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
212 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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4answers
621 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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1answer
698 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 ...
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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
75 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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2answers
241 views

Additive White Gaussian Noise (AWGN) and Undecimated DWT

One of the benefits of DWT is that it is an orthonormal transform. There are statements that the energy of noise component mainly concentrates on the high-frequency (detail) part and distributes ...
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1answer
298 views

Undecimated DWT vs. CWT. In what cases is one preferable over another?

Talking about undecimated DWT let's focus here on SWT algorithm. SWT is said to be: numerically more stable due to Mallat algorithm. And the inverse operation is capable of returning the original ...
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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
935 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
285 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 ...
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2answers
16k 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: $ \...
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2answers
458 views

Optimal Level of Wavelet Decomposition for Denoising

If a certain mother wavelet is defined and the optimal threshold shall be defined via Donoho, how can I define the optimal decomposition level to achieve the best denoising results.
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1answer
855 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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1answer
75 views

Wavelets in time series predictions

Wavelet transforms are linear in nature. Then how good they are for time series predictions. Can they analyze nonlinear relations in data well??
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263 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
197 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 ...
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1answer
882 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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1answer
258 views

Haar Wavelets vs STFT for graceful audio quality degradation (newbie question)

I'm playing around with FFT (using Naudio library) and with Wavelets (using TarsosDSP library) trying to get better understanding of both of them. I've noticed that when I zero out FFT/Wavelet ...
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1answer
88 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 ...
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1answer
304 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 ...
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1answer
776 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
35 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
170 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
367 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 ...
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1answer
303 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
365 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
654 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: ...
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1answer
826 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 ...
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1answer
88 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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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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1answer
37 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 ...
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2answers
368 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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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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3answers
2k views

“Fourier Transform can localize signals in frequency domain, but not in time domain.” — What does it mean in layman's terms?

I was studying the introduction to wavelets and its benefit over the frequency domain. I said that: Fourier analysis can't localize signals both in time and frequency domain. Fourier analysis can ...
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1answer
155 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
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-\...
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3answers
675 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??
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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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1answer
433 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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0answers
45 views

DWT initialization from nonuniform samples

Let $D\subset\mathbb R$ be compact, let $f:\mathbb R\to\mathbb R$ be a contintinuous function with support $D$. Let $\phi(x)$ be a well-defined scaling function, in the sense that it generates a ...
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1answer
458 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
1k views

Adaptive Piecewise Constant Approximation (APCA) with wavelets/DWT

I am trying to approximate a vector or a time series, in order to have as little changes as possible. To do so, I pretend to apply the Adaptive piecewise constant approximation (APCA) algorithm. ...
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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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0answers
252 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
1k views

Wavelet transform in MATLAB

Suppose I have a wave with $20 \textrm{ kHz}$, $100 \textrm{ kHz}$ and $300 \textrm{ kHz}$. Sampling frequency used is $1000 \textrm{ kHz}$. I apply the discrete wavelet transform on the wave like <...
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0answers
426 views

What the difference between the family of Discrete Wavelet Transform?

When I useed Mathematica,If found many Transforms in the list of Discrete Wavelet Transforms. For example: discrete wavelet transform (DWT) stationary wavelet transform (SWT) lifting wavelet ...
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1answer
56 views

Wavelet Fidelity Filter (video compression)

I have read a specification of Dirac (video compression format). A key element of this format is the use of the discrete wavelet transform. Section 15.6.3 of the specification defines individual ...
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1answer
227 views

Subsampling property of wavelet transform

One of the properties I have seen for isotropic tight wavelet frames is $$\sum_{i\in\mathbb{Z}} \left|h(2^i\omega)\right|^2 = 1$$ where $h(\omega)$ is the frequency spectrum of the original wavelet. ...
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1answer
107 views

possibility of applying ridgelet transformation on signals

After converting a 1D signal to 2D using matlab code, can the ridgelet transform be applied? Is this transformation effective compared to wavelet?