# 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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### What is "modified frequency slice wavelet transform"?

What is "modified frequency slice wavelet transform"? It was written in an article but It's not been described on the web.
25 views

### Question about the derive of a theory of the scaling function in the wavelet analysis

Page 5 in link: For the scaling function, it holds: $\int \phi(x)dx = 1$ or, equivalently: $\Phi(0) = 1$ How is this derived?
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### Question about the definition of wavelet

From the definition, we will use wavelet for expanding signals the same way Fourier series use sinusoids: $$f(t) = \sum a_{l}ψ_l(t)$$ The definition then defines that if $ψ_l(t)$ form an orthonormal ...
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1 vote
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### Discrete Wavelet Transform With Overlaps

Maybe this is a trivial question, but I couldn't find an answer yet. Is there some discrete wavelet transformation which works with overlapping wavelets (half on half)? In other words, is there some ...
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### How to get frequency axsis from pythnon CWT

I did the cwt on a chirp signal : ...
190 views

### Algorithm to detect down-up-down pattern in time series

I'm trying to write an online algorithm in Python to detect this below Down-Up-Down pattern in time-series. It's not hard to do roughly if I calculate 3 contiguous non-overlapping moving averages, and ...
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### Wavelet transformation to analyse time series

I am new to wavelet transformation. I am learning it as a tool for signal processing. I have a time series that I want to analyze. I tried to learn wavelet transformation by applying it to a periodic ...
1 vote
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### Weird Noise arises on the small scales: one question about the fast CWT algorithm implemented in real space

Background: I am learning an interesting Fast CWT algorithm(PPCWT) by reading this paper published in 2019. The algorithm is summarized as below. The continuous wavelet transform of a signal can be ...
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### Estimate Power spectral density using Discrete wavelet transform form pycwt

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 ...
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484 views

### How to calculate FIR filter coefficients?

I have EEG signal data (19 channels) sampled at 128Hz. I am trying to retrieve the coefficients that are mentioned in a research paper included below. To decompose an EEG signal, a digital FIR filter ...
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### Do wavelets at a given scale $2^j$ sum up to 0 when summing over all discrete translations of size $n$?

suppose I have a wavelet $\psi:\mathbb{R}\to\mathbb{R}$ satisfying $\int \psi(t)dt=0$. Do we also have that for all $j\in\mathbb{Z}$ $$\langle f\,,\sum_{n\in\mathbb{Z}} \psi_{j,n}(t) \rangle = 0$$ ...
286 views

### Practical applications of wavelets

I know wavelets were all the rage a few years ago, but I missed that boat and am wondering if it is worth putting significant effort into learning about them. My impression is that they were a little ...
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### What is the purpose of wavelet extraction from the seismic trace?

I did a basic google search but, I wasn't really satisfied with the output info. I would love to know what exactly we can do with the extracted wavelet. What kind of information extracted wavelet can ...
1 vote
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### Questions about the paper titled "Rapid computation of the continuous wavelet transform by oblique projections"

This paper introduced a fast method for computing the real CWT and achieved $O(N)$ complexity per scale. However, in the context of this article, I'm not sure what the definition of oblique projection ...
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1 vote
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### What is the most likely imaging processing step associated with the term 'Riesz' in clinical MRI?

I understand that it is an odd question, and this is arguably not the ideal forum, but I am at a loss. Some of you may be familiar with DICOM as a consensus or standard format for medical image ...
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### Interpretation of wavelet trasformation (synchrosqueezing)

I'm working on a dataset of spectroscopies and i'm classifying them by transforming the 1D signal into a 2D one by the ssqueezepy library. For instance, consider to ...
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### Inverse continuous wavelet transform output has significant error in magnitude and phase

For the inverse continuous wavelet transform, I am using a for-loop which runs through each frequency. At each frequency, I convolve the corresponding morlet wavelet with the signal at that frequency, ...
1 vote
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### Meaning of "standard deviation noises of wavelet coefficients"

I am currently working on a research project based on the paper titled A deep learning approach for anomaly detection based on SAE and LSTM in mechanical equipment. The paper uses data in the acoustic ...
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### Not showing the right frequency in ssqueezepy CWT plot

I am following the ssqueezepy simple example. The plot should show f=12 but it shows around 33. Is this a bug or have I scaled the y-axis wrong? Also the plot is not a straight plot as it waves at ...
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### what are the advantages of higher-order Generalized Morse Wavelets?

What are the advantages of the higher-order Generalized Morse Wavelets in comparison with the first-order ones? Are they also more computationally expensive?
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### Is online Continuous Wavelet Transform possible?

I have recently created a real-time STFT with 50% overlap. I wanted to know if this window-based is possible for scalogram, especially continuous wavelet transform. I haven't found anyone ...
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### Does Fast Continuous Wavelet Transform (fCWT) have theory-supported novelty or just simply a computation optimization?

A recent publication, The fast Continuous Wavelet Transform (fCWT), enables real-time, wide-band, and high-quality, wavelet-based time–frequency analysis on non-stationary noisy signals. I'm a ...
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### Is it possible to update wavelet packet from fixed-sized window of data without repeating the whole process?

Assume that a scalogram is generated from performing wavelet packet in a fixed size window of data. Then, is it possible to update the scalogram with the incoming and outgoing data points without ...
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### Standard method of smoothing (amplitude envelope) of continuous wavelet transform

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?" When using wavelets ...
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### Down-sampling a signal after convolution

I was trying to understand more about image compression using the Wavelet transform and I got quite confused about the down-sampling step. I took a picture from here for reference: At each step a ...
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### Calculating signal power from Continuous Wavelet Transform in MATLAB

I would like to ask a question about the calculation of the signal power using CWT in Matlab. Assume a signal of length N points with sampling frequency $f_{s}$. Using conventional approach, the power ...
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### Discrete wavelet transform - DWT (beginner)

I recently stumbled upon this article: A wavelet-based multivariate multi scale approach for forecasting (PDF) In the paper they use DWT and I am having trouble understanding how to construct them. ...
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### Estimation of scaling exponent in the wavelet leaders multi-fractal formalism

I am trying to extract multi-fractal features from time-series data by estimating the singularity spectrum using the wavelet leaders multi-fractal formalism (WLMF) method. Specifically, I want to be ...
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### Output of pywt.dwt

I am using 'dwt' function and I can't understand what the values in the approximation and detail lists actually represent. I have read that in each level the function uses high pass filters and low ...
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### How to achieve a periodized Mexican hat wavelet with period L by using Python?

Now I have a scaled Mexican hat wavelet, i.e. $$\psi(a,x)=\frac{1}{\sqrt{a}}…\left(1-\frac{x^2}{a^2}\right)e^{-x^2/(2a^2)},$$ which decays quickly along the x-axis. Here I want to define a ...
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### Adjust Wavelet output to CNN

I want to extract features from the signal using DWT and then feed the results into CNN, after calling the 'dwt' library function I got a runtime error. ...
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1 vote
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### Why some implementation of Wavelet transform use reconstruction filter instead of decomposition filter?

I'm using MODWT (Maximal Overlap DWT) to extract features from a signal. Matlab implementation is using reconstruction filter instead of decomposition filter. In the first level of modwt decomposition,...
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### How to inject a 2D plane sine wave to the array of seismic sensors?

I've several sensors positioned at various points in the $X$,$Y$-Cartesian coordinate system, and I've experienced a problem to inject a planar Sine wave to the spatially positioned sensors, the ...
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### Calculating instantaneous power of a frequency band in a 1-d signal

I am trying to calculate the instantaneous power of a 1-d signal within a particular frequency band in an on-line, real-time, streaming application. I have tried using sliding window FFTs but these ...
1 vote
255 views

### Classification of Signals using Features Extracted from Wavelet Scattering Coefficients

I have a set of RF signal samples of 2s length each recorded at 2MHz sampling rate, such as this IQ file: https://www.dropbox.com/s/dd6fr4va4alpazj/move_x_movedist_1_speed_25k_sample_6.wav?dl=0 I can ...
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### Pywavelets applied to time series

I'm new on this field. I am applying a discrete wavelet decomposition to a timeseries and the decomposition yields subsets of the data, specifically the half. Nothing wrong with that since that is the ...
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### Why NMSE is the same as output SNR but with an opposite sign?

I am doing denoising on signal, and as performance measures Normalized Mean Squared Error (NMSE) and output-SNR between original/clean and denoised signals are used. However, for several cases the ...
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### Detecting whether the signal is increasing intensity or decreasing intensity

I am trying to determine whether the signal is increasing intensity, decreasing intensity, fade-in, fade-out or peak using an audio file. The graph has an x-axis with time and a y-axis with the data. ...
1 vote
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### How to make a time/period (1/frequency) plot with CWT

This is a question about producing a time/period (1/frequency) plot from a CWT, instead of the time/scale output. I am trying to use the ssqueezepy python library to perform the CWTs. Then I ...
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