The tag has no wiki summary.

learn more… | top users | synonyms (1)

0
votes
0answers
14 views

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
-3
votes
0answers
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 ...
0
votes
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 ...
3
votes
1answer
17 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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
1answer
832 views

Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
1
vote
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? ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
0
votes
0answers
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
vote
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 ...
0
votes
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 ...
1
vote
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.
0
votes
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 ...
0
votes
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 ...
0
votes
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 = ...
0
votes
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 ...
18
votes
5answers
8k views

Difference between Fourier transform and Wavelets

While understanding difference between wavelets and Fourier transform I came across this point in Wikipedia. The main difference is that wavelets are localized in both time and frequency whereas ...
1
vote
2answers
484 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 ...
0
votes
0answers
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 ...
1
vote
0answers
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 ...
2
votes
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 ...
0
votes
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 ...
2
votes
0answers
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 ...
1
vote
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 ...
0
votes
0answers
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
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 $$ x_t = ( 5, 6) $$ $$ X(z) = 5 + 6z $$ ...
0
votes
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 ...
2
votes
1answer
146 views

Best way to find magnitude and phase of a specific frequency in an empirical time series…

I've a discrete, univariate time series, and I'm interested in to investigate a specific frequency component. Assume I'm interested in a frequency with a cycle-time of $f$ samples - and I need to get ...
0
votes
0answers
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 ...
3
votes
0answers
573 views

Wavelets: Cone Of Influence

While reading this paper I came across the term Cone of Influence which is described as ...
3
votes
1answer
1k views

How to intuitively interpret Gabor lambda param?

I have troubles understanding in an intuitive way (not by writing complicated math formulas) what is the meaning of the lambda parameter in the Gabor functions. (I have basic math understanding, grad ...
0
votes
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} ...
2
votes
1answer
69 views

Daubechies wavelet

I have two question about Daubechies wavelet are they really orthogonality? for example daub4 has the support equal $[0-3]$, and for scale function we have must: $$ \int_0^3\phi(x-n)*\phi(x-m)dx ...
2
votes
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 ...
3
votes
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
2
votes
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 ...
0
votes
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 ...
3
votes
0answers
78 views

Regularity of Daubechies wavelet

I am reading the book Wavelets: Theory and applications by A. K. Louis, D. Maass, A. Rieder ...
2
votes
2answers
228 views

Morlet's wavelet reconstruction formula

The CWT (continuous wavelet transform) of a signal $x(t)$ is $$X_w(a,b)=\frac{1}{\sqrt{|a|}} \int_{-\infty}^{\infty} x(t)\psi^{\ast}\left(\frac{t-b}{a}\right)\, dt$$ In order to reconstruct the ...
3
votes
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 ...
0
votes
0answers
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 $$ ...
0
votes
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 ...