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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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11 views

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

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

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

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

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

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

Multifractal analysis of an image using wavelets

I want to measure the fractal character of images using a wavelet approach (if possible) in python. (E.g., maybe things like roughness, anisotropy, or just the fractal dimension - perhaps just ...
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157 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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322 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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37 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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80 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
35 views

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

I am trying to understand the following piece of text. I am not used to dealing with sound intensity and power so I'm not familiar with the derivation of the formula $(*)$ below. Statement: 1. We ...
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151 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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65 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
307 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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237 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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75 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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36 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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50 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
1k 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
106 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
48 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
103 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
522 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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43 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
87 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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280 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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793 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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1answer
227 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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51 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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47 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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214 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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86 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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22 views

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

I am working on wavelet decomposition.As read by the theory i have implemented wavelet decomposition in MATLAB. CA and CD for wavelet decomposition of db1 matches with the inbuilt function but not ...
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121 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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140 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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71 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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2k views

How to implement a filter associated to a specific wavelet

I am working on ECG signals, to eventually extract features in order to detect an arrhythmia and classify it. I am using Discrete Wavelet Transform with biorthogonal wavelet bior6.8 During my research,...
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2answers
407 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 ...
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3answers
129 views

Denoise techniques when clean signal and pure noise is available

I have the clean version of the signal. I can obtain the environmental noise. I want to apply an effective denoising technique on a noisy signal (i.e., clean plus environmental noise). Some ...
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1answer
85 views

What the entropy equations mean?

In wavelet packet image compression, different types of entropy methods can be used, like Shannon and log-energy. Shannon entropy uses this equation $\mathrm{ent}= -\sum (x^2 \times \log(x^2))$, ...
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183 views

Log energy and Shannon entropy?

For best tree decomposition using wavelet packets, i have tried both Shannon and log energy entropy functions. I noticed that log energy leads to images with higher PSNR values. Could you please help ...
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68 views

Selection of transforms, windows, wavelets for current signal analysis

I am new to this topic but I already read about the propperties of different signal analysis methods. I am stuck with the obvious advantages of FFT, STFT and Wavelet transforms but can't find good ...
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1answer
11k views

Discrete Wavelet Transform - Visualizing Relation between Decomposed Detail Coefficients and Signal

I'm trying to directly visualize the relation between discrete wavelet transform (DWT) detail coefficients and the original signal/its reconstruction. The goal is to show their relation in an ...
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1answer
119 views

Wavelets and bank filters

The wavelet transform has a problem as it gives poor time resolution for low frequencies and poor frequency resolution for high frequencies according to uncertainty conditions. This appears well ...
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1answer
123 views

Question about normalization before estimate the spectrum

I work with a Electrophysiologist Team and i have seen something who interrogate me (i'm a noobs in DSP). They acquires a signal into a brain structure (an LFP to be precise) : in a first time they ...
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1answer
760 views

Making sense of Haar transform and inverse Haar transform

Yesterday, my teacher taught us about the Haar transform (for pictures). We had to implement it in Python and when I finished I was wondering: what was the point? I can't explain the purpose of what I'...
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77 views

Integer Wavelet with Only Positive coefficients

Is there any Integer Wavelet Transform which produce only positive coefficients? Currently i'm using Haar wavelet but it produces both positive and negative coefficients.
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1answer
25 views

Are there analogues to orthogonal transformations in non-orientable surfaces?

I am working on extremely large, symmetric matrices of counts, and attempting to identify patterns/shapes within them. Wavelets are a popular tool in image processing, and have some nice statistical ...
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128 views

Perfect reconstruction of 2 channel filter bank

I am studying Perfect reconstruction of 2 channel filter bank for using Biorthogonal Spline wavelet for decomposing ECG signal. I am using Wavelets and Filter Banks By Gilbert Strang, Truong Nguyen to ...
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1answer
79 views

Dimensional analysis in the Morlet wavelet

I'm a complete beginner on signal processing, so please forgive the basicness of this question - but I'm very confused by this. Regarding the Morlet wavelet, Wikipedia says: The wavelet is defined ...
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1answer
292 views

Programming the IDWT for image processing

I want to program the 2D inverse discrete wavelet transform (only 1 level) in the case of image processing. In the matlab website there's this diagram: now, I want to program the IDWT with haar ...