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two dimensional wavelets construction

I am trying to construct 2D wavelets for function approximation. Please suggest some references for constructing and implementing 2D Legendre Wavelets and other variants of it. thanks
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25 views

Where can i download “Tight wavelet frames on local fields”? [closed]

I need this article: "Tight wavelet frames on local fields" http://www.degruyter.com/view/j/anly.2013.33.issue-3/anly.2013.1217/anly.2013.1217.xml Is this article at these famous sites there? ( I ...
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0answers
11 views

Wavelets - clarification of vanishing moments post

.I have read the post What is a "vanishing moment"? regarding vanishing moments. Here, it is stated in an answer how "In a sense, these conditions mean that the wavelet is "unbiased." It ...
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1answer
18 views

Admissability of wavelets

Can someone explain why the admissability of wavelets allows us to conclude the limit of the Fourier transform of a wavelet approaches 0 when $\omega $ approaches 0. Then if the Fourier transform of ...
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0answers
14 views

Larger image after wavelet reconstruction

Depending on the size of the original image and depending on the kind of padding used during 2D discrete wavelet transform and reconstruction, the reconstructed image has a larger size. Is there a ...
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0answers
19 views

Is there a cost function for row equivalent matrices?

I am working on a minimization problem as follows: argmin$_x$ ||x-y||$_2$$^2$+$\lambda$||$\Psi$x||$_1$ where x and y are 2D or 3D complex arrays ||$\cdot$||$_1$ and ||$\cdot$||$_2$ are the L1 and L2 ...
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0answers
17 views

Can anyone provide a sketch as to what a wavelet transform of the dirac delta function look like?

I was trying to motivate the idea of a time frequency localization using wavelet transform to a peer today and I thought the impulse function would be a good example. In my mind I was thinking of a ...
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4 views

Short-Time-Fourier-Transform: why overlapping the window?

For STFT, we impose window of certain size onto the original signal, then we perform fft on each window. The uncertanty about frequency and time is determined by the width of the window, however, I ...
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1answer
24 views

How do you obtain a connected (staircase looking) representation of the scaling and wavelet coefficients in Python

How do you obtain a connected (staircase looking) representation of the scaling and wavelet coefficients instead of the unconnected result in the image below? It looks nicer in Matlab than in Python? ...
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16 views

Wavelet Transform of a shift invariant function

I want to calculate the wavelet transform of a shift invariant function. For example Gaussian - $\exp{-\|x-y\|^2_2} $. There is no restriction on the wavelet basis that can be used here. Can anyone ...
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9 views

Continuous wavelet over piecewise functions

Is there a wavelet function that spans the space of piecewise: linear functions(as Haar is a basis for piecewise constant functions) polynomial functions I am almost sure there is one for ...
1
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1answer
25 views

confusion about Morlet Wavelet: What is it exactly?

I was trying to follow and implment a method propose on the research paper. And currently, I have having some trouble to understand the wavelet transform. In particular, the paper I am looking at is ...
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0answers
15 views

how do i integrate to solve for \psi_k,_n for part A?

For part A, I need to integrate f(t) times phi(t) to find C_0, so I plug in 1 for phi(t) because from 0 to 1 phi(t) is 1. But for the second part of part A, what do I plug in for psi(t)_k,_n and how ...
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1answer
30 views

Is fourier transform or Wavelet transform better for this applicaiton?

I am currently designing an alogirthm that is either based on Fourier Transform approach, or the Wavelet Transform Approach, or the combination of the two. Since Wavelet is new to me, I am having ...
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0answers
14 views

What does it mean to do scale multiplication of DWT?

I stumbled across this paper, and I'm not too sure what they mean by 3.2 "Scale Multiplication". How do you multiply two DWT scales together? DWT reduces the image matrix to 1/4 its original size, so ...
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0answers
16 views

How to implement the Integer Wavelet Transform for images?

I have a description of a wavelet transform, but I am unsure on how to implement the algorithm based on the information given: $A_i,_j = ((I_{2i,2j} + I_{2i+1,2j}) / 2 )_{floor}$ $V_i,_j = ...
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0answers
20 views

How do I derive the analytical form of a discrete wavelet transform?

I guess this is more of an "applied maths" question than pure maths, and here's to hoping this is the right forum :) I am using a fast discrete wavelet transform (DWT) of a 1D vector of 2^N numbers ...
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25 views

Frequency response of wavelets and scaling functions

I am getting started with wavelets! And I am having trouble going from scaling function to the frequency response of the scaling function. The scaling function and wavelet is defined on some axis ...
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29 views

Daubechies Wavelet orthogonality of scaling function

I am a newbie to the Wavelet world! Right now I have a problem with understanding the Daubechies Wavelet's scaling function (for D4), which is defined on $[0,3]$ for $\phi(x)$. Now as mentioned in ...
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1answer
31 views

Definition of “uniformly regular” signals (as used in the book “Wavelet Tour of Signal Processing”)

The author uses the term "uniformly regular" and I get the idea of it's meaning through the context, yet the phrase is used as if could also have a precise mathematical meaning. Is there a definition ...
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1answer
29 views

Confusion about space and multiresolution

I don't have a background in functional analysis so I find this hard to understand. How could it possible that each "dyadic" dilation of a function f(x) (where the dilation is f(2^i (x))) forms a ...
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2answers
489 views

What is difference between Fourier Transform and Fast Fourier Transform?

If you think about Fourier Transform, in the classical cases, say on the real line, what it is? Just a waded sum. Right? You take a function $f$, and you take it's Fourier Transform at particular ...
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33 views

Why the $L^1(R)$ space does not have a unconditional basis

Why the $L^1(R)$ space does not have a unconditional basis. It is a known fact that $L^p(R)$ ($1<p<+\infty$) has unconditional basis. A simple example is the dyadic wavelet or Haar system. I ...
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2answers
48 views

Is there an equivalent of Plancherel's theorem with wavelets transform?

For the Fourier transform, we know that: $$||f||_2=c||\hat{f}||_2$$ where $c$ depends on the normalization. Is there an equivalent with wavelet transform? Thanks.
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30 views

Finding relation between $\omega$ and scaling coefficient of mexican hat wavelet

I am not looking for complete solution as it is a homework problem. I would like to know how to start about finding the relation between $\omega$ of a sine wave and the scaling coefficient $a$ of a ...
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1answer
83 views

What are unconditional bases and which wavelets have this property?

What are unconditional bases and which wavelets have this property? Haar wavelet seems to be one but how common is it? Unconditional bases are related to Riesz basis condition (ordering of the terms ...
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1answer
124 views

Wavelet or FFT for Transient signal analysis?

For now I use FFT to analyze the response of an electrical system to some transient signal. The transient signal is $x(t)$, which translates to $X(w)$ in the frenquency domain. On the other hand I ...
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1answer
54 views

How are generalized frames related to biorthogonal bases?

How are generalized frames related to biorthogonal bases? It seems like frames are a possible solution if neither orthonormal nor biorthogonal bases are available. I thought the generalized frames ...
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1answer
29 views

The use of wavelets in time series modelling ( feature extraction part)

I have been working on modelling a time series using wavelets for a long time. I am quite familiar with the wavelet theory and all...However, I have a big understanding issue and really appreciate it ...
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1answer
62 views

Amplitude Spectrum, Nyquist Frequency, mixed/min/max wavelets

The problem is here. Now I know the definition of mixed/max/min phase wavelets, whether the roots lie within the unit circle or not. Starting from n = 1, let $$ x_t = ( 5, 6) $$ $$ X(z) = 5 + 6z $$ ...
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20 views

use relevant wavelet basis for periodic components

i would like to understand how should i use following code for code for detection of uknown frequencies?let us consider following signal ...
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0answers
26 views

Evaluating an integral involving Haar scaling function

Let $\phi(t)$ denote the Haar scaling function, and let $\psi(t)$ be the corresponding wavelet. My problem is to evaluate the integral $I = \int_{t} \phi(t - 1/2) \frac{\partial \psi(t)}{\partial t} ...
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1answer
26 views

A relation for Fourier series

For $f$ and $f'$ in $L^2(0,1)$, define $e_k(x)=e^{2\pi ikx}$, $k \in \mathbb{Z}$. And define the Fourier series: $f=\sum _{k \in \mathbb{Z}}c_ke_k$, where $c_k=\left \langle f,e_k \right ...
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0answers
75 views

Matlab's dwt2 in publication quality notation?

I used Matlab's dwt2in my algorithm, what notation have you folks seen that describes the 4 resulting wavelets? How do I express ...
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0answers
45 views

Does these two operators commute?

It is an exercise, $z\in\mathbb T$, which is the unit circle $$m(z)=\sum_{k\in\mathbb Z}a_kz^k$$ set $$Sf(z)=\frac{1}{\sqrt N} m(z)f(z^N)$$ So the adjoint operator is ...
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1answer
27 views

How to show that the limit of $\frac{\omega_1}{N^n}+\frac{\omega_2}{N^{n-1}}+…+\frac{\omega_n}{N}$ exist

$$\omega=(\omega_1, \omega_2,...)\in \{0, 1, 2,...,N-1\}^\mathbb N$$ How to show that the ...
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1answer
36 views

Bessel Sequence proof check.

I have a similar question to definition of Bessel sequence, where it was solved using Banach-Steinhaus. A sequence $\{f_k\}_{k=1}^{\infty}$ is called a Bessel sequence in a Hilbert space ...
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2answers
95 views

In which case should a wavelet transform be applied instead of a Fourier transform?

I was wondering what are the advantages (and possibly the drawbacks) of using a wavelet transform instead of a Fourier transform for the signal processing, are there simple examples to illustrate that ...
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0answers
18 views

Are effective degrees of freedom after discrete wavelet transforms additive across scales?

I'm looking into effective degrees of freedom estimation with wavelets. Methods for estimating scale-specific effective degrees of freedom (EDOF) from the discrete wavelet transform of a signal are ...
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0answers
78 views

Regularity of Daubechies wavelet

I am reading the book Wavelets: Theory and applications by A. K. Louis, D. Maass, A. Rieder ...
3
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1answer
63 views

definition of Bessel sequence

A sequence $\{f_{k}\}_{k=1}^{\infty}$ is called a Bessel sequence in a Hilbert space $H$, if there exists $B>0$ such that $$\sum_{k=1}^{\infty}|\langle f,f_{k}\rangle|^{2}\leq B\|f\|^{2}$$ for all ...
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32 views

Integral involving wavelet

Let $\hat{\psi}_m$ be a Fourier transform of Daubechies wavelet of order $m$ and $\chi_I$ is a characteristic function of interval $I$. How to bound from above the following integral $$ ...
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0answers
15 views

Fast transpose of undecimated wavelets

I am using undecimated Daubechies wavelets and I need to compute the forward and adjoint of the wavelets several times. I am using the Rice Wavelet Matlab toolbox ...
2
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1answer
128 views

Need to learn wavelet, suggest steps and resources

I am looking for a good introduction to wavelets and wavelet transforms. that covers the following: Basics Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and ...
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0answers
40 views

Error bounds in representing a vector using a truncated Moore-Penrose biorthogonal basis

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 ...
2
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1answer
88 views

Biorthogonal Projector Construction

I was trying to prove that the biorthogonal projector matrix $P$ given on the Wikipedia page on biorthogonal systems does in fact construct biorthogonal systems from input bases $\mathbf{u}$ and ...
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1answer
40 views

Wavelets on $\mathbb{R}^{n}$

I want to study Wavelet theory on $\mathbb{R}^{n}$ and I can't find any book on this topic. Can you recommend me any good book that considers that?
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97 views

Wavelets, How can a zero padding lengh n signal be truncated to n coeficients from which a signal can be reconstructed

Wavelet transform is defined for infinite lengh signals, finite lengh 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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111 views

Continous wavelet transform and shannon Entropy.

Note: I have asked the same question on signal processing forum,but didn't get any answer. so it might be more like a math or physics question. Hope you don't consider it as cross-post. I am trying to ...
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48 views

Strange values of approximating coefficients returned by matlab's wavelets decomposition

I'm trying to get wavelet decomposition of arcsin(x) using, say, haar wavelets When using both Matlab's dwt or wavedec functions, I get strange values for approximating coefficients. Since applying ...