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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How to plot output of discrete wavelet in python?

There is a a vector with dimension of (1, 720). I have done DWT transform on it and get wavelet coefficients. i have tried to plot DWT transform but it's failed. can anyone helps me to plot it? Thanks ...
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19 views

Log derivative interpretation

In the origin paper on Synchrosqueezing Wavelet Transform, the phase transform, used to extract the instantaneous frequency of a signal $f(t)$, is defined as $$ \omega (a, b) = -j[W_\psi f(a, b)]^{-1} ...
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Unclear time-to-frequency integration step

From here; $\hat f=\mathcal{F}(f)$, bar = complex conjugate: Time-shift property: $x(t-b) \Leftrightarrow e^{-j\omega b}{\bf X} (\omega)$, so why is it $+$ (red)? What at all is happening? Looks like ...
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Suitable signal processing techniques for frequency response functions?

Good day everyone I have recorded experimental frequency response functions (frfs) for a loose bolt monitoring project. Please see figure 1 below for an example of the frf. Figure 1 The purpose of my ...
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27 views

How is wavelet center frequency computed?

PyWavelets (1) takes index of max DFT magnitude, (2) adds 1 to it, (3) divides by domain, which is the range of input values to the wavelet ("support"). ...
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Alternative convolution theorem?

Instead of padding $x_1[n]$ and $x_2[n]$ then taking $$ \text{iDFT}(\text{DFT}(x_1[n])\cdot\text{DFT}(x_2[n])), \tag{1} $$ assuming we know $x_1(t)$ and $x_2(t)$, and their FT's, what if we do $$ \...
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59 views

Multiple peaks in a same signal?

I am working on peak detection in different signals, the signal plot looks like this: After applying peak detection algorithm and tuning it for each signal, final output looks like this: As you can ...
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33 views

CWT at low scales: PyWavelets vs Scipy

Low scales are arguably the most challenging to implement due to limitations in discretized representations. Detailed comparison here; the principal difference is in how the two handle wavelets at ...
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Wavelet denoising. Simple explanation

I am studying wavelet transform. In the matlab in the "wavemenu" package, I use "SWT denoising 1-D". I loaded my signal, performed a Haar 5 wavelet squelch. I got a good result. I ...
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59 views

How to test wavelet transforms?

One pertinent attribute is normalization, which measures performance in describing signal spectral amplitude and energy, like here. Others are robustness to noise, time vs frequency resolution. ...
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86 views

PyWavelets CWT: normalization? Vs Scipy?

Related. The equation being implemented normalizes by sqrt(1 / scale): $$ C_{a, b} = \frac{1}{\sqrt{a}} \sum_k s(k)\left( \int_{-\infty}^{k+1} \overline{\psi \left(\...
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PyWavelets CWT: resampling vs recomputing wavelet

Related. The implementation pre-integrates a wavelet once, and resamples it at each scale, finally differencing to implement ...
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54 views

PyWavelets CWT implementation

I seek to understand PyWavelets' implementation of the Continuous Wavelet Transform, and how it compares to the more 'basic' version I've coded and provided here. In particular: How is integrated ...
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Decompose a Morlet wavelet in a sine wave to its gaussian and sine components

I have a sine wave where there is a morlet wavelet inside: Now, first I'd like to decompose my signal (func) to 2 components which are the sine wave and the wavelet. After this, I'd like to decompose ...
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How can a thresholding method in discrete wavelet transform be adaptive and denoising is performed level independent?

I am a bit confused regarding the thresholding methods and noise estimation options found in Matlab regarding Discrete Wavelet Transform. Please correct me if I am wrong. I am understanding that noise ...
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Is convolving a signal by a wavelet (in time domain) equivalent to wavelet filtering?

I am a noob in signal processing. Please help me understand if the following relation is true or not: ...
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36 views

What does voices per octave means?

I was studying the description of continuous wavelet transform in Matlab and I came across this term '**cwt uses 10 voices per octave**' ...
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Morlet wavelet: DFT vs Fourier Transform

I find what seem to be contradictions between the two. "Morlet" defined here, and its Fourier Transform (FT) below it. DFT's imaginary component zeroes with large ...
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Fbank back to wav

Here's my problem. I have some wav files. I use the wavs as input to compute the fbanks. Then I want to do some stuff with the fbanks and then I want to recreate a wav file associated to the new fbank....
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What are the wavelet packet functions and how are they different from the wavelet and scaling functions?

I understand that in the decomposition process, wavelet and scaling functions are used to split the signal to approximation and detail coefficients. Most of the time I saw the wavelet and scaling ...
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52 views

EEG signal processing with wavelet or fft?

I have confusion about signal processing related with EEG signal. I have done some of my research and that made me more confused about processing and filtering the signal. Let me jump into the problem ...
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82 views

Why does MATLAB's dualtree3 function not return the lowpass subband of the imaginary tree?

MATLAB has a function named dualtree3 which computes 3-D dual-tree complex wavelet transform. This function only retains the last low-pass coefficients/subband of ...
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Energy of coefficients of wavelet decomposition?

I have recently been working with a dataset associated with the paper Human Activity Recognition from Accelerometer Data Using a Wearable Device. In Section 3.1 - Feature Selection for Motion Data, ...
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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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31 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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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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35 views

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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32 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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54 views

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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28 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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43 views

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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60 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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31 views

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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71 views

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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29 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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33 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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30 views

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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