.com/questions/15178/use-wavelet-transform-to-extract-frequencies-from-given-signal | <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
5.90
-38.91... | <p>To answer inside the framework you set:</p>
<p>In the CWT domain the frequencies will stay the same, the wavelet will behave just like any other filter. It will only filter out frequencies, not change them. You can see banded regions in the image where the peaks are. Since you picked a wavelet that does not have a ... | 289 |
wavelet transform | Discrete Wavelet Transform (DWT) Filter Bank | https://dsp.stackexchange.com/questions/58209/discrete-wavelet-transform-dwt-filter-bank | <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 J. L. Sem... | <p>In the DWT scheme, whether it is the classical <span class="math-container">$2$</span>-band or the <span class="math-container">$M$</span>-band wavelet setting, the very same analysis filter bank (lowpass/highpass + subsampling) is used at each level. Under this condition, one can derive the <a href="https://en.wiki... | 290 |
wavelet transform | Trying to understand WAVELET TRANSFORM Frequncy-Time diagram | https://dsp.stackexchange.com/questions/9319/trying-to-understand-wavelet-transform-frequncy-time-diagram | <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>
<blockq... | <p>I believe by the WT, you are talking about the discrete wavelet transform, DWT.</p>
<p>This can be thought of as a subsampling of the continuous wavelet transform, CWT. In the case of the DWT, we pick frequencies of the form $2^{j-1}$ for ($j=1,2,\dots$) and then pick times seperated by multiples of $2^j$.</p>
<p>... | 291 |
wavelet transform | Wavelet transform and FFT using to extract feature power bands with EEG signals | https://dsp.stackexchange.com/questions/49272/wavelet-transform-and-fft-using-to-extract-feature-power-bands-with-eeg-signals | <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 based on thet... | <h3>Alpha rhythm</h3>
<p>Generally, alpha-band oscillatory activations (8-10Hz) relate to relaxation and in principle accompanied with closure of eyes. This is the prime marker that is used to detect drowsiness, but surely not the only one (see alpha dropout, NREM1, eye-rolling EEG artefacts).</p>
<h3>Event detection</... | 292 |
wavelet transform | Phase Information at Higher Frequencies in Continuous Wavelet Transform | https://dsp.stackexchange.com/questions/38055/phase-information-at-higher-frequencies-in-continuous-wavelet-transform | <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, 10, 65536)
... | <p>As you can see there is energy also in higher frequencies than your original.
This is probably since every level of the wavelet has a band, so the wavelet can show energy at frequencies higher.</p>
<p>The phase exists only as long as there is energy... so it directly connected to it. You can see if the data on the ... | 293 |
wavelet transform | Spectogram: Short-time Fourier Transform vs Time-Frequency Wavelet Transform | https://dsp.stackexchange.com/questions/95008/spectogram-short-time-fourier-transform-vs-time-frequency-wavelet-transform | <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 have read... | 294 | |
wavelet transform | In continous wavelet transform, all wavelets must have the same energy regardless of their scales,why? | https://dsp.stackexchange.com/questions/87188/in-continous-wavelet-transform-all-wavelets-must-have-the-same-energy-regardles | <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>
| 295 | |
wavelet transform | Log vs. linear frequency scales of Fourier and wavelet transforms | https://dsp.stackexchange.com/questions/41259/log-vs-linear-frequency-scales-of-fourier-and-wavelet-transforms | <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>$$F(a,b) =... | <p>And FFT can be considered a filter bank. The bandwidth of each filter is inversely proportional to the length of the FFT. The width of each filter sets the spacing such that there isn't either too much overlap or gaps between filters. In an STFT spectrogram, the window width is fixed for the entire FFT, thus the fi... | 296 |
wavelet transform | Continuous Wavelet Transform time vector in python | https://dsp.stackexchange.com/questions/40502/continuous-wavelet-transform-time-vector-in-python | <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 the time ve... | <p>Similar question here <a href="https://dsp.stackexchange.com/q/651/29">Which time-frequency coefficients does the Wavelet transform compute?</a></p>
<p>The picture you've shown is used for DWT such as <a href="http://pywavelets.readthedocs.io/en/latest/ref/dwt-discrete-wavelet-transform.html#multilevel-decompositio... | 297 |
wavelet transform | Difference between these two Continuous Wavelet Transforms? | https://dsp.stackexchange.com/questions/66889/difference-between-these-two-continuous-wavelet-transforms | <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.com/PyWave... | 298 | |
wavelet transform | The downsampling step with discrete wavelet transform | https://dsp.stackexchange.com/questions/82508/the-downsampling-step-with-discrete-wavelet-transform | <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. Downsampling is the... | <p><strong>TL' DR:</strong></p>
<p>When you down-sample a real signal that is sampled at <span class="math-container">$f_s$</span> by a factor of two, the new sampling rate will be <span class="math-container">$f_s/2$</span>. The frequency span from <span class="math-container">$0$</span> to <span class="math-container... | 299 |
signal denoising | Signal Denoising Uniformly in Frequency Domain | https://dsp.stackexchange.com/questions/54897/signal-denoising-uniformly-in-frequency-domain | <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 following plot ... | <p>This sounds like a great opportunity to attempt to use singular spectrum analysis (SSA):</p>
<p>It appears you have some observed signal, <span class="math-container">$Y[n]$</span>, which is some sort of mixture, and we take <span class="math-container">$Y[n]$</span> and create a Hankel matrix from it using some de... | 300 |
signal denoising | Time averaging denoising signal | https://dsp.stackexchange.com/questions/72762/time-averaging-denoising-signal | <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 = row vecto... | <p>Your approach will only denoise anything, if your signal is actual periodic. That's typically the case if you use a sine wave or periodic random noise or sweep as an excitation signal for a measurement. It can also work, if you vibration source is periodic (e.g. an engine running an constant rpm).</p>
<p>In this cas... | 301 |
signal denoising | Denoising a signal | https://dsp.stackexchange.com/questions/50664/denoising-a-signal | <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 period is a... | <p>As @matthewjpollard has already indicated, you are acting too complex for a possibly simpler problem. You shall always begin with the simplest solution.</p>
<p>I hope the following OCTAVE code can convince you on the justification of this principle. Note that I've used the simplest (yet more complex than simple pol... | 302 |
signal denoising | Denoising Signal With Butterworth-Filter | https://dsp.stackexchange.com/questions/87273/denoising-signal-with-butterworth-filter | <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 noise
f_0 = 5... | <p>AWGN, by definition, is "white" and therefore has a constant power spectral density expectation across all frequencies. Therefore, your signal is buried in noise that is also partly at the exact same frequency. You cannot simply filter to "de-noise" because your filter passband will pass both s... | 303 |
signal denoising | Implications of adding gaussian noise after denoising original signal | https://dsp.stackexchange.com/questions/96644/implications-of-adding-gaussian-noise-after-denoising-original-signal | <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, almost manda... | <blockquote>
<p>Wouldn't be contradictory to do denoising to add noise afterwards?</p>
</blockquote>
<p>Maybe. Maybe not.</p>
<p>This is turning out to confuse <em>me</em> as I explain it, so bear with me:</p>
<p>Just adding Gaussian noise to your denoised data -- not contradictory per se., but possibly not the best w... | 304 |
signal denoising | How do you apply Kalman Filter to track a signal? | https://dsp.stackexchange.com/questions/17333/how-do-you-apply-kalman-filter-to-track-a-signal | <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 matrix cannot ... | <p>You'd probably be better off with a an adaptive filter like LMS (Least Mean Squares) or RLS (Recursive Least Squares) than Kalman for something like an EEG signal. As you've pointed out, it can be difficult or even impossible to develop the state model for Kalman for that type of signal. LMS and RLS are "learning" ... | 305 |
signal denoising | Denoise a randomly occuring signal | https://dsp.stackexchange.com/questions/11485/denoise-a-randomly-occuring-signal | <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 originally 1... | 306 | |
signal denoising | Denoise Techniques When Clean Signal and Pure Noise Are Available | https://dsp.stackexchange.com/questions/47815/denoise-techniques-when-clean-signal-and-pure-noise-are-available | <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 across all fre... | <p>I'm not sure I understand the question, but if you have the exact waveform you want to recover, you can basically employ a <a href="https://en.wikipedia.org/wiki/Matched_filter" rel="nofollow noreferrer">matched filter</a> to detect the existence of the signal in the acquired data. </p>
<p>This does not really cons... | 307 |
signal denoising | sparse representation for image denoising | https://dsp.stackexchange.com/questions/30557/sparse-representation-for-image-denoising | <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 dictionary elem... | <p>I will start the explanation from the compression viewpoint. There are two main types: lossless compression, and lossy compression. Noise, at least divergence or loss from the original data, arises only with lossy compression. </p>
<p>When one considers the original data as the "clean" reference, lossy compression... | 308 |
signal denoising | Denoising a signal using eigendecomposition | https://dsp.stackexchange.com/questions/53269/denoising-a-signal-using-eigendecomposition | <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 class="math-co... | <p>So I'll get this answer started by saying again that what you are describing reminds me a lot of Singular Spectrum Analysis. The process is pretty much exactly how you describe: you have some observed signal, <span class="math-container">$Y[n]$</span>, which is some sort of mixture, and we take <span class="math-co... | 309 |
signal denoising | what is a Gaussian signal? | https://dsp.stackexchange.com/questions/27890/what-is-a-gaussian-signal | <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 Gaussian sign... | <p>The stochastic description of signals is realized by random processes. The book you cite actually speaks of a Gaussian random process. By definition, every random variable drawn from that process has a Gaussian probabilty density function. Mathematically speaking: let $\mathbf X(n)$ be the random process representin... | 310 |
signal denoising | FFT denoising vs low pass filter | https://dsp.stackexchange.com/questions/82676/fft-denoising-vs-low-pass-filter | <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 Fourier d... | 311 | |
signal denoising | Bibliographic References on Denoising Distributed Acoustic data with Deep Learning | https://dsp.stackexchange.com/questions/85371/bibliographic-references-on-denoising-distributed-acoustic-data-with-deep-learni | <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 strain ra... | <p>I'll compare this to the problem of equalization in optical fibres.</p>
<p>Assume a single straight fibre for a start, and neglect noise.</p>
<p>There's some localized phenomenon that effects a pressure wave to propagate through the water in which that fibre is suspended, straining it in different positions. Probabl... | 312 |
signal denoising | PSNR decreases while denoising | https://dsp.stackexchange.com/questions/89794/psnr-decreases-while-denoising | <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 with <cod... | 313 | |
signal denoising | Best way to measure effectiveness of discrete wavelet denoising? | https://dsp.stackexchange.com/questions/69076/best-way-to-measure-effectiveness-of-discrete-wavelet-denoising | <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 way to check... | 314 | |
signal denoising | A self-supervised learning technique to denoise my specific signal | https://dsp.stackexchange.com/questions/84570/a-self-supervised-learning-technique-to-denoise-my-specific-signal | <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 while convent... | <p>You may have a look at the method called <a href="https://ieeexplore.ieee.org/document/9693096" rel="noreferrer">JOT: A Variational Signal Decomposition Into Jump, Oscillation and Trend</a> (You may access it in <a href="https://www.ipol.im/pub/art/2023/417/" rel="noreferrer">A Two Stage Signal Decomposition into Ju... | 315 |
signal denoising | understand short time fourier transform | https://dsp.stackexchange.com/questions/83023/understand-short-time-fourier-transform | <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 in the fr... | <p>To understand:</p>
<blockquote>
<p>Using these features allows us to abstract many of the phase
uncertainties and to focus on ``turning off" parts of the input
spectral frames that are purely noise.</p>
</blockquote>
<p>check out <a href="https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.49.9812&rep... | 316 |
signal denoising | Disadvantages of wavelet transform | https://dsp.stackexchange.com/questions/15148/disadvantages-of-wavelet-transform | <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 analysis. It is ... | <p>If you consider the whole set of potential wavelet transforms, then you have a lot of flexibility. </p>
<p>For instance, should you use 1D continuous complex wavelet transforms, by analyzing the modulus and the phase of the scalogram, and provided you use well-chosen wavelets (potentially different for the analysis... | 317 |
signal denoising | Help with denoising signal and periodogram analysis resources | https://dsp.stackexchange.com/questions/71917/help-with-denoising-signal-and-periodogram-analysis-resources | <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 timeserie... | <blockquote>
<p>Firstly, I am confused if I am supposed to filter my signals to get rid of any frequencies above the Nyquist frequency. My sampling frequency is 32Hz and my time series is somewhat noisy and has some artifacts. I am also unsure of which filter to select for this.</p>
</blockquote>
<p>That ship has saile... | 318 |
signal denoising | Solving Convex Optimization Problem Used for High Quality Denoising | https://dsp.stackexchange.com/questions/3465/solving-convex-optimization-problem-used-for-high-quality-denoising | <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 function:</p>
... | <p>Boyd has <a href="http://www.stanford.edu/~boyd/l1_ls/l1_ls_usrguide.pdf" rel="nofollow">A Matlab Solver for Large-Scale ℓ1-Regularized Least Squares Problems</a>. The problem formulation in there is slightly different, but the method can be applied for the problem.</p>
<p><a href="http://eeweb.poly.edu/iselesni/te... | 319 |
signal denoising | Using Total Variation Denoising to Clean Accelerometer Data | https://dsp.stackexchange.com/questions/14968/using-total-variation-denoising-to-clean-accelerometer-data | <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.pdf" rel="n... | <p>Apart from Total Variation Denoising you could try a first much simpler approach: a <a href="http://en.wikipedia.org/wiki/Median_filter" rel="noreferrer">median-filter</a>. You just move a window along your data and replace the current input value by the <a href="http://en.wikipedia.org/wiki/Median#The_sample_median... | 320 |
signal denoising | Online Noise Reduction on Non-Stationary, Broadband Signals | https://dsp.stackexchange.com/questions/91556/online-noise-reduction-on-non-stationary-broadband-signals | <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 environmental noise.... | 321 | |
signal denoising | Can discrete wavelet transform for denoising purposes be implemented in real time? | https://dsp.stackexchange.com/questions/68400/can-discrete-wavelet-transform-for-denoising-purposes-be-implemented-in-real-tim | <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 (power line i... | <p>Even though I'm not much of a wavelet expert, I can answer with a definitive <strong>YES</strong>!!</p>
<p>Now, do you have any messy details to complain about, like the size of the box, the power that it consumes, or the number of frames of delay between the taking of the image and its display? Because that's your... | 322 |
signal denoising | How do I know if my EEG signal need denoising? | https://dsp.stackexchange.com/questions/45527/how-do-i-know-if-my-eeg-signal-need-denoising | <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 an artifa... | <p>It primarily relies on,</p>
<ul>
<li><strong>what are you looking for in the EEG</strong>: define the frequency band that
relates with the phenomena you are interested to investigate and
filter out the rest (e.g. for sleep events bandpass ~= 0.8-30Hz).</li>
<li><strong>power line of your area</strong>: notch filter... | 323 |
signal denoising | Bag of Tricks for Denoising Signals While Maintaining Sharp Transitions | https://dsp.stackexchange.com/questions/3066/bag-of-tricks-for-denoising-signals-while-maintaining-sharp-transitions | <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 know what I... | <p>L1 norm minimization (compressed sensing) can do a relative better job than conventional Fourier denoising in terms of preserving edges.</p>
<p>The procedure is to minimize an objective function</p>
<p>$$
|x-y|^2 + b|f(y)|
$$</p>
<p>where $x$ is the noisy signal, $y$ is the denoised signal, $b$ is the regular... | 324 |
signal denoising | Applying Wavelet on energy disaggregation as denoising technique to remove uncertainties | https://dsp.stackexchange.com/questions/62904/applying-wavelet-on-energy-disaggregation-as-denoising-technique-to-remove-uncer | <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>
<li>Aggrega... | 325 | |
signal denoising | Denoising approach for a combination of several ADC voltage channles | https://dsp.stackexchange.com/questions/24360/denoising-approach-for-a-combination-of-several-adc-voltage-channles | <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 summation... | <p>According to your processing chains (filter --> sum vs sum --> filter) the two approaches, by being LTI systems, should produce the same results under infinite precision arithmetic. You can show this mathematically by using the properties of convolution operation.</p>
<p>Note that a moving average filter is just an... | 326 |
signal denoising | Denoising / thresholding via wavelets | https://dsp.stackexchange.com/questions/25519/denoising-thresholding-via-wavelets | <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 signal and... | <blockquote>
<p>I expect that when this processed series are submited to denoising / thresholding will result in a clean series with smaller values than the submited signal</p>
</blockquote>
<p>No, you can get values that are greater. For example, consider the Fourier series of a signal. The Fourier series basis fun... | 327 |
signal denoising | How can I denoise this signal? | https://dsp.stackexchange.com/questions/93113/how-can-i-denoise-this-signal | <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://i.sstatic... | <p>Note that it appears that the interference is isolated to 1 Hz and it's higher harmonics. We can implement a multiband notch filter easily to reject those specific frequencies while minimizing impact to the desired signal.</p>
<p>A harmonic notch filter is simplified (elegant) when the sampling rate is also a harmon... | 328 |
signal denoising | Denoising a digitalized electric signal with spikes (probabaly due to EMI) | https://dsp.stackexchange.com/questions/96061/denoising-a-digitalized-electric-signal-with-spikes-probabaly-due-to-emi | <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, the sensor ... | <p>As indicated in my comments: good denoising starts with an analysis of signal and noise and exploits as many identifiable properties as possible.</p>
<p>Taking a casual look at the spectra, I would say that the noise has a lot more high frequencies than the the signal so even a simple lowpass filter could improve th... | 329 |
signal denoising | Estimating a Signal Given a Noisy Measurement of the Signal and Its Derivative (Denoising) | https://dsp.stackexchange.com/questions/52150/estimating-a-signal-given-a-noisy-measurement-of-the-signal-and-its-derivative | <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 filter seems ... | <p>This is a really nice problem.</p>
<h2>Problem Formulation</h2>
<p>I will formulate it as following:</p>
<blockquote>
<p>Let <span class="math-container">$ x \in \mathbb{R}^{n} $</span> be a signal. Given <span class="math-container">$ y \in \mathbb{R}^{n} $</span> which is a noisy measurement of <span class="math-c... | 330 |
signal denoising | Basic audio denoising in the frequency domain using minimum statistics? | https://dsp.stackexchange.com/questions/87096/basic-audio-denoising-in-the-frequency-domain-using-minimum-statistics | <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>Then I used... | <p>Once you have calculated the gain function in the frequency domain, you can apply it to your noisy signal to obtain a denoised signal. The steps you should follow are:</p>
<p>1- Multiply the noisy signal's Fourier transform by the gain function in the frequency domain. This gives you the processed Fourier coefficien... | 331 |
signal denoising | What Techniques Are Used for Signal / Image Denoising (Example Image Provided)? | https://dsp.stackexchange.com/questions/42110/what-techniques-are-used-for-signal-image-denoising-example-image-provided | <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 outdated ther... | 332 | |
signal denoising | wavelet denoising routine for environmental data series | https://dsp.stackexchange.com/questions/7817/wavelet-denoising-routine-for-environmental-data-series | <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', 2, 'db4... | <p>First, a comment - before you denoise, you are basically going to be converting your data from the (time)-domain into the wavelet domain. This is nothing but a series of projections of your data unto user-picked basis functions. (The wavelets). </p>
<p>When you denoise, you will be zeroing out, or shrinking, coeffi... | 333 |
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