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
258 views

change the central frequency of a wavelet

I am using the discrete meyer wavelet in MATLAB for time series decomposition. I would like to change the central frequency of this wavelet but I do not know if this is possible or if I would need to ...
0
votes
1answer
34 views

Number of datapoints after decimation in discrete wavelet wavelet analysis

I am following an example provided by MATLAB on 1-D wavelet decomposition (DWT). The number of datapoints is 10000. If we do a level 3 decomposition following a similar example provided by MATLAB ...
2
votes
1answer
666 views

MATLAB: Generating and Visualizing Mother Wavelet of different scale

In MATLAB, there is a function wavefun that outputs both the scaling and wavelet functions. To generate a Daubechies, the following command can be used: ...
2
votes
1answer
196 views

Extract approximation and detail coefficients

I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)?
1
vote
1answer
208 views

2D DWT computation order

In 2D the discrete wavelet transform (DWT) of an image using lifting based 5/3 filter, if I perform a row-wise operation first then perform column-wise operation then I will get 4 sub-band LL, LH and ...
0
votes
0answers
26 views

CWT coefficients as features for ML algorithms

I use CWT coefficients as features in ML algorithms and then I did the feature selection using the chi-square test but recently I figured out that the chi-square test can only be applied for ...
2
votes
2answers
159 views

Wavelet Filter Coefficients from Scaling Filter Coefficients

I am trying to develop a new type of wavelets and I found out a function that following a particular two scale relation. The function at a scale $t$ say $x(t)$ can be related in a finer scale $x(2t)$ ...
0
votes
0answers
80 views

Stuck with plotting wavelet transform in Python

I want to plot the frequency composition of a sampled signal data versus time by using surf or any 3D plot. Normally time resolution of FFT is zero so I want to use wavelet transform where I want to ...
0
votes
1answer
92 views

Meaning of wavelet and scaling coefficients

What is the meaning of wavelet coefficients and scaling coefficients? E.g. for a sequence I obtained the following wavelet coeffients. How am I supposed to interpret them? I used ...
0
votes
1answer
18 views

Clarification regarding discrete wavelet transform

One of the books on "Conceptual Wavelets" by Fugal explains some major differences between the undecimated discrete wavelet transform (UDWT) vs. discrete wavelet transform (DWT). In UDWT the scale of ...
0
votes
0answers
13 views

What wavelet should i use to analyze harmonic function?

If i have the following signal: $$ s(t) = cos\left [ t\cdot \left (\frac{a}{2}t+b \right ) \right ] $$ What is the best family of wavelet to analize the signal, and what is its scale range? Do i ...
1
vote
1answer
126 views

For discrete wavelet transforms, is redundancy needed to ensure perfect reconstruction?

So I was using pywt and I noticed that in the padding mode documentation they explain the following: DWT performed for these extension modes is slightly ...
2
votes
1answer
174 views

Scaling Function in Wavelet Analysis

I was watching a YouTube tutorial on wavelets https://www.youtube.com/watch?v=wgRgodvU_Ms, where the presenter showed that if we multiply a Gaussian with a sine wave (and follow some other conditions),...
2
votes
1answer
84 views

Discrete wavelet transform disadvantages

I read in a paper that the discrete wavelet transform (DWT) has two disadvantages The first one is the shift variance property due to the downsampling process. Could you please help me understanding ...
0
votes
0answers
33 views

Why my Time-Frequency plot is time reversed?

I'm trying to build my own code implementation for Continuous Wavelet Fourier Transform. But when I compare the time-frequency plot created with my function with time-frequency plot created with the ...
0
votes
1answer
35 views

Can anybody recommend a good source for material of Gaussian and Complex Gaussian wavelet? [closed]

Can anybody recommend a good source for material of Gaussian and Complex Gaussian wavelet? Please share the link if possible.
2
votes
2answers
58 views

Daubechies Wavelets in mulitresolutional analysis decomposition

I have an understanding problem with Daubechies wavelets. When I use a multiresolutional analysis, I want to approximate the given input Signal $f\in L^2(\mathbb{R})$ on the subspaces $V_i$. By ...
10
votes
2answers
17k views

What Is the Difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat Wavelet?

There are three techniques used in CV that seem very similar to each other, but with subtle differences: Laplacian of Gaussian: $\nabla^2\left[g(x,y,t)\ast f(x,y)\right]$ Difference of Gaussians: $ \...
3
votes
1answer
66 views

What Is Proper Paper and MATLAB Toolbox Describing and Discussing Wavelet, Ridgelet, Curvelet and Contourlet Transforms in Detail?

Question 1: Does anybody know any paper proper for getting started understanding the concept of Wavelet, Ridgelet, Curvelet and Contourlet transforms and their differences in detail? Question 2: ...
1
vote
1answer
98 views

Critically Sampled Laplacian Pyramid from 2nd Generation Wavelet

I'd like to know if a technique I have in mind is already used and has a name I can look up, and whether it is likely to work and be useful! My aim is to produce a discrete wavelet transform that is ...
0
votes
1answer
89 views

Energy Preserving Laplacian Pyramid

Both Discrete Wavelet Transform (DWT) and Undecimated DWT possess an important property of energy preservation: on each level $$\sum_i W_i^2 + \sum_j V_j^2 = \sum_k X_k^2$$ where $W$ and $V$ are ...
3
votes
2answers
95 views

Orthonormal Dictionaries for Band Limited Signals

If $\mathbf{x} = [x_0, x_1, \ldots, x_{N-1}]^T$ is the time sampled input signal and $\mathbf{Y} = [Y_0, Y_1, \ldots, Y_{N-1}]^T$ is the Fourier transform of the input signal, then a linear ...
11
votes
3answers
3k views

What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform?

At a glance, the constant-Q fourier transform and the complex Gabor-Morlet wavelet transform seem the same. Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, ...
0
votes
0answers
14 views

What are the Red-Black Wavelets transformation for color (RGB) images?

I am looking for Red-Black Wavelet transform implementation on internet but I am unable to find it. Or How wavelets can be used for Images. Please help if you know how wavelets can be used for images.
1
vote
1answer
168 views

Any experiences for plotting a stationary wavelet transform?

I am experimenting with wavelets for my thesis and am currently working with the stationary WT pywavelets provides. There are very nice plots for CWTs, but does anyone know a technique for producing ...
1
vote
0answers
64 views

Difference in the meaning of kernel, filter, and dictionary atoms

While reading literature on wavelets, I have encountered keywords filters and dictionary atoms and their exact meaning is confusing for me. Basically, one can use them interchangeably and I won't see ...
0
votes
0answers
6 views

Scaling factor in lifting scheme wavelet transform

I have a small question why the scaling factor coefficients K1 and K2 are interchanged in the inverse process in lifting scheme wavelet transform. thank you in advance
2
votes
1answer
384 views

Wavelet transform: How to compute the initial coefficients when only samples are available?

In standard MRA we have that the space of functions at scale J can be expressed as $$V_j = V_0\oplus \left(\bigoplus_{j=0}^{J} W_j\right)$$ where $V_0$ is spanned by the orthonormal system of the ...
2
votes
2answers
136 views

Constrained LASSO Problem - $ {L}_{1} $ Regularized Least Squares with Linear Equality Constraints

I have an optimization question. I want to solve the following problem: $$ \arg\min_S\frac{1}{2}\|s-c\|_2^2 +\lambda\|\Phi s\|_1 \mbox{ s.t. } As = 0 $$ in which $\Phi$ is the wavelet transform ...
0
votes
0answers
22 views

Wavelet synthesis boundary conditions

I am interested in discrete wavelet decomposition using the D4 wavelet and am having issues understanding how the boundaries are handled during the synthesis step. Say I want to use a smooth boundary ...
0
votes
1answer
156 views

What is Wavelet packet transform (WPT) time complexity

I have read in many papers that time complexity of WPT is $O(N \log(N))$, but I would like to know what is the effect of Levels in the time complexity. Must it be one of the following ? $O(2^{L} ~N~...
0
votes
1answer
80 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
13k 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
18 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
78 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
41 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
10 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
563 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
184 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
14 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
213 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
48 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
635 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 ...
6
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
306 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
322 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
49 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 ...
7
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
2
3 4 5
9