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1answer
7 views

Filter output of a signal

So I have a filter $$H(z) = 0.5 + 0.5z^3 = (1/2, 0, 0, 1/2)$$ and need to find the output of it on a cyclical signal $$x = (..., 3, -1, 2, 1, 5, 2, 3,-1, 2, 1, 5, 2, 3,...) $$ Would the output be ...
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0answers
13 views

How to express a signal in terms of Riesz bases?

Fast discrete wavelet transform allows us to express any discrete signal in terms of wavelet bases by convolution with filter coefficients. How can one express a digital signal in terms of ...
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1answer
46 views

Equivalence of sums

I was hoping someone might be able to help me justify this sum equivalence I ran across in a proof. I'm sure it is something simple but never the less I am confused. I have the following for a ...
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0answers
18 views

What are the wavelet coefficients of a time series that is linear interpolated?

I want to know the relationship between the wavelet coefficients of a time series before and after linear interpolated. Suppose we have a time series $x(0),x(1),x(2),\cdots$. When this time ...
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1answer
23 views

Verification of a certain identity in wavelet basis lemma.

This is from Lemma 7.1 in Mallat's Wavelet Tour 2nd edition. I am trying to show that $$ b(2x)h(x) + c(2x)g(x) = a(x) $$ when \begin{align*} b(2x) &= \frac{1}{2}\left[ a(x)h(x)^* + ...
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1answer
28 views

Uniform Approximation by Finite Wavelet Sum

Suppose $\psi:\mathbb{R}\rightarrow\mathbb{C}$ is a rapidly decreasing, bounded function with zero integral. For $j,k\in\mathbb{Z}$ define a function $\psi_{jk}(x):=\psi(2^{j}x-k)$. Suppose is the ...
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1answer
42 views

Maximal Function Estimate

Suppose $\psi$ is a rapidly decreasing function; i.e. for all $N>0$ there exists a constant $C_{N}$ such that $\left|\psi(x)\right|\leq C_{N}(1+\left|x\right|)^{-N}$. Define a family of functions ...
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1answer
43 views

Book recommendation for wavelet analysis

I am master student doing research in data mining, i read a paper about wavlet analysis for data mining, so i think it may help me in the future. But in my undergraduate degree the last course in ...
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1answer
21 views

Application of wavelet analysis in computer science

I am doing research in computer science (data mining), do you think wavelet analysis is useful for me?
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1answer
50 views

Wavelet Theory and Wavelet Series

I am new to Wavelet Theory. My mind came across one question. We learn about Fourier Series (FS) and then about Fourier Transform (FT). Then, why are we not dealing with "Wavelet Series" as FS and ...
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0answers
8 views

using wavelet transform for espisific frequencies

I want to analyze a signal in the time-frequency domain, at the frequency : 10,15 and 20 Hz, so should the input "scales" for matlab function 'cwt' be [.1 .15 .2], since the scale is the inverse of ...
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0answers
26 views

Continuous second derivative over the support of a Daubechies4 wavelet

I can not entirely follow the proof from section 3.1.1 from the book "A primer on Wavelets" by Walker. After the first part (listed below), I can grasp the rest so if you could help I would greatly ...
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0answers
29 views

Significance of orthonormal basis in wavelet analysis

I've recently been looking into wavelet analysis and I have the question: What is the importance of wavelets having an orthogonal basis, say as opposed to a bi-orthogonal basis or otherwise? I'm ...
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0answers
42 views

Derivative of an L1 norm of transform of a vector.

I have to take derivative of the l-1 norm. L1 is the function R in the following expression: $$ R(\psi Fx) $$ where x is a vector, F is the inverse Fourier transform, and $\psi$ is a wavelet ...
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1answer
19 views

Let $x_{0}=1$ and $x_{1}=-1$ For $n\geq0$ inductively define $x_{n+2}=x_{n+1}+6x_{n}$

I am not so sure how to do this problem and would like some help here. How would you induct a relation given this information here? I mean I know what induction means but I'm not so sure what I'm ...
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0answers
11 views

Terminology with wavelets

I have seen in textbooks that the wavelet transform is stated as two different types of filters. When texts are defining the wavelet transform they call it a band pass filter. However when they talk ...
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0answers
23 views

Can wavelets be used for texture discrimination?

I've recently been studying wavelet analysis with a view to differentiating certain areas of texture images where the texture differs from the background pattern (which is quite random); for example a ...
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1answer
17 views

show that $Q(z)=1/2\sum_{k\in \mathbb{Z}}(-1)^k\overline{p}_{1-k}z^{k}$

Let $P(z)=\sum_{k\in \mathbb{Z}}p_{k}z^{k}$ and define $Q(z)=-z\overline{p(-z)}$. for $\left | z \right |=1$, show that $Q(z)=1/2\sum_{k\in \mathbb{Z}}(-1)^k\overline{p}_{1-k}z^{k}$.
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0answers
12 views

EZW parent-child relation

I’m trying to learn the EZW principle. I’m having trouble understanding the parent-child relationship. In my case, I want to use it on a 1 dimensional signal. So, let’s say for example a signal of 4 ...
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0answers
26 views

The Heisenberg uncertainty principle in the time-frequency plane

The Heisenberg uncertainty principle says that it is impossible to have a signal with finite support on the time axis which is at the same time band limited. Is the following reasoning correct: When ...
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0answers
186 views

How to calculate wavelet energy?

Part of my assignment about signal processing says the following: Compute the Discrete Wavelet Transform for the input signals Group the wavelet coefficients in trees growing across scales ...
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0answers
17 views

the meaning of frequency resolution

I have found in the literature the word "frequency resolution" in the comparison between DFT and wavelet transform WT , and they said that DFT provides the same frequency resolution , but WT allow ...
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1answer
149 views

Implementing 1D Discrete Wavelet Transform in Matlab

I'm trying to write my own version of the Discrete Wavelet Transform using the bior4.4 filters. I think my implementation is not properly working yet, because whenever I input a signal and a number ...
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1answer
70 views

How to prove these equations? ( theorem in multiresolution analysis)

Suppose $\left \{ V_{j} ; j\in \mathbb{Z} \right \}$ is a multiresolution analysis with scaling function $\varphi$ . then the following scaling relation hold: $ \varphi (x)=\sum_{k\in \mathbb{Z}} ...
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0answers
21 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
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0answers
24 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
23 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
22 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
25 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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0answers
18 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
27 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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0answers
18 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 ...
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1answer
33 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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1answer
38 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
30 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
23 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
28 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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0answers
35 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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0answers
58 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
41 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
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1answer
31 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
1k 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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0answers
35 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
56 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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0answers
38 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
103 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
189 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
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1answer
61 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
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1answer
33 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 ...
0
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1answer
71 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 $$ x_t = ( 5, 6) $$ $$ X(z) = 5 + 6z $$ ...