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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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, ...
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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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Can I calculate the DFT of a specific wavelet by its FT formula?

I'm going to use a Morlet wavelet to filter my signal. The first step is to calculate the DFT (or FFT) of the signal and the wavelet kernel respectively. I guess that as the FT of a Morlet wavelet can ...
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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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4 votes
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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

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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generating wavelets from a mother wavelet by scaling and translation

According to equation 3 in the following reference https://www.cs.unm.edu/~williams/cs530/arfgtw.pdf Energy normalization is performed, why do we need the wavelets generated from the mother wavelet to ...
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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 ...
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1 vote
1 answer
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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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Difference between Discrete Wavelet Transform and convolution

Sorry in advance if my question is too dumb. I'm going through the book of Mallat, and from what I understand, the approximation/wavelet coefficients $a_j[n] = <f, \phi_{j,n}>$ and $d_j[n] = <...
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2 votes
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When is a continuous wavelet in the Schwartz space?

I was thinking if the continuous wavelet transform can be in the Schwartz space or not? If someone knows can help me and tell me what are the conditions on the mother wavelet or the signal so that the ...
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1 vote
1 answer
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Why does using a log scale ruin (warp) my scaleograms?

I'm trying to make a scaleogram of neural data using the continuous wavelet transform (with Morlet wavelets). As a starting point, I use just a simple sine wave built from two frequencies, 50 and 80 ...
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How to set the "widths" parameter for continuous wavelet transform using Morlet wavelets? (scipy.signal.cwt)

I'm trying to use scipy.signal.cwt() to do a time-frequency decomposition of neural data. However, I don't completely understand the "widths" parameter. I ...
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Wavelet Scattering (Kymatio) Zero Divison Error

I'm attempting to make use of wavelet scattering to analyse my signal samples. The example IQ Wav file I am using is as follows: https://www.dropbox.com/s/dd6fr4va4alpazj/...
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Function reconstruction after a DWT

I'm new to this field, my apologies if my question sounds too naive. From what I understood, a function can be decomposed using the scaling function at a given scale $\{\phi_{J, k}\}_{k \in \mathbb{Z}}...
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1 answer
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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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-1 votes
1 answer
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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. ...
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1 answer
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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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How can the detail coefficients in discrete wavelet transform (DWT) be downsampled?

This question is asked with reference to this paragraph For the high-pass filter, the frequency content lies in the range $\frac{F_s}{4} \rightarrow \frac{F_s}{2}$. There is no content in the range $...
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3 votes
1 answer
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custom raw compression

I'm planning to acquire between 50k and 200k image per day with a 50MPixels (or 68MPixels or 130MPixels) sensor; I'll be acquiring the raw data (10 or 12 or 14 bits) from the sensor through SLVS-EC ...
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2 votes
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Implementation boundary-corrected wavelets on the unit interval

I was wondering if there is a 'ready-to-use' implementation available of the (boundary-corrected) wavelets constructed in Cohen, Albert, Ingrid Daubechies, and Pierre Vial. "Wavelets on the ...
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Near Real Time Algorithm For Approximating Fundamental Frequency

I'd like to analyse the notes being played on a cello C2(65.4Hz) to C6(1046.5Hz) recorded on a PC and thus a likely sampling rate of 44.1kHz. If I can get that to behave then I'd like to be able to ...
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1 answer
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Choosing a good low pass filter in the wavelet scattering transform

What's the impact of a specific filter $\phi$ when building the wavelet scattering transform? I mean, if I compute the MFCC choosing different windows, (Hamming, Blackman, etc.), the behaviour ...
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1 answer
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Time support for wavelets in scattering transform

In 1 they say that the energy of $\psi_\lambda(t)$ is concentrated in an interval of length $2\pi Q/\lambda$. I understand the inverse proportionality between the frequency band $\lambda/Q$ and the ...
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1 answer
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Building the low pass filter in the wavelet scattering transform

In 1, analyzing the equivalence between MFCC and wavelet transform, the scaled wavelets are truncated for $\lambda < 2\pi Q/T$ to fit the time spread of the wavelets within the length $T$ of the ...
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8 votes
2 answers
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Advantage of STFT over wavelet transform

I have learned about STFT and wavelet transform recently, and wavelet transform seems better than STFT in my opinion. So, I wonder if there is any advantage of using STFT than WT, and if so, what are ...
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1 answer
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Understanding stability in frame theory. Wavelets

I'm trying to grasp some understanding of the concept of stability in the context of the frame theory. The definition of frame in ref1 states that a sequence of functions $\{ \phi_n \}_{n \in \Gamma}$ ...
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Calculate and plot CDF 5/3 wavelet phi and psi functions

For a FOSS project I've to work with the CDF 5/3 wavelet. And while I understand the implementation by lifting scheme and my code works well, I want to understand the math theory behind wavelets in ...
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1 vote
1 answer
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How to do appcoef and detcoef using pyWavelets?

I am new to signal processing and currently doing a school project in wavelet transform using Python. I want to extract all details and approximations (Example: cA2, cA1, cD2, cD1), pywt could return ...
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How can we divide our long-time domain signal into equal segments and then apply Wavelet transform?

I have a time-domain signal and the samples size is 80000. I want to divide these samples into equal sizes of segments and want to apply wavelet transform to them. How I can do this step. please guide ...
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Multilevel DWT wavedec - How to get each coefficient (approximations and details) in the same length as the original signal?

I am doing a school project referring to the research paper https://www.tandfonline.com/doi/abs/10.1080/0952813X.2013.813976?journalCode=teta20 The overall concept of the research is as the following ...
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9 votes
1 answer
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Image / Video Upscaling (Super Resolution) Algorithm Explanation (Image and Video Upscaling from Local Self Examples)

So, I'm trying to implement the classical algorithm described in this paper Image and Video Upscaling from Local Self-Examples and this presentation to serve as a baseline for comparison with AI/NN-...
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Level dependent threshold in wavelet coefficients to compress an image

What's the way to choose a threshold in a certain level decomposition? I found about S-median threshold but at this point I'm not working with noise so I think implementing this wounldn't make sense
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1 vote
1 answer
67 views

Should i use window with hop_size in Wavelet Transform or Discrete Wavelet Transform?

I have a signal (audio - voice) with 1 second of duration with sample rate of 50000 Hz. It is big signal and I wish extract some features and apply pattern recognition or classification. My question ...
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1 answer
124 views

Joint Time-Frequency Scattering structure & implementation?

How does JTFS differ from wavelet time scattering in its computation graph, and how does FDTS discriminability work, at a lower level? How is it implemented in practice, and how can one visualize ...
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1 vote
1 answer
265 views

Joint Time-Frequency Scattering explanation?

How does JTFS work, intuitively? What are its motivations, and how's it differ from the Wavelet (time) Scattering transform? Can it be visualized?
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1 answer
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Wavelet Scattering time-warp equivariance

Is scattering equivariant to multiplicative time warps? Defined as $$ x(t) \rightarrow x(\tau(t)t),\ \text{sup}|\tau'(t)| < 1 $$ This post claims it holds approximately - what are the arguments, ...
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