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.

Filter by
Sorted by
Tagged with
0
votes
1answer
38 views

Is it possible to extract peak locations in the time domain using help from fourier/wavelet analysis?

The signal I'm studying has fundamental frequencies of 20 and 60 cycles per minute (shown in the Periodogram graph). It is straight forward to extract the peaks in the time domain belonging to the 20 ...
0
votes
1answer
68 views

Data Adaptive technique

I am doing data analysis. I used the wavelet transform and now I am trying the Hilbert–Huang transform (HHT). In the literature, I read that Hilbert–Huang transform (HHT) is an adaptive technique. I ...
7
votes
1answer
12k views

Feature extraction/reduction using DWT

For a given time series which is n timestamps in length, we can take Discrete Wavelet Transform (using 'Haar' wavelets), then we get (for an example, in Python) - ...
0
votes
0answers
17 views

Does the set of Hermitian Wavelets include fractional derivatives?

According to Wikipedia, Hermitian wavelets, "The $n^{{\textrm {th}}}$ Hermitian wavelet is defined as the $n^{{\textrm {th}}}$ derivative of a Gaussian distribution." Are the wavelets defined by ...
0
votes
1answer
58 views

CWT Disapointing Frequency Separation

I'm attempting to perform multi-resolution analysis via Continuous-Wavelet Transform (CWT) using Pywavelets. I've heard that CWT is supposed to be superior to STFT due to varying frequency content as ...
0
votes
0answers
20 views

Morse / Morlet wavelet relationship?

Does anybody know what the relationship between Morse and (complex) Morlet wavelets are? I'm looking at images in papers about the Morse, and it looks like a Morlet to me. Is the Morse a ...
1
vote
0answers
6 views

can I combine 2 raster with wavelet transform in R? [closed]

I Have same problem, i will combine 2 raster data with wavelet fusion r1<-brick("mask data/r1_mask_black.tif") r2<-brick("mask data/r2_mask_black.tif")
0
votes
1answer
503 views

2D DWT Image Issue

In the literature, I see that a 2D signal can be transformed by first doing a 1D transformation on each row of the matrix followed by the same procedure on each column. It seems that $k^{th}$ level ...
1
vote
1answer
87 views

What is the correct order of operations for a 2D Haar wavelet decomposition?

The source code of iqdb contains a 2D Haar transform implementation. The author claims to have implemented it according to the paper "Fast Multiresolution Image Querying", which is freely available ...
1
vote
0answers
13 views

Expectation of power spectrum for nonorthogonal wavelets

I'm working through "A Practical Guide to Wavelet Analysis" by Torrence and Compo, and I am confused about section 3d ("Wavelet Power Spectrum"). Let $x_n$ denote the signal, sampled at increments $\...
4
votes
1answer
133 views

Is there an equivalent of Parseval's theorem for wavelets?

Parseval's theorem can be interpreted as: ... the total energy of a signal can be calculated by summing power-per-sample across time or spectral power across frequency. For the case of a signal $x(...
0
votes
1answer
37 views

Peak Detection on ECG signal

I've been working on a ECG signal collected during exercise through my chest mount heart rate monitor. My goal is to accurately detect the location of the R-wave; R-wave is the narrow peak similar to ...
1
vote
3answers
268 views

Why is the high-pass filter result in a discrete wavelet transform (DWT) downsampled?

From Wikipedia's description of the Discrete Wavelet Transform, a signal yields a set of: approximation coefficients (low-pass: by averaging + downsampling) detail coefficients (high-pass: convolving ...
5
votes
1answer
1k views

Haar series approximation of a function?

I'm trying to code the Haar wavelet approximation of a function. I'm a complete newbie. Edit Below is a pseudo-code of my algorithm for $f: [0,10] \to \mathbb R$, $f(x)=x$. I picked it here and ...
3
votes
1answer
279 views

Is Wavelet Transform better than FT if I'm only interested in knowing the frequencies and not interested of when did they happen?

I'm still in the first stages of learning about these different transformations. But one thing that came to my mind while learning about them is the question above. I learned that ...
3
votes
3answers
311 views

Does it make sense to use a wavelet that is equal to a sine of one period?

Would I get same results with STFT method (short-time Fourier transform) if I try this?
0
votes
1answer
40 views

What happens if I zero out the initial terms of the fft output and take inverse fft? [duplicate]

I am new to signal processing domain. When I run fft on data of length 1000, I get 1000 complex numbers. Now, if I want to extract the low frequency information or signal approximation, I take the ...
0
votes
0answers
10 views

Morlet-based Cross Spectral Density vs Wavelet Transform

I am interested in the frequency distribution and power of neural alpha waves (8-12Hz), and have been using WT to examine them. I am quite new to the techniques involved, however, and have noticed ...
6
votes
1answer
13k views

Comparison between Fourier transform, short time Fourier transform and wavelets

What is the difference between the Fourier transform, short time Fourier transform and wavelets?
1
vote
3answers
33 views

General form of dilations and translations of wavelet function

In some papers, the dilations and translations of a wavelet function is written as follows: $$\psi_{j,k}=\frac {1}{\sqrt {2^j}} \psi\left({2^{-j}t-k}\right),\quad\text{where $j$ and $k$ are integers}$...
0
votes
1answer
167 views

what method for thresholding?

I want to do one threshold method on high pass components of a wavelet frame decomposition approch,for edge detection in image. I have 14 high pass components. for thresholding, I need keep the ...
0
votes
0answers
26 views

Obtaining Continuous Wavelet Transform coefficients from Discrete Wavelet Transform

On an earlier StackExchange question, I read that for a given signal, "From the resulting DWT the corresponding full CWT can be obtained by convolving the DWT with the reproducing kernel of the ...
2
votes
2answers
412 views

How to extract features of individual spikes in non-negative signal?

I have data of non-negative (in the sense there's no signal below baseline) spiking waveforms, which are in the form of a 1D array of numbers: Spikes that cross some threshold are considered real ...
0
votes
0answers
22 views

Is the convolution between a decomposition and reconstruction filter a scalar?

I'm very new in a research topic about wavelet filtering and I received an observation by a professor, but I actually cannot understand it, so I ask you to help me. Suppose to perform a stationary ...
0
votes
1answer
226 views

Wavelet central frequency

What is the definition of the central frequency of a Wavelet and the bandwidth of a Wavelet? How do they affect the resultant waveform of the wavelet? Thanks.
0
votes
1answer
115 views

High frequencies disappear when applying discrete wavelet transform

Trying to decompose and reconstruct a signal using a to some extent self-made implementation of DWT for some reason fails. The result looks highpass filtered and/or shifted. I wanted to write the code ...
0
votes
0answers
42 views

What's the difference between Wavelet transform coherency and Singular Spectrum Analysis

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 ...
0
votes
0answers
147 views

How to calculate Continuous Wavelet Transform (CWT) for specific frequency range in Python?

My first question what is a scale and how to convert it into a frequency? Secondly, I want to get CWT of a signal, but I want to have the option to choose the frequency range to work on. I found ...
1
vote
1answer
40 views

What's the maximum allowable amplitude modulation frequency for a given carrier frequency?

I'm currently studying wavelets and had an interesting thought experiment: If you were to calculate the wavelet transform of a signal using a wavelet of a fixed frequency, you would get time varying ...
0
votes
1answer
29 views

What does it mean for a Wavelet transform to commute with translations?

Referencing this article here https://arxiv.org/pdf/1203.1513.pdf It states "A wavelet transform commutes with translations, and is therefore not translation invariant". Now I understand why it is a ...
0
votes
0answers
45 views

scalogram for huge data

I have a huge data for which I want to apply wavelet and plot scalogram. the below code works for small data. However, I have a huge signal, for which I am not able to plot scalogram. Can anyone ...
2
votes
3answers
7k views

Adding noise to an ECG signal

I am doing a project on ECG arrythmia analysis using matlab. I have designed notch filter for removing 50 Hz noise but don't know how to add a 50 Hz powerline interference noise to a clean ECG signal?...
0
votes
0answers
16 views

Continuous Wavelet Filter Bank Frequencies

I have followed instructions on how to create a single Morlet wavelet, and can change the centre frequency of the wavelet. My question now, is I would very much like to create a filter bank. How do ...
0
votes
0answers
20 views

Wavelet Transform Implementation Method

I have been watching the wonderful youtube videos here: https://www.youtube.com/watch?v=4TTpwIZrUAo&list=PLn0OLiymPak2G__qvavn3T8k7R8ssKxVr&index=3 detailing morlet wavelets and fit ...
0
votes
0answers
213 views

Using Wavelet Transform on a 1D signal while updating the values

I'm working on a NN that uses Wavlet Transformed signals (with different wavelets and levels) and combines them with an additional Statistical Features input (input_4) to provide one step ahead ...
0
votes
0answers
22 views

Can coefficients of a DWT be computed using least squares approximation?

I assume that it can be computed given function values for each sample as a vector and wavelet values for each scale and translation packed in a matrix. Can anyone clarify the matrix construction and ...
0
votes
0answers
20 views

Take a wavelet function as a transfer funtion

Is there anyone having the experience of taking the wavelet funtion as a transfer function? That is: if we have $\psi_{m,n}(x)=a^{-m/2}\psi(a^{-m}x-nb)$, $\psi_{m,n}$ is the dilated and shifted ...
-1
votes
1answer
114 views

CWT matlab function [closed]

i'm trying to apply the cwt function from matlab in the first graph and from the different articles that i've read i should get something that shows different peaks to determine the location of damage,...
0
votes
1answer
58 views

Is there a reason why with symmetric padding, the inverse wavelet transform is not the adjoint of the wavelet transform?

I recently stumbled upon a bothering fact when using the pywavelet library in Python. When we use the default "symmetric" ...
0
votes
0answers
36 views

What are the constraints in design of discrete orthogonal wavelets?

Can anyone point me to literature that explains a quote from here : Why is a wavelet transform implemented as a filter bank? So not all wavelets can be implemeted perfectly (invertible) with ...
0
votes
0answers
60 views

Calculating the Mean Square Error (MSE) in Wavelet Denoising

I´m currently reading the paper (to be more precise: it´s a chapter from the book "Shearlets, Multiscale Analysis of Multivariate Data" by Kutyniok and Labate) "Image Processing Using Shearlets" by G....
0
votes
0answers
11 views

Why packet wavelet transform for frequency analysis gets non-informative results for some frequencies and phase?

I wrote the following code in Julia for packet wavelet transform. It uses Haar transform (I've chosen low-pass filter to keep average value of the signal). As usual, it works recursively filtering ...
2
votes
2answers
251 views

Other time-frequency-plane tiling than STFT, DWT, ConstantQ-Transform: multiresolution STFT?

It is known that a) the STFT gives a rectangular tiling of the time-frequency plane b) the Wavelet transform gives a non-linear tiling (better frequency resolution for low-frequencies, and better ...
1
vote
2answers
67 views

Wavelet is a small wave, what is problem with using sin(x) of one cycle?

As far as I know a $\sin(x)$ which is one cycle long can be made into a wavelet and then we can use its dilated and translated versions to represent another function, effectively a wavelet transform. ...
0
votes
3answers
607 views

How Are Images Considered Non Stationary Signal When They Are Invariant to Time?

I have read Wavelets are better than Fourier in dealing with non-stationary signals such as images, but I don't understand how images are considered stationary??
0
votes
0answers
19 views

Which algorithms can efficiently identify rectangular regions in noisy greyscale image?

I have a large number (~50000) of square greyscale images, about 180x180 pixels. I need to efficiently scan them for containing significant block like regions. See the following pictures where I have ...
0
votes
0answers
207 views

Multifractal analysis of an image using wavelets

I want to measure the fractal character of images using a wavelet approach (if possible) in python. (E.g., maybe things like roughness, anisotropy, or just the fractal dimension - perhaps just ...
3
votes
1answer
183 views

Wavelet Transform and STFT

How wavelet transform is different from STFT. I'm not able to understand what is resolution in frequency domain means?
3
votes
0answers
260 views

Why does the Stationary Wavelet Transform shift this image?

I am running a stationary wavelet transformation on a brain image. I can't understand why it shifts with each level so that the image is no longer centered. You can see that the X component shifts to ...
3
votes
3answers
335 views

Why does decimation make a system time variant?

On Wikipedia I read this : "The Discrete Wavelet Transform, often used in modern signal processing, is time variant because it makes use of the decimation operation." Why does decimation makes system ...