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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2answers
146 views

Compression Ratio in ECG compression using Wavelet Decomposition

I have compressed and reconstructed an ECG signal using wavelet coefficients. In the compression part, many of wavelet coefficients are set to zero. For example, if in original ECG $5000$ wavelet ...
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2answers
85 views

Factor $|a|^{-1/2}$ in definition of mother wavelets

The mother wavelet is defined as $$\Psi_{a,\tau}(t) = \lvert a\rvert^{-1/2}\Psi\left(\frac{t-\tau}{a}\right)\tag{1}$$ in which the factor $$ \lvert a\rvert^{-1/2}\tag{2}$$ is supposed to serve ...
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1answer
115 views
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2answers
214 views

Is MATLAB documentation wrong on when to use discrete versus continuous wavelet transform?

I was reading some of the MATLAB documentation and I get confused when reading the part about When is Continuous Analysis More Appropriate than Discrete Analysis? My knowledge before reading the ...
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2answers
217 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 ...
12
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1answer
700 views

Which transform most closely mimics the human auditory system?

The Fourier transform is commonly used for frequency analysis of sounds. However, it has some disadvantages when it comes to analyzing the human perception of sound. For example, its frequency bins ...
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4answers
631 views

Why are wavelet transforms (Multi Resolution Analysis) used more in practice for compression rather than Fourier series?

I know that both Fourier and wavelet can be used for compression of signals. The Fourier series guarantees that it gets the closest approximation of the original signal in the least squared sense. ...
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0answers
788 views

Relationship between Wavelet transform and Fourier Power Spectral Density

Is there anyway to obtain the Fourier Power Spectral Density from a wavelet transform of a time series? I am particularly interested in this problem because I was wondering if there is any ...
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2answers
374 views

Whether convolution followed by down sampling equals wavelet decomposition

I know that wavelet decomposition equals convolution followed by down sampling by two.I tried to test this on mat lab on haar wavelet. I write the below code and compared with the default wavedec ...
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1answer
712 views

Edge map based on a Haar Wavelet Transform

I have been implementing the paper Blur Detection for Digital Images Using Wavelet Transform and was asking myself how the following formula could reconstruct the edges given a Haar Wavelet ...
2
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1answer
167 views

Phase Information at Higher Frequencies in Continuous Wavelet Transform

I'm using the code I found here to compute the wavelet transform of a sine wave with a constant frequency. ...
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1answer
78 views

Does SWT/ISWT require intermediate approximation coefficients to represent/reconstruct the original signal?

Taking into account that Stationary Wavelet Transform (Algorithme à trous) is not an orthogonal transform do we need intermediate approximation coefficients for signal decomposition? For example, in ...
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1answer
87 views

Does Wavelet Packets (WPT) decompose signal on dyadic scales like DWT?

As far a I understand WPT is a generalization of DWT in a sense that you get a whole binary tree of possible orthogonal decompositions where DWT is only a one branch. And WPT also downsamples a signal ...
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1answer
954 views

Bandpass filter to get EEG frequency bands?

I'm doing a project with an EEG to detect driver drowsiness and learned about EEG frequency bands (alpha, beta, gamma...). As the frequency bands are simple frequency ranges, I wonder if I can use ...
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1answer
286 views

What are the known use cases for different wavelet families?

There are numerous wavelet families that differ by a number of parameters (like the number of vanishing moments, symmetry, etc.). What are the known use cases where one particular family is known to ...
2
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1answer
862 views

Implementing Continuous Wavelet Transform

I need to implement the discretized continuous wavelet transform from scratch. Could someone please point me to useful papers and references available online for this?
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0answers
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 ...
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0answers
268 views

Help understanding constant q output

I'm trying to visualise and understand the output of constant q transform. Based on my experience with FFT and the articles I've read so far, I would expect that each output bin would represent one ...
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1answer
870 views

How to do edge detection using Curvelet transform?

I wanted to use Curvelet thresholding for edge detection, that is first take discrete curvelet transform then choose coefficient which are for curve and then reconstruct back to get an edge map. ...
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1answer
909 views

Bandpass filter using wavelet transform

I'm working on a speech recognition project. The first step of this project is to find phoneme in the speech signal. To do that, I found this paper that discusses about it. In the paper, wavelets are ...
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5answers
1k views

Removing periodic spike noise from ECG signal

The signal shown in the following figure is collected from a ECG sensor. The spike noise that is observed with a periodicity of 30 seconds was traced to the periodic blip of the LED as it draws ...
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0answers
259 views

Transfer functions from wavelet transform

So I have this problem where I need to measure the phase of a signal and correct for a delay associated with the travel time of the signal while simultaneously determining the transfer function of my ...
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1answer
368 views

How to extract features from nonstationary signal using SVD (singular value decomposition)?

I am trying to extract features from a nonstationary signal (frequencies and time locations). For this purpose, I computed a wavelet transform (complex morlet) of the signal in MATLAB and obtained the ...
5
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1answer
501 views

wavelet transform boundary

I am doing 1D wavelet decomposition and I am particularly interested in parts at the border of the signal. These parts are affected by boundary effects. I know that some of the methods to extend the ...
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1answer
167 views

DWT architecture using filter bank

I am studying this paper. In one of the figures in the paper (Fig 5.b and Fig 5.c) DWT architecture is given using db2 and filter bank. I don't understand how Lo_D and Hi_D have size half of input ...
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1answer
308 views

Difference(relation?) between filter banks and wavelet decomposition

I'm implementing multirate system and met concepts of filter banks and polyphase decomposition of filters. While trying to understand them, I've found that they look very similar to wavelet ...
2
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1answer
784 views

Why do Dyadic filterbanks downsample the high pass signal portions?

I'm currently programming a dyadic filter bank and have a question. I notice in all of the visual representations: (from here (Dyadic Analysis Filter Bank)), the high pass filtered output for each ...
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1answer
36 views

How can I change parameters into a text string in MATLAB? [closed]

I am trying to compute the Morlet wavelet transform (cmor) of a signal, but I have to do it several times with different parameters Fb and Fc. Is there a way to automate it? For example, I have to do ...
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1answer
43 views

How can dilation of a wavelet function lead to its sign reversal? [closed]

I am studying wavelets and it has been given that $$ \psi_{a,b} = \frac{1}{\sqrt{|a|}} \psi \left(\frac{t-b}{a}\right) $$ now the function $$ \psi(t)= \begin{cases} 1,& \text{if } 0\leq ...
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1answer
171 views

Wavelet image denoising: dual-tree versus double-density

What is the main difference between the dual-tree DWT and the double density DWT image denoising techniques? How does the combination of them improve the quality of the denoised image?
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1answer
307 views

Reconstruction of a signal using 1D discrete wavelet

There is a signal of $50\textrm{ Hz}$ and $120\textrm{ Hz}$ corrupted with noise. The sampling rate is $1000\textrm{ Hz}$. Here I used a 3-level DWT to extract this two components of the signal ...
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0answers
372 views

Differences between $\tt wentropy$ in MATLAB and entropy definition

MATLAB offer's a Shannon entropy calculation in its wavelet package: $$ H(X) = -\sum_{i=0}^{N-1} x_i^2\log(x_i^2) $$ I'm wondering what this formula means, since it has no relation with the ...
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1answer
128 views

Find the maximum frequency in the signal section?

I'm recording the received signal after sending a 20Khz signal. I make some rotations with hand before the device and get some variations in the signal.I obtain a very noisy signal and do some pre-...
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2answers
257 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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1answer
841 views

Obtaining normalized matrix for the Haar Wavelet Transform

I've been reading this article: http://aix1.uottawa.ca/~jkhoury/haar.htm which explains the Haar Wavelet Transform. At a certain point, the author says: ... Since the transformation matrix $W$ is ...
3
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1answer
188 views

Wavelet decomposition

For the following code, X=[2 2 3 100 4 0 98 100 90 2 3 67 98 0 6 6 89 9 21 78] [C,L]=wavedec(X,N,'db1'); where N is the ...
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1answer
38 views

Testing for changes in auto-covariance

I am working with uniformly-spaced time series data where I am interested in knowing whether there are changes in temporal auto-covariance. The mean can be assumed constant. Visually, there are no ...
2
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1answer
89 views

Biorthogonal Wavelet Expansion

Consider a multiresolution analysis (MRA) $\{V_j\}$ in $L^2(\mathbb R)$ generated by the scaling function $\phi(x)$ and such that for each $j\in\mathbb Z$, $V_j\subset V_{j-1}$. For a given function $...
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0answers
956 views

CWT for filtering / feature extraction

I had asked a question last night in regards to how to process my data (Noise rejection / feature extraction) but I have a more specific question now that I hope someone can answer. As mentioned in ...
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1answer
206 views

What is the delta parameter in $\tt scal2freq$?

I am running complex morlet (cmor1-1.5) wavelet transform. I want to have the transformation for the range of $[1,150]\textrm{ Hz}$ with a step of $1\textrm{ Hz}$. ...
2
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0answers
242 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); ...
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6answers
5k views

What Properties Make Certain Wavelets “Better” Than Others In Image Compression?

I am trying to teach myself more about image compression using the wavelet transform method. My question is: What is it about certain wavelets that make them preferable when compressing images? Are ...
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1answer
2k views

Wavelet-based C/C++ Peak finding libraries

What wavelet-based peak finding functions are there for C++? I'm looking for something similar to: http://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.signal.find_peaks_cwt.html. ...
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2answers
142 views

Perfect reconstruction: what properties must the analysis LPF satisfy

I have been reading on conjugate quadrature filters (CQF). The linked article explains that, if we have a lowpassfilter $h_0$, we can create a set of filters for a perfect reconstruction filterbank. ...
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1answer
107 views

Question about vanishing moments in wavelet transforms

I am reading the book Noise reduction by wavelet thresholding by Maarten Jansen. About vanishing moments, it reads To create a really sparse representation, we try to make coefficients that live ...
4
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1answer
460 views

How to Map CWT to Synchrosqueezed wavelet transform?

I don't understand the mapping time-scale plane to the time-frequency plane in synchrosqueezed wavelet transform, i.e. $(3)$. You can find the paper here. For the given signal of $x(t)$ and mother ...
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1answer
160 views

Raw signal to short for DWT

The algorithm i use to apply a discrete wavelet transform only accept raw-data with a certain number of samples (2,4,8,..128..). I have to either interpolate the raw signal or padding it with zeros (...
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1answer
445 views

Multiplication in the wavelet domain, what does it look like in real space?

Say you wavelet transform a signal, multiply by some values, and untransform. Is there anything we can say about the effect in real space? I know that it's not exactly a convolution, because the ...
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1answer
1k views

Wavelet transform 3D plot for CoP

I'm trying to perform wavelet transform and make a 3D plot like : With the wavelet transform function : $$ \textrm{CWT}_x^\psi (\tau, s)=\frac{1}{\sqrt{\lvert s\rvert}}\int x(t)\psi\left(\frac{t-\...
10
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3answers
2k views

Slow Down Music Playing While Maintaining Frequency

Playing a piece of music audio at a slower speed would lower its pitch (frequency). Is there a tool and theory to slow down the song playing while keep the frequency the same? I suppose one can do ...

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