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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How to get the center frequency of wavelets in octave?

I am using Wavelab with gnu Octave to compute the continuous wavelets transform. Now I want to get the frequency from scale, to do this I need to get the center frequency of the wavelet but I cannot ...
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1answer
20 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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25 views

4-band FIR filter equivalency with 2-band filter compositions?

On pg. 18 of this paper: On the Dual-Tree Complex Wavelet Packet and M-Band Transforms there is a discussion about creating a single 4-band filter bank from a 2-level, 2-band set. There are two ...
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45 views

Wavelet domain Gaussian processes

Maraun et al, "Nonstationary Gaussian processes in wavelet domain: Synthesis, estimation, and significant testing" (2007) defines a class of non-stationary GPs that can be specified by multipliers in ...
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10 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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27 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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25 views

Wavelets: how to determine scales from frequencies?

(Reposted from StackOverflow) In the following code sample, I would expect the rows of the printed output to match each other, at least approximately. ...
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11 views

How to take half window in wavelets signals and taking for different signals

I want to know how to take few cycles in a signal by half window technique. And how to do standard deviation,min,max points and how to use window analysis, taking different cycles and doing half ...
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11 views

Time shift in DWT using Mallat algorithm over the $2^{10}$ scale

I am doing DWT on $2^{10}$ scale using the Mallat algorithm. As I know, DWT using the Mallat algorithm decimate sampling frequency 2 times at every next scale, it means $F_s$ is different for each ...
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0answers
15 views

Inverse Discrete Wavelet Transform - partial reconstruction

I'm pretending to approximate a time series/vector usind dwt , with haar filter, in R. I can apply the full ...
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1answer
25 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
34 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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27 views

Transfer functions from wavelet transfrom

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
39 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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10 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
35 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
90 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
19 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?
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1answer
33 views

Code for a wavelet based hilbert transform? [closed]

I normally implement the Hilbert transform using the Fourier transform. I have noise related issues I want to solve. Does anybody have an (apodized) implementation of the Hilbert transform handy, ...
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8 views

Is it required to quantize wavelet coefficients before one derives features from?

I am using wavelet coefficients for feature extraction in classification problem. As the wavelet coefficient values are real, positive and negative, is it required to quantize them before feature ...
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1answer
27 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 ...
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18 views

Example of radial frequency functions that give scale shiftability

Simoncelli's "Shiftable multi-scale transforms" paper talks about shiftability of the parameters of a wavelet transform, in particular translation, rotation and scale. The first two are used in his ...
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12 views

how to use dwt2 function for correct multiresolution decomposition of image using db2 and higher order filters?

I want to perform multilevel decomposition of a image using Daubechies, symlets,coif filters of all order. When i use dwt2 function for order higher than 1 the subband size is not the half of input. I ...
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37 views

Are wavelets for audio spectrograms available as a simple FIR filter?

I have read that "Debauchies Wavelet is simply a short FIR" so i am searching for a single FIR that i can make into a filterbank, a precise "bandpass filter" that detects narrow frequencies, i.e. 1Hz ...
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43 views

Expanding piecewise polynomial using Daubechies wavelet

What is the best Daubechies wavelet (i.e. the number of vanishing moment) to expand a signal $\boldsymbol{x} \in \mathbb{R}^n$? $\boldsymbol{x}$ consists of $m$ pieces of polynomial with $d$ degree. ...
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6 views

Known Rolling computation for fast wavelet packet transform?

Is there a known way to update the wavelet packet coefficients (approximation & detail at all scalings) such that you don't have to recompute the entire wavelet packet transform if you move the ...
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1answer
43 views

How to implement a $j$-level $M$-band wavelet transform of an image?

I want to implement an $M$-band (or multi-band) wavelet transform, to be used for feature extraction on images. Is there a built-in Matlab function available? Do I have to implement is using filter ...
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37 views

Wavelets vs FFT based spectrogram for RF signal identification/analysis

What are the advantages / disadvantages of using a Wavelet based spectrogram vs an FFT based spectrogram (as shown by Baudline, for example) for RF signal analysis / identification ? This paper seems ...
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1answer
29 views

Shift invariant in wavelet

I always hear that wavelet transform is not shift invariant, and that there are other types of wavelet, like stationary wavelet and double density dual-tree wavelet transform, that are shift invariant....
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1answer
17 views

Measures that can be used to truncate linear series of functions

Say we have the following (wavelet) series representation at some location and scale in a signal: $$ f = \sum_{k=1}^{K} c_k \psi_k$$ where $c_k$ is the coefficient, in order of magnitude ($|c_k| >...
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29 views

Is there R package that combines wavelet and GARCH?

I am new to R but I need to solve a problem related to high frequency data. I need a R package which combines Wavelet and Garch. I found similar approach in MATLAB but not in R.
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1answer
72 views

Downsampling in DWT algorithm

I was working on wavelet signal decomposition and got confused with the downsampling part of Discrete Wavelet Transform algorithm. If we consider a signal $\{a_0[0], ... ,a_0[N-1]\}$ of length N and ...
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1answer
78 views

Discrete wavelet transform

I am unable to understand the discrete wavelet transform on images. I followed Robi Polikar's tutorial and got a brief idea about the theory. But I'm unable to understand w.r.t images. Using Matlab's ...
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22 views

Extract the frequency range/mean from time series using Wavelet

I am working with Wavelet for the first time, and I need your help. I have time series of velocity collected for 2 min at 32 Hz: x = [n] where n = 120 (sec)*32 = 3840 counts. I am using Morlet ...
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37 views

questions on the wavelet digital filters

I am new in wavelet transform and digital filters. My knowledge on wavelet transforms was mainly from its applications with the implementation using Matlab or mathematica. So my question might be too ...
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0answers
48 views

Wavelet transform of time series(PyWavelets)

I am a newbie in wavelet transform and I would be glad if you help me. I have different time series(ECG with rate = 1000 points in second, length = 100 000 points). I need to classify them in two ...
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37 views

How to find the energy of a single frequency from its time-frequency distribution?

I have a non-stationary time series. I am interested in finding the energy content of a single frequency (actually the ratio of that single frequency over the total energy of the signal). The problem ...
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1answer
27 views

Question about vanishing moments in wavelet tranforms

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 ...
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3answers
168 views

What are the spike removal techniques in matlab without using filters

output from wavelet filter using daubechies 4 wavelet. Using wavelet filter this is the output obtained. The problem is elimination of the spikes at 0.023,0.043,0.063 and so on. Please note: no ...
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1answer
141 views

Daubechies wavelet transform

i have N samples obtained by sampling a signal with lot of frequency contents. How will i apply daubechies wavelet transform to obtain the frequency and its location? i need to write a program which ...
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8 views

Interpretation of Diagonal detail wavelets

I am a statistics grad student, and I have just begun exploring the topic of wavelet regression (specifically, Haar wavelets for discrete functions). I understand the generalization from a one ...
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69 views

Undecimated discrete wavelet transform in Python and Matlab

Loosely based on the above figure: I need to make an array like this: array = [(image),(1,ll),(1,lh),(1,hl),(2,ll),(2,lh),(2,hl)] Here, image is a numpy 2D ...
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32 views

Cohen-Daubechies-Fauraue 7/9 wavelet in Matlab

I just want to ask what the wavelet filter name used for Cohen-Daubechies-Fauraue 7/9. what name should I used in 'wname' when I want to use this type of wavelet in Matlab. some say that it is bior4....
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1answer
32 views

Compression Ratio in ECG compression using Wavelet Decomposition

I have compressed and reconstructed an ECG signal using Wavelet Coefficient. In compressing part, many of Wavelet Coefficient have set to zero. for example, if in original ECG, 5000 wavelet ...
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1answer
110 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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2answers
324 views

Is R suitable for digital signal processing

While asking a question about representing large time series in R I was discouraged from using R for digital signal processing. I understand that R is geared towards statistics. However, a signal is ...
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1answer
96 views

Optimized 2D wavelet transform using FFT

I'm currenty aiming to optimize my fast wavelet transform (FWT) algorithm for 2D signals (images). It works as follows: one iteration of 1D FWT does convolution of 1D input data with a selected 1D ...
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1answer
74 views

Implementing wavelet transform for finding transients in the power supply

I am new to the concept of wavelet transforms. Can somebody please help me in understanding this ? and also how to implement it in c. Is Short term Fourier transform more efficient than Wavelet ...
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26 views

How to choose a wavelet order

I'd like to perform the DWT on a signal in order to find the time-frequency information. I've read from a textbook that the coiflet performs best on this type of signal (ECG), I guess due to the shape ...
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1answer
41 views

This is an expression for the computation of kurtosis.

However, I don't understand what the subscript '4x' or the parameter (0,0) stand for. Could anyone explain ?