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Questions tagged [wavelet]

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.

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

I have an optimization question. I want to solve the following problem: $$ \arg\min_S\frac{1}{2}\|s-c\|_2^2 +\lambda\|\Phi s\|_1 \mbox{ s.t. } As = 0 $$ in which $\Phi$ is the wavelet transform ...
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Wavelets - how many scales to keep? [on hold]

I have a daily signal from which I need to automatically withdraw the noise everyday. I use the wavedec function to get the coefficients to the different scales, the number of scales being ...
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13 views

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

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

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

Wavelet Transform and STFT

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

Why does decimation make a system time variant?

On Wikipedia I read this : "The Discrete Wavelet Transform, often used in modern signal processing, is time variant because it makes use of the decimation operation." Why does decimation makes system ...
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1D Pattern Recognition in PPG signal with motion artifacts

I am working on a project that aims to measure (or estimate) blood pressure using PPG signals, which are measured from the wrist area instead of the fingertip. When the PPG data is taken from the ...
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13 views

Threshold both detail and analysis coefficients?

Suppose I perform a discrete wavelet transform on some noisy signal $x$ and obtain ${a_1, d_1, d_2, \ldots, d_n}$ where $a_1$ is the set of analysis coefficients and $\{d_j\}$ are the detail ...
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Why is it my wavelet transform works for % returns but not for a price time series?

So im trying to apply wavelet transforms to denoise stock data just to get a feel for the methodology. My plot looks good when I reconstruct on a series of daily percent returns centered at 0, but ...
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11 views

Discrete wavelet transform, different sampling factors for low and high pass filters

I'm a student from the math program, who's been doing some independent research and study on the wavelet theory. Recently I was reading some papers from engineering to seek as many concrete examples ...
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30 views

Discrete Wavelet Transform: Specifics of Filter Bank

So I have been given to understand that the discrete wavelet transform is able to provide both time and frequency resolution in ways that classic Fourier and even short time Fourier cannot. By ...
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1answer
33 views

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

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

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

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

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

I have submitted this paper "Detecting a Valve Spring Failure of a Piston Compressor with the Help of the Vibration Monitoring" to figshare.com. I would like to get some feedback on the methodology ...
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1answer
38 views

Wavelet transform of a spatial convolution

Does anyone know if there exist a kind of convolution theorem for the discrete wavelet transform (decimated or undecimated)? In other words can I find a simple form of $W\left[ \int f(t) g(x-t) \, ...
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118 views

Other time-frequency-plane tiling than STFT, DWT, ConstantQ-Transform: multiresolution STFT?

It is known that a) the STFT gives a rectangular tiling of the time-frequency plane b) the Wavelet transform gives a non-linear tiling (better frequency resolution for low-frequencies, and better ...
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35 views

RMS value from wavelet coefficients

I am confused on how to calculate the RMS value fo a signal from the wavelet coefficients. Here is a minimal python code for a sinusoidal sigmal of amplitude $1$ and $RMS=1/\sqrt{2}$ ...
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Understanding wavelets via 1-D PyWavelet example

I have been reading about wavelets for few weeks now and I have bumped into subjects like scaling functions, wavelet functions, filter banks and multiresolution analysis. Despite reading and getting ...
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1answer
34 views

Find Fourier series $f(t) = e^{jx t}$ , $−\pi < t < \pi$ [closed]

I need to find the Fourier series of the $f(t) = e^{jxt}$ , $− \pi < t < \pi$ What will be the first step to solve it?
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35 views

Efficient audio power spectrum estimation

I am working on a small personal project where I want to control a matrix of roughly 100 actuators with an audio stream. The goal would be that the user can see/feel the music features in the movement ...
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1answer
571 views

wavelet decomposition for time series signal

Is it possible to use stationary wavelet decomposition as a tool to extract wavelet features for a time series? I can see how it works for image cases, but for a time series prediction problem say $...
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1answer
50 views

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

I have been reading this PhD theis about wavelets and I am trying to reproduce some of the results but I don't know the specific code to use to generate similar results. The original time series ...
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1answer
40 views

Phase of a signal with multi delayed windowed (rectangular window) signal with different amplitudes

I have a signal $x(t)$ which is composed of multi delayed linear chirps with different amplitudes and phases but they share the same $w$ and $\alpha$, the signal can be expressed as follows: $$\...
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1answer
44 views

Dimensional reduction from DWT with threshold

I have been trying to find out how can the discrete wavelet transform (DWT) be possible to reduce dimension of data. Then I saw the question which is seemingly related to my work: Feature extraction/...
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3answers
148 views

Denoising a signal

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 ...
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29 views

From Fourier (k space) to wavelet domain in MRI sensing

In compressed sensing MRI (cSENSE MRI) technology the idea seems to entail sampling from the Fourier domain (k space) in a way that, when transformed to the wavelet domain ("sparsification"), the ...
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2answers
76 views

Orthonormal Dictionaries for Band Limited Signals

If $\mathbf{x} = [x_0, x_1, \ldots, x_{N-1}]^T$ is the time sampled input signal and $\mathbf{Y} = [Y_0, Y_1, \ldots, Y_{N-1}]^T$ is the Fourier transform of the input signal, then a linear ...
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1answer
101 views

Detection of Troughs and Notches in a PPG Signal

I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below... I'm having problem in finding the troughs and dicrotic notch for ...
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52 views

signal denoising by continuous wavelet transform

i want to use Morlet mother wavelet for signal denoising so i should employ cwt only. Is there any proper MATLAB code for this target?
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314 views

How does the Scipy implementation of CWT actually work?

I'm trying to use the SciPy implementation of the Continuous Wavelet Transform to analyze EEG data. I am using The problem is that I have no idea what the width parameter should be. It says that it's ...
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174 views

How to interpret Discrete Wavelet Transform Coefficients?

I want to extract features from DWT coefficients like Power Spectral Density, Max frequency, Min frequency etc. After taking DWT, we get coefficients D1, D2, A2 etc. But my question is, Are D1, D2, ...
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108 views

Wavelet transform and FFT using to extract feature power bands with EEG signals

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 ...
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14 views

Do the magnitude of the signal changes in the wavelet filtering

I am using Daubechies 4 wavelets to extract a required signal. In my signal there is a magnitude change. My raw signal lies from $-3$ to $3$, but when I choose the detail coefficients of the Db4 ...
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1answer
41 views

Isolating frequency-specific oscillation from transient

I am performing time-frequency analysis on electrophysiological data with complex morlet wavelets. Each decomposition in the attached figure shows total power following the onset of a stimulus (top ...
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43 views

Determine scales for continuous wavelet transform (cwt) obtained

How to obtain the corresponding scales for frequencies while computing cwt in Matlab or any other formulae?
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29 views

Does a “chirp”-like generalization of the Gabor or Morlet wavelets definitions exist in the lit somewhere?

I have asked this at the Math SE also. Predicating this on the definition of the continuous Fourier Transform preferred by most electrical engineers: $$ X(f) \triangleq \mathscr{F} \Big\{ x(t) \Big\}...
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42 views

Wavelet central frequency

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

Algorithm Question for Haar Scaling Function and Discrete wavelet transform

Let $\displaystyle f(x)= \begin{cases} 4x^2-4x+1 & 0\le x\le 1, \\ 0 & \text{otherwise}. \end{cases} $ a) Find the approximation $f_{-3}$ of $f \in V_{-3}$ using the Haar scaling function ...
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261 views

Plot CWT (Continuous Wavelet Transform) in 3D using Python

I am working on a project using signal processing. Part of my work is to apply the CWT on the signal I have. As I read, that I can plot the signal in the frequency-time domain using CWT. So my ...
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15 views

Implementing Wavelet family matrices

I want to use CS to reconstruct an image from fewer samples, and I would like to use wavelet coefficients but I don't know how to define them when making a Psi matrix. I have written wavelets ...
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13 views

Wavelet Quality factor

I read in my lectures that a wavelet should have a constant quality factor Q but without any explanation. Can anyone please explain what do we mean by a quality factor. Thanks..
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1answer
49 views

Can I apply CWT on a digital signal?

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

Daubechies orthogonal Wavelets

I read a document that it said: "Daubechies orthogonal wavelets D2-D5". Then I've searched on the Internet to get information about this kind but I haven't found any information about it. Moreover, to ...
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24 views

Qrs complex detection using haar wavelet

I am using this algorithm to detect QRS complex from ECG signal that is samled at 360Hz that is decomposed to level 5 with haar wavelet In the fourth step it says that the duration of the QRS ...
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17 views

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

I am working on wavelet decomposition.As read by the theory i have implemented wavelet decomposition in MATLAB. CA and CD for wavelet decomposition of db1 matches with the inbuilt function but not ...
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1answer
58 views

Alternative function for Matlab Stationary Wavelet Transformation

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

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

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

wavelet reconstruction

I am doing mtech project now. Actually I am working on discrete wavelet transform.I have done till wavelet decomposition. I have been stuck in reconstructing the signal back to original .please help ...
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2answers
460 views

How to implement a filter associated to a specific wavelet

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

How to extract features of individual spikes in non-negative signal?

I have data of non-negative (in the sense there's no signal below baseline) spiking waveforms, which are in the form of a 1D array of numbers: Spikes that cross some threshold are considered real ...