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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Why should wavelet re-synthesis produce an output when the main component is suppressed and what does this mean for denoising?

I understand that aliasing occurs in DWPT if the wavelet used is of low order since the "filters" are not perfect and the combination of down sampling and overlapping between bands causes ...
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Discrete wavelet center frequency

I am understanding that mother wavelets have a center frequency. Wavelets are limited in duration and oscillate then decay, so the center frequency is the mid pulse of the wavelet or so. But my ...
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How well can discrete wavelet packet transform reduce noises that are similar to the input signal in the same frequency band?

If I had 50Hz noise coming from power line, and signals in the same frequency range (EEG for example 0.1Hz to 100Hz). If my sampling frequency is 30kHz but I downsample my signal to 937kHz and use the ...
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Best way to measure effectiveness of discrete wavelet denoising?

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 ...
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52 views

Faded line in spectrogram for a chirp

I've generated this spectrogram using wavelet convolution. The chirp is generated like so: ...
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25 views

Plotting a Time Frequency contour/colormesh plot of a Discrete Wavelet Transform

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 ...
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61 views

Understanding Parseval's Theorem with Discrete Wavelet Transform

I have difficulty to understand the results I get with implementing Parseval's Theorem in Python to DWT. I have the good results getting the Energy with Fourier transform and the time series in python:...
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How does the band pass wavelet act as a high pass filter in DWT

I am understanding that wavelets have a bandpass filter response due to their compact support, and when doing decomposition they are used as a high pass filter along with the scaling function as a low ...
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Some questions about the intuition of the DWT

Assuming a DWT of a signal of length 8 with Haar filter taps. At the lowest level, I end up with a3 and d3 both of length 1, d2 of length 2 and d1 of length 4 which is the same number of coefficients ...
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How to choose the appropriate number of samples for discrete wavelet transform denoising?

I want to make sure I am understanding the filter bank frequencies correctly in DWT decomposition. If my sampling frequency is 30kHz, then would I need to input data with 30k samples which later will ...
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Filtering out symmetric noise from an oscilloscope reading

I have a signal that looks like this: The data is readings from two oscilloscope channels, one color coded blue, the other color coded orange. I would like to filter out the supply noise (all the ...
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29 views

Does Discrete Wavelet Consider Sampling Frequency or Cutoff Frequency of Bandpass Filter?

I have EEG signal with a sampling frequency of 128 Hz, and filtered from 1-30 Hz using a bandpass filter. Now I want to know ...
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Can thresholding in wavelet transform be implemented on the approximation coefficients?

Sorry as it might be a silly question since I am a beginner in wavelets. I have been using the matlab wavelet toolbox for denoising purposes and saw that thresholding is only applied on the detail (...
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Can discrete wavelet transform for denoising purposes be implemented in real time? [closed]

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 ...
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25 views

wavelet packet transform and lifting scheme?

so the lifting scheme is basically an alternative to performing the discrete wavelet transform with several advantages. But here are three questions which I did not find an answer to: is it ...
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How to generate the filter bank for a wavelet adapted to a pattern?

Some textbooks like Daubechies (1991) and Strang & Nguyen (1996) give algorithms to construct wavelets with specific properties. But, I am trying to construct a filter bank for a wavelet that is ...
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65 views

Time location of the DWT detail coefficients using MATLAB

When performing the Discrete Wavelet Transform in MATLAB using the command DWT or WAVEDEC, what it the exact time or pseudo-time location of the DWT coefficients? At each level the time series is ...
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What are the differences between the DWT and the MODWT?

What are the differences between the DWT (Discrete Wavelet Transform), which is the most classical algorithm and the Maximum Overlap Discrete Wavelet Trasnform (MODWT)? Both these algorithm are ...
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57 views

Discrete Wavelet Transform output: coefficients or FIR-filtered signals?

I have a theoretical question about the calculation of the Discrete Wavelet Transform, using MATLAB specifically. According to this video-tutorial on the MATLAB lagorithm: https://it.mathworks.com/...
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Is it possible to compute the wavelet transform of a unit step function?

Is it possible to find theoretically the continuous or discrete wavelet transform of a unit step function (consntly 0 for t<0 and constantly 1 for t>=0) or of a function starting from zero and ...
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Downsampling, shifting, high pass and low pass filter commutativity

strong textI have been reading "The Stationary Wavelet Transform and some Statistical Applications" by Nason and Silverman, and there is a claim in the their paper of which I cannot convince myself. ...
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How to correctly perform Continuous Wavelet Analysis

I have a signal coming from an accelerometer which has already been filtered in the band 0.5-15Hz. I would like to understand in particular how frequencies are distributed in two bands (0.5-3, 3-6) ...
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27 views

Wavelets / Identifying bursty signals

I thought my network was experiencing outages. I collected bandwidth (Mbps) measurements every 30 min. A cumulative probability distribution shows the probability that bandwidth will exceed any given ...
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29 views

How do I implement a nonorthogonal quadratic spline wavelet into discrete wavelet transform?

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 ...
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How to use background noise information to de-noise a (non-stationary) signal

I performed some measurements, which unfortunately include some noise. The measured signals are non-stationary, because the phenomena I am capturing is a transient. Before the transient, I recorded a ...
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Continuously tunable low-pass filter that “interpolate” wavelet filter for multi-resolution analysis

I am using wavelets to analyse some complicated 1D signal, where I am able to come up with multiple filtered signals with different level of details. However, the cutoff of wavelet filters follow a ...
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R wavelets package inverse dwt does not always recover original signal

I recently worked with R's "wavelets" package. I tried the very simple dwt and inverse dwt as follows: yi = idwt(dwt(y)); plot(y,yi); where y is a vector. ...
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Reconstruct a signal via continuous wavelet transform (CWT)

I want to use the continuous wavelet transform (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 ...
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Difference between these two Continuous Wavelet Transforms?

I am porting Synchrosqueezing to Python, and came across an implementation difference on CWT between mine and PyWavelets' - details below. The idea is to merge this implementation to PyWavelets if ...
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54 views

Determine the haar wavelet function is linear or nonlinear

I'm looking for analytical justification of linearity or non linearity of the wavelet transform with the real Haar mother wavelet function. I have googling already. But I can't find and understand ...
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Signal reconstruction using discret wavelet

I am doing a discrete wavelet transform on a Lena.bmp image using the code ...
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43 views

Standard deviation of Morlet wavelet's Fourier transform

MATLAB has the complex Morlet Wavelet in the following form: $$\psi(t) = \frac{1}{\sqrt{\pi f_b}}e^{\frac{-t^2}{f_b}}e^{j2\pi f_ct}$$ I arrived at its Fourier transform as shown below (another ...
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Visualization of wavelets coefficients using python

I need to prepare a plot similar to figure below using coefficients of details of a wavelet transform.I am trying for more than 2 weeks to find how I can do it. This plot represents coefficients of ...
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Wavelet transform : how to recover wavelet basis matrix?

In this article, It is said that an image $x$ can be sparsely expressed, if the basis is well chosen. It is said something like "$x$ can be expressed as follows : $x = \psi\theta$ [...] Many ...
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Wind Turbine Vibration Analysis: Which approach?

I'm analysing vibration data from 4 wind turbines (WTs). 8 different sensors are sampled at 25.6 kHz for 10 seconds once a day. I have data from around 400 days (intervals). The plot underneath is for ...
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How do wavelet levels depend on one another?

I am working with wavelets for my thesis, and I would like to know if there is an intuitive dependency between the levels of a DWT. To make it clear: The DWT performs a convolution, and then the ...
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Smoothing the signal by integrating and then differentiating using a gaussian CWT

Recently, I have started implementing CWT on accelerometer signals. A method stated in an article stated that the signal is smoothed by integrating and then differentiating the signal using a Gaussian ...
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Wavelets: Manipulate its phase and reconstruct

Usually when I read about wavelets in image processing, the authors tend to make use of its coefficients and rebuild based on certain criteria, for example de-noising an image where you usually filter ...
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Right approach for activity classification based on EMG signal?

I want to train a classifier that is able to identify different activities based on EMG data that is sampled at 41Hz with 8 channels, I read this paper that summarizes a lot of different approaches to ...
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performing cwt and inverse cwt using fft

I'm currently working on my project related to implementing an speech enhancement algorithm on fpga which uses continuous wavelet with morel wavelet, how can i use efficient fft algorithm to calculate ...
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64 views

Step-by-Step calculation of stationary wavelet transform gives shifted results?

Good morning, I am doing an SWT by hand to understand it better, and have a couple of questions. Maybe someone here has experience with this? I am using the book "Conceptual Wavelets" by Fugal, ...
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How to tell, which coefficient corresponds to which frequency while computing wavelet transform?

I am applying wavelet transform on functional Near Infrared Spectroscopy (fNIRS) signal. My aim is to get the info that which coefficient corresponds to which frequency in the signal. Is it possible ...
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153 views

Scaling a wavelet in continuous wavelet transform

The mexican hat wavelet, obtained from the second derivative of a Gaussian, has a functional form of $$ \frac{2}{\sqrt{3 \sqrt{\pi} \sigma \ }} \left(1-\frac{t^2}{\sigma^2} \right) e^{-t^2/(2\sigma^...
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How to create different Time frequency images from a data

I'm new to Python. I have a time series in a CSV file that has about 5000 rows and 3 columns. I have split the data into training and testing in ratio 70:30 respectively. However, I have a problem ...
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37 views

Refinement equation and orthogonal wavelets basis

I have a wavelet function space defined by, $ \phi(x) = \sqrt(2) \sum_n h_{\phi}(n) \phi(2x-n) $ . given the Fourier transform of the function is: $\hat{\phi}(\omega) = \frac{1}{\sqrt(2)} \hat{h}...
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Applying Wavelet on energy disaggregation as denoising technique to remove uncertainties

I would like to apply Wavelet in MATLAB 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 ...
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82 views

Difference between “scaled white noise ” vs. “unscaled white noise”

I have been searching Matlab user-guide for Wavelets. In their graphical user interface for denoising, there is an option for "unscaled white noise" and "scaled white noise" for the noise structure. ...
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Fourier Transform of the full Morlet wavelet

In 2014 someone asked here the Fourier transform of the Morlet wavelet; link below: Fourier Transform of Morlet wavelet Function? However, it was the approximated Morlet wavelet not written with the ...
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192 views

Relationship between wavelet shape and wavelet filters

MATLAB has a library of wavelet functions, showing their "continuous forms" as well as the the decomposition and reconstruction filters. In decimated wavelet transform the filter size remains the ...
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Plotting a scalogram of a signal's Continuous Wavelet Transform (CWT) in python

So I've been learning about wavelets for a few weeks because I'd like to use them in a research project I'm working on and I've been trying to grasp the general ideas behind them.I've been struggling ...

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