# 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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### Continuous Wavelet Transform with Scipy.signal: what is parameter “widths” in cwt() function? How do time-frequency?

I search to display a time-frequency signal with an original discrete temporal signal (sampling step = 0.001sec). I use Python and the library Scipy.signal. I use the function ...
1k views

### Fast Fourier Transform and Clustering of Time Series

I'm making a project connected with identifying dynamic of sales. That's how the piece of my database looks like: There are free columns: Product - present the group of product Week - time since ...
2k views

### use wavelet transform to extract frequencies from given signal

let us suppose that we have following signal values,which consists by deterministic components and random noise(white noise) ...
185 views

### Algorithms for removing oscillations?

I am interested in removing oscillations from a signal to capture the lower-frequency variations, similar to the objective of this problem. The oscillations vary in frequency in the time domain, so ...
6k views

I have a question related to wavelet transform: we know that while the Fourier transform is good for a spectral analysis or which frequency components occurred in signal, it will not give information ...
221 views

### Is there any difference between the 2D continuous and discrete Gabor filter when it comes to MATLAB implementation

I want to know the difference between the 2D continuous and discrete Gabor filter when it comes to Matlab implementation. I found many files related to 2D Gabor filter on Mathworks File Exchange but I ...
376 views

### Causal Wavelet Decomposition

I've seen the use of a Causal wavelet mentioned a few times but have never seen any examples of them in use with Matlab. Is it possible to to perform a Wavelet Decomposition using a causal wavelet i....
227 views

### Convolve a minimum phase wavelet with delta peak

let's assume I have two time series: one with a delta peak at position $x$ and another time series with a minimum phase wavelet that starts at time $y$ with a maximum peak at position $z$. Now, when ...
158 views

### Derive Maximum of zero phase rotated wavelet from rotated wavelet

I have one question concerning phase rotation of signals and I am not sure wether it works or not: Let's assume we have a zero-phase wavelet x(t) i.e. Ricker wavelet. Unfortunately, in our ...
2k views

### Convolution of Signal with a Wavelet

I know that the complex wavelet transform is given by $$\int_{-\infty}^{\infty}f(x)\psi^*_{s,u}(x)\,dx$$ where $f$ is the signal, $\psi_{s,u}(x)=\frac{1}{\sqrt{s}}\psi(\frac{x-u}{s})$ is the wavelet. ...
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### Suggestions for FFT based tools to analyze music - Preferably MATLAB/free software packages [closed]

I am interested in analyzing full length songs for general features of the track which are not otherwise apparent. For e.g., I want to look at various parts of the song with time-frequency plots/...
8k views

### Why does a narrower window in a Fourier transform or STFT give poor frequency resolution?

In theory of FT(Fourier transform) and STFT(Short Time Fourier Transform) it is said that "A wide window gives better frequency resolution but poor time resolution. A narrower window gives good time ...
470 views

### Combining two images

I am working with speckle noise reduction in ultrasound images. I have used wavelet transform for removing the noise by eliminating certain frequencies in order to eliminate any existing noise. Since ...
1k views

### Fourier Transform of Morlet wavelet Function?

One definition of the Morlet wavelet function is given by: $$\frac{1}{\sqrt{\pi f_b}}e^{\frac{-t^2}{f_b}}e^{j2\pi f_c t}$$ The Fourier transform of this equation is: $e^{-\pi^2 f_b(f-f_c)^2}$ (is it ...
3k views

### Why does the high frequency component of an image contain more noise?

I am working with wavelet transforms. When we apply a discrete wavelet transform to an image, it decomposes into four components named the approximation component, thevertical component, the ...
178 views

### mean of wavelet for image processing

For many papers which talks about using wavelet transforms for feature detection in image processing, it is stated that it is advantageous for the wavelet to have zero mean? Why is this so? Thanks in ...
243 views

### How can I change the frequency band ($\tt Fb$ parameter) using $\tt cwtft$? [closed]

MATLAB's implementation of cwt uses the complex morlet wavelet as: psi(x) = (pi*Fb)^(-0.5)*exp(2*1j*pi*Fc*x)*exp(-(x^2)/Fb); ...
160 views

### how can i call the input data in wavelet transform and generate code for gabor wavelet manually? [closed]

I am an ECE student, and i am doing my project I want to generate a code for gabor wavelet transform. I have no idea could you help me with a sample program I have DNA as input sequences and how ...
415 views

### Need to learn wavelet, suggest steps and resources [closed]

I am looking for a good introduction to wavelets and wavelet transforms. that covers the following: Vector Spaces ā Propertiesā Dot Product ā Basis ā Dimension, Orthogonality and Orthonormality ā ...
546 views

### Shifting of Shift-Invariant Wavelet Transforms

Main Question: Why would iterative wavelet/inverse-wavelet transforms cause a shift along the x-axis for undecimated (shift-invariant) wavelet transforms? I am attempting to remove backgrounds from ...
849 views

### Inverse of Wavelet Transforms - Background and Noise Removal

Main Problem: How can you inverse Wavelet Transforms (Using the data given by signal.scipy.cwt) I was wondering if anyone understands the ...
108 views

### Are all isotropic bandpass filter kernels, wavelets?

Are all isotropic bandpass filter kernels, wavelets? Are there any properties that the radial frequency profile has to meet to be considered a wavelet?
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### How do I implement the CDF wavelet inverse?

I understand and have implemented a 2D discrete wavelet transform that uses a Haar wavelet to process images. Now I would like to implement a 2D Cohen-Daubechies-Feauveau wavelet transform, but I am ...
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### Error bounds in signal compression represented by truncated Moore-Penrose biorthogonal bases using von Neumann wavelets

I was reading and trying to reproduce the results in the arXiv preprint of Periodic Gabor Functions with Biorthogonal Exchange: A Highly Accurate and Efficient Method for Signal Compression by Asaf ...
514 views

### gabor wavelet and gabor transform

I was reading a paper 'A Flexible Framework for Local Phase Coherence Computation' (paper URL) on using wavelets for local phase coherence. I just want to be sure. Is the gabor wavelet the same as the ...
413 views

### Relationship between windowed fourier transform and wavelet transform

I was reading on windowed fourier transform and wavelet transform, and i was thinking that the windowed fourier transform is a subset of wavelet transform. Is that true?
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### How to undecimate and make shift invariant a Dual-tree Complex Discrete Wavelet Transform in R

I have the following vector and wavelet transform (from R waveslim package) ...
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### Two-dimensional wavelet analysis

Could you tell me why wavelets without scaling functions can't be used for two-dimensional analysis? What is the role of scaling function?
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### Denoise EEG signal by using Daubechies function

I have an EEG signal and it contains eye blink artifacts. I read some references and know that it is possible to detect eye blinks and remove them by using wavelet transforms, but I don't know that ...
291 views

### How can a zero-padded length n signal be truncated to n coefficients from which a signal can be reconstructed?

A wavelet transform is defined for infinite length signals. Finite length signals must be extended in some way before they can be transformed. I know that periodic replication and zero padding are ...
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### Get spectral picture from a wavelet transform

According to my previous question, I have changed the generate command to: y=generate1(100,1000,1); and got the following picture: Now I want to test a wavelet ...
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### Help me with BM3D algorithm's aggregation scheme

BM3D is considered state of the art in Image Denoising. I am trying to implement the algorithm in Matlab. Right now, I am done with the 3D wavelet transform in the first step, and to be precise, the ...
859 views

### What are the main advantages and disadvantages of the lifting scheme?

Can anybody tell me the advantages of the lifting scheme and why it is better then a normal filter bank?
638 views

### Cross correlation coefficient using MATLAB

Actually I want to calculate the cross correlation coefficient of any signal on comparing with all mother wavelets like Morlet, Daubechies using MATLAB.
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### Any idea how can I optimize morlet wavelet parameters by Heisenberg uncertainty principal and Shannon entropy?

Based on a paper in here, they have proposed a method to optimize morlet function parameter. I have tried to implement their technique, but I can't get rational results. any idea? In here you can see ...
149 views

### Differences observed on the complex wavelet transform applied on the same signal

I have applied a complex wavelet transform on two signals : a first one a second one that is a concatenation of the first signal and another one For the 4th coefficient (as an example, i've got the ...
3k views

### How to calculate CWT shannon entropy?

I am trying to calculate shannon entropy of CWT. I am not sure if I am doing it right. Assume that $W(a_i,t), i=1;2;...;M$ is a set of wavelet coefficients. The ...
777 views

### what is Shannon entropy?

I was reading a paper about finding optimal morlet wavelet function for CWT, and they were minimizing Shannon entropy. what is Shannon entropy and it uses? (specially on continuous wavelet transform)
418 views

### Wavelet signal analysis for ultrasound echo

I am new to the wavelet field, and I am working with ultrasound signal. For my study, I needed to measure material using the pulse echo reflection method. Basically, when the transducer transmits ...
1k views

### Nonlinear wavelets transform?

Is wavelet a Nonlinear transform, or Not? specifically, continuous wavelet transform with morlet function. I am studying behavior of a dynamic system, and it has nonlinear behaviour. can I employ ...
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### Need to understand how wavelet is applied on Image matrix?

i want to understand ,how to find out Discrete wavelet transform of image 4 by 4 size using Haar wavelet on paper ?
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### DWT with more precise scale

With a signal x of length $2^{16}$, the DWT (computed for example with pyWavelet's wavedec) has only 16 or 17 rows (the wavelet ...
510 views

### Audio watermark embedding text attack resistant

I'm developing an audio watermarking algorithm which embeds text (binary form) in DWT-DCT coefficients. The goal of the algorithm is to hide song information (like artist, song, album,...). Everything ...
588 views

### Reconstruct DWT for each cD1,cD2,cD3 and cA3 signals

This question must be basic for this forum, but I'm only start working with DWT recently, and I was working with CWT before. I ...
2k views

### Discretized CWT vs. DWT vs. FWT vs. MRA

By reading some books about wavelets, it seems that Discretized CWT is not the same thing as DWT. Can we give a classification of Discretized CWT vs DWT vs FWT etc. ? A few remarks : All I read ...
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### 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~...
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### STFT and DWT (Wavelets)

STFT can be successfully used on sound data (with a .wav soundfile for example) in order to do some frequency-domain modifications (example : noise removal). With ...
265 views

### In image compression using transforms, how to deal with the transformed coefficients as they are not integers?

I am new to the field of image compression. While going through various texts, I read about how transforming the image to another domain using, for example, the wavelet transform, or the DCT, makes it ...
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### Image watermarking in wavelet domain (data hiding in images)

I am working and researching on Image watermarking/steganography and I'm stuck at a point and want to know which technique is better in image processing for data hiding. Bit Plane Complexity ...