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# Wavelet Transform - Science topic

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Questions related to Wavelet Transform

Wavelet transform can distinguish the positions of different elements well, where the x-axis and y-axis represent the distribution of data in K space and R space respectively.

When I compare data obtained from different samples in the same batch of experiments, using the same conditions to process the EXAFS signal, what does it mean that the peaks are in the same position but with different intensities?

Actually, I wish to understand the process and coding to define new wavelet transform. So that I can understand and modify some wavelet transform to get better results. There is inbuilt wavelet transform in MATLAB and we just have to choose wavelets. I wish to define new wavelet transform.

I am currently working on Image Processing of Complex fringes using MATLAB. I have to do the phase wrapping of images using 2D continuous wavelet transform.

I have been doing research on different issues in the Finance and Accounting discipline for about 5 years. It becomes difficult for me to find some topics which may lead me to do projects, a series of research articles, working papers in the next 5-10 years. There are few journals which have updated research articles in line with the current and future research demand. Therefore, I am looking for such journal(s) that can help me as a guide to design research project that can contribute in the next 5-10 years.

I am working on a classification task and I used 2D-DWT as a feature extractor. I want to ask about more details why I can concatenate 2D-DWT coefficients to make image of features. I am thinking to concatenate these coefficients(The horizontal,vertical and diagonal coeeficients) to make an image of features then fed this to CNN but I want to have an convincing and true evidence for this new approach.

In systems analysis, wavelet transform is used compared to Fourier transform, because wavelets are functions in which most of their energy is concentrated over a short period of time and converges rapidly.

Are there any articles that discuss the applications of wavelet transform?

Hello, I am going to research the signal, which is the demand for electricity, decomposing it into its components using the DWT wavelet transformation. This gives me the detail factors and the approximation factor. the research will consist in finding the best explanatory variables. I have two questions: how to forecast low frequency and how high frequency coefficients? Do you have any advice or suggestions? Best wishes

instead of wavelet transform theories, have you ever used techniques that have the ability to treat with signals processing specially non-stationary signals like a brain signal and was superior?

Although the FRFT has a number of unique properties, it cannot obtain information about local properties of the signal. In addition, the drawback of the short-time FRFT is that its time- and fractional-domain resolutions can not simultaneously be arbitrarily high. As a generalization of the WT, the FRWT combines the advantages of the WT and the FRFT, i.e., it is a linear transformation without cross-term interference and is capable of providing multiresolution analysis and representing signals in the fractional domain. Thus, the FRWT may be potentially useful in the signal processing community and will attract more and more attention.

The interactive wavelet plot that was once available on the webpage of colorado (C. Torrence and G. P. Compo, 1998) does not exist anymore. Are there any other trusted sites to compare our plot? And, in what cases we normalize our data by the standard deviation to perform continuous wavelet transform (Morlet)? I have seen that it is not necessary all the time. Few researchers also transform the time series into a series of percentiles believing that the transformed series reacts 'more linearly' to the original signal. So, what actually should we do? I expect an explanation by mainly focusing on data-processing techniques (standardization or normalization or leaving as it is).

As we know that, Wavelet variance decomposes variance on a scale by scale basis? So, what kind of conclusion can we draw from the wavelet variance analysis? How does it differ from the normal variance?

Picture_Source: Tian, G., Qiao, Z., & Xu, X. (2014). Characteristics of particulate matter (PM10) and its relationship with meteorological factors during 2001–2012 in Beijing.

*Environmental pollution*,*192*, 266-274.Dear community, after using the wavelet transform to extract the important features from my EEG signals , i'm wondering about how to calculate the Shanon entropy of each value of my coefficients (cD1,cD2,....cA6), another thing is how to use the Shanon entropy for dimension reduction ?

Thank you .

I have used the wavelet decomposition and reconstruction of a specific signal (for, e.g., rainfall). Among the all-available levels (suppose I have ten low-frequency reconstruction signals), which level provides the information that consists of deterministic components, reflecting the variation characteristics of the provided signal? To add more, the higher approximation levels (such as a8, a9, and a10) indicated the residual of the decomposition process. This level contains the average value of the data series, so the variation characteristics that we are looking into the signal don’t necessarily present as they start showing a flat curve in these levels. On the other hand, Levels a0, a1, and a2 include most of the high frequencies that reduce the correlation and do not significantly improve the signal characterization. So, in between them, which level should be taken into account to study the particularities of the signal. Should we follow the level with high correlation coefficients?

I have applied CWT technique in various solar related disturbances to study temporal variation in TEC over the geographical latitude (26 - 29 degree N) and longitude ( 81 to 87 degrees E). However, none of the results provide better representation in the time-frequency domain. What is the reason behind this? Is there any factor that we can change in CWT code to observe the transients more clearly? Or is there any relevant sites which produce GIM with filtered TEC?

Dear all

I have a 2-dimensional mode shape of one concrete beam and I put the data of mode shape in a matrix (69*3) which the first column in the matrix is x coordination of my beam and the second column of the matrix is the coordination of y and the third column is the mode shape point of each nodal point.

In the case of damage detection can I calculate 2-dimensional wavelet transform for f(x,y)

while I did not define any curve for it and it is a discrete function?

I would appreciate if you help me with Calculation in MATLAB for 2d continuous wavelet transform.

Wavelet transform is being widely used as a method to denoise ecg signal. But it can be argued that it lacks self-adaptation. We need to find a suitable wavelet function but in clinical applications, there are complex noises so we cannot make a universal wavelet function. Is this a correct assumption and if it is then are there any better ways? There is some research going on using deep neural networks to achieve better denoising.

In several discussions, I have often come across a question on the 'mathematical meaning of the various signal processing techniques' such as Fourier transform, short-term fourier transform, stockwell transform, wavelet transform, etc. - as to what is the real reason for choosing one technique over the other for certain applications.

Apparently, the ability of these techniques to overcome the shortcomings of each other in terms of time-frequency resolution, noise immunity, etc. is not the perfect answer.

I would like to know the opinion of experts in this field.

In essence, the WT is equivalent to a bank of differently scaled linear time-invariant bandpass filters in the Fourier transform (FT) domain [3]. Thus, the WT may be ineffective in dealing with non-stationary signals whose energy is not well concentrated in the FT domain.

Recently, the fractional wavelet transform (FRWT) started to play a very important role in the area of signal analysis.

Dear community , I tried to extract features using continuos wavelets transform using python on my data , but I faced some problems ; my dataset are sleep recordings for 10 patients (physionet sleep dataset) , after selecting a patient randomly ,I kept just 2 eeg channels and dropped the other channels (eog , ecg , emg ) , I extracted the epochs (channel , time , event) , how I can do my feature extraction ?

Thank you

I am dealing with vibration signals which were acquired from different systems. They are mostly non-stationary and in some cases cyclostationary. What are the less expensive methods for removing noise from the signals? It can be parametric or non-parametric.

SARIMA model is considered a decomposition model. However, in the literature, I only found figures about its forecasts results and none about its components. By cntrast, in the case of STL algorithm od DECOMPOSE or wavelet transform, the components are usually extracted and visualized.

So is it possible to extract the components and visualize them?

Medical Image fusion based on Complex wavelet transform

In hydrology

The signal In the Fourier analysis is decomposed into sinusoidal functions of different frequencies. This method allows the frequency spectrum of the signal to be obtained, but not its location over time. The size of the window during the Fourier analysis of a signal does not give us all the information; therefore, we have to choose between the location of high frequencies and the location of low frequencies. It was therefore necessary to find a tool that induced a construction method that was independent of the scale of analysis. To overcome this difficulty, a new approach, called ‘wavelet transformation’, has been introduced (Meyer et al.1987). Because of their non-stationarity, Meyer et al. (1987), Benner (1999), and Morizet (2006) have already highlighted the ability of wavelet analysis to show that most climate oscillations are non-stationary and do not persist throughout the time series. Among the numerous available techniques (Ghil et al. 2002), powerful wavelet analysis is much preferable to classical Fourier analysis, due to the natural non-stationarity of the hydrological series (Labat et al. 2000). Currently, the studies based on time series analysis are leading to important results, Anderson and Woodhouse (2005) consider the wavelet transform as ‘elegant and appropriate’ for the analysis of climate time series.

If multirate filter banks have been used by engeeniers before wavelets theory, why it is important and useful to know that those filter banks correspond to wavelet functions?

Power Quality Disturbances with Synthetic Data Classification using specially wavelet transform signal processing Techniques in MATLAB

To increase the fields that can be covered with applying Wavelet transformations inside it, we need to know any related cases that need or can get benefits of applying the WT.

Matlab/GNU Octave time frequency analysis code for LTFAT package (morlet wavelet transform)

Do anyone know where to read about optimised gabor filters ? is optimised gabor filter a wavelet transform ?

I want to know the procedure for apply wavelet transform to PQDs in MATLAB software,

Maximum of image watermarking scheme has been implemented in DWT domain. In that also watermarking is done in LL Sub band . Why watermarking is not preferred in other sub-band specially in HH sub-band.

I'm trying to analyse the similarities between the two different audio signals I had used cross-correlation, but I'm finding difficulty in analyzing the correlated output, In general, what are parameters have to be considered for analyzing the audio signals, Is wavelet transform a better option or STFT?

Currently, I am working on image restoration. I know about DFT, DCT, but my work is related with wavelet transformation (specially, DWT). Can anyone help me through his/her valuable suggestions that from where I need to begin to learn wavelet transformation (specially, DWT)?

What is mean by directional wavelet transform? can anybody share the code for 2D directional wavelet transform?

I have fNIRS signal and I have applied wavelet transform both continuous and discrete but I am unable to separate the different frequencies on the basis of coefficients . I want to know how can I tell that which coefficient is for which frequency.

Since, when i compressed my image by using wavelet transform upto the 3rd level , now i want to reconstruct the image by using compressive sensing , so would you please suggest me , this is the correct step or not. I am not want to use the idwt for reconstruct the image.

I'm trying to design a wavelet. I extracted signal from transient for my wavelet. How to calculate coefficients of low-pass and high-pass filters for wavelet transform filter bank?

Maybe you can recommend some literature. I have read many literature about wavelet (Mallat, Daubechies and other mathematical books) but it's require deep knowledge in mathematics.

Hi,

I was reading an article, it used

**to decompose the following signal in its fundamental modes. Please, can anyone explain why I can't reach the same conclusion using "***synchrosqueezed wavelet transform***wsst**" function in MatLab?As can be seen, the modes (curves) I extracted are not exponentially decaying like the article.

Here's the link of the paper. Please read section 2.2 : sciencedirect.com/science/article/pii/S0952197615002341

I've attached my code and results. Thanks in advance for the help.

I wanted to Know detailed method in steps for detecting Feature Extraction of ECG signal

I am doing mathematical analysis of Wavelet transform, my problem is a Single Degree of Freedom (SDOF) self excited linear vibrations (both damped and undamped cases). The following are required for doing wavelet analysis:

1. selection of mother wavelet,

2. construction of mother wavelet equation.

3. construction of real signal for the defined problem

Kubios has not yet implemented it.

Previously I worked with the attatched dataset in order to classify the normal and ictal EEG signals. Which is available at

- V. Bajaj and R. Pachori, “Classification of seizure and non-seizure EEG signals using empirical mode decomposition,” IEEE Trans. Inf. Technol. Biomed., vol. 16, no. 6, pp. 1135–1142, Nov. 2012.
- EEG Time Series Download Page 2012 [Online]. Available:http://epileptologie-bonn.de/cms/front_content.php?idcat=193&lang3

But in the following research paper I come to know about CHBMIT EEG dataset

- V. Geethu & S. Santhoshkumar (2018): An Efficient FPGA Realization of Seizure Detection from EEG Signal Using Wavelet Transform and Statistical Features, IETE Journal of Research.
- http://physionet.org/physiobank/database/chbmit.

The attatched file contains the information about normal (Z) and ictal (S) EEG signals. But in case of CHBMIT dataset I am getting confused which dataset is exactly containing almost same information like subset S and subset Z. because lots of information is given in the link of CHBMIT dataset. Can anybody, give me the clean dataset of CHBMIT that will contain only the normal and ictal EEG signals of length 2048 samples as found in the research paper V. Geethu et al..

Maximum of research paper on Dwt Watermarking follows the equation Watermarked=Cover +(alpha * watermark) but few paper uses, Watermarked=(1-alpha)Cover +(alpha * watermark). What is the difference between these two equation and whats its impact on watermarking scheme.

I am using a haar wavelet packet to extract the EEG brain rhythms (alpha, beta, theta, delta and gamma) and i would like to know if it is possible to extract the individual alpha frequency (IAF) using this wavelet and how to do it.

Thank you in advance.

I am using PyWavelets to make wavelike transform to the images by using python language. PyWavelets convert my images to grayscale images, How can I use PyWavelets with color images?

I know that Wavelet transform Coherence is the most common method to find the linkage between two time series, in field of finance.

- Can we use Singular Spectrum Analysis to find out the linkage of two time series?
- If it's possible so what is the disadvantages of Singular Spectrum Analysis that most of researchers use Wavelet transform coherence?

Geometric wAvelet transform for seismic attributes, curvature attributes seismic interpretation

Hi...

Can anybody share the code for smoothing a signal using continuous wavelet transform method in matlab

Esteemed Academicians,

May I request you to kindly provide me an opportunity for joint research work on wavelet transform seismic signal

WITH BEST REGARDS

SUNJAY

I am working on a project where I have to collect real time data of dc drives using harmonic analyzer and then have to analyze the data using wavelet transform using Matlab to find inter-harmonics in system.

I am having problem while plotting and analyzing wavelet transform?

we are trying to implement this journal.

what kind of wavelet transforms can be used instead of discrete wavelet transform(dwt) and empirical wavelet transform(ewt) and in an hybrid approach either increasing the accuracy or making the time complexity less .

**Dear Researchers,**

I want to perform

**periodicity**analysis in**hydro-climatology**data series. I have gone through some literature but did not successfully solve the problem. Your expert opinion is required.I have attached some pictures as an example, what I actually want.

Regards

Naveed.

I am working on Brain Tumor Detection. I have to apply Berkeley Wavelet Transformation in segmentation. Can any one guide me how can i do the segmentation?

Anyone please suggest me some tutorials/documents where I could learn about the de-nosing technique of Ultrasound Images?

Hi,

I need to know the computational complexities to extract the texture feature from an image using the Wavelet Transform . Also, I should know the limitations of Wavelet while it captures texture features from an image. Besides, I need to know the advantages of Gradient Local Auto-correlation texture descriptor over the Wavelet texture descriptor. I expect your invaluable feedback regarding the issue. Thanks in advance!!!!

Good Evening Sir/ Ma'am.

I work in research right now about feature extraction from ECG signal, for beat classification. I use wavelet transformation to get the feature. But the one thing that I'm not sure about, is the approach for extracting feature from wavelet decomposition.

I using DWT 1D for the signal and use 2-Level only. I still curious about how to extract the feature, with statistical approach or another else. Because there're lack information about wavelet feature, due most publication using wavelet as pre-processing step only, not to extract the feature.

Any helps are appreciated. Thanks

Hello, could somebody help to compute the phase angle of more than two images (Sequences of images) using complex morlet in wavelet transform?

Trying to figure out why some singularity signal processing papers use:

|Wf(a,u)| = A*s^(alpha) to determine lipschitz regularity after wavelet transform and some papers use:

|Wf(a,u)| = A*s^(alpha + 1/2).

I would like to do a least squares regression across scales to determine lipschitz regularity and there seems to be a small delta between the CWT and the DWT (DWT seems to be a little greater, but not by 1/2).

I looked through the Mallat's papers on signal processing singularity detection, but the 1/2 term does not show up. Not sure if the 1/2 is from going to a DWT versus a CWT.

Hi, I am working on image watermarking using dtcwt(dual tree complex wavelet transform).

My question is:

1)Does my understanding that decomposition using this technique produces 8 sub bands for each tree(4 real and 4 imaginary)? And if yes, how can I get the coefficients of each sub band(HL,LH,HH).I see the explanation of MATLAB, but I can't get it.

I've crossed with a question about the time stamp (dt = time resolution) of my series and the frecuency resolution (number of sub octave) for my data. At first I think that for quarterly data dt must be 1/4 because 4 quarters make a year, but i don't have any idea about the sampling resolution.

Currently I'm using the WaveleComp package from R (https://cran.r-project.org/web/packages/WaveletComp/WaveletComp.pdf)

Any help or reference would be great,

Thanks

It is not clear to me how the CWT function handles edge effects for a finite length time series. How to remove this edge effect in wavelets using the MATLAB toolbox and any procedure is there for it?

I have a signal from an accelerometer of a cantilever beam and I did a wavelet transformation of the signal where you can see it in foto1. But in order to study the damping, I need to get the average power of the wavelet and plot the time-overall power of wavelets. How can I do this in Matlab? What function may I use?

Thank you in advance.

In DWT by using

**wavedec**function we can decompose the signal and by using**detcoef**function we can find out the approximation and detail coefficients at different levels. Is there any such function in MATLAB for Complex wavelet transform ? Can anyone help me in this?Both the techniques, wavelet and independent component analysis are used to decompose signal or image, such that they can be used to find the relevant components. On what factors, we can compare them?

Working on Music synthesis of Indian Classical Instruments .

So first want to do analysis of Music signals.

I’m interested in building up an experimental setup for motor current signature analysis. Since I’m not from an electrical engineering background I do have some doubt regarding the equipment like sensors and DAQs. Many literatures are showing expensive equipment used for experimental setup. Will it be enough to use a DAQ (https://www.dataq.com/products/di-1110/) with up to 160 kHz maximum throughput sampling rate and 4-20-mA to get current waveform required to do motor signature analysis using discreet wavelet transform? Can you also suggest a cost effective current sensor?

Free tool.

HRV analysis.

Wavelet transform.

Morlet mother wavelet.

I'm analyzing fatigue in brachii muscles during cyclic dynamic contractions. from literature, i came to know that RMS and median mean frequency are not proper parameters to estimate muscle fatigue during dynamic contractions. some researchers suggested RQA time analysis, iEMG, instantaneous mean and median frequency, IIS, wavelet transform etc etc.

are the instantaneous mean, instantaneous median frequency, integrated EMG for RMS are correct options???

I have found some integer wavelet transforms whose names are like

**analysis filter coefficients/ synthesis filter coefficients**. And some represented as**analysis filter coefficients/ synthesis filter coefficients-X**. Here I need to know what that**X**implies.Example for first case:

5/3

2/6

2/10

Example for second case:

9/7-M

13/7-T

9/7-F

Thank you.