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Questions tagged [orthornormal]

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Why is my implementation of the Haar wavelet not normalized?

The Haar wavelet system is defined by $$ \psi_{j,k} (x) = 2^{j/2} \psi(2^jx - k), $$ where $$ \psi (x) = \begin{cases} 1, & 0 \leq x < \frac{1}{2} \\ -1, & \frac{1}{2}\leq x\leq 1 \\ ...
Sim's user avatar
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How to compute moving dot products of time series with exponentially decaying weights?

I have to apply the Gram Schmidt algorithm on discrete time series to make them orthogonal and normalized. This implies that I compute dot products, but it is of course not applicable for very long ...
chmike's user avatar
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How to find the orthonormal basis for these three signals

I've been given these signals: $$S1(t) = 1$$ $$S2(t) = t$$ $$S3(t) = t^2$$ I have to find 3 basis functions using Gram - Schmidt algorithm on the interval $|t| \le 1$. Now, I know the procedure and ...
dina's user avatar
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Other Examples of Complete Orthonormal Systems

I am interested in other examples of finite and complete orthogonal basis. I am not confident in my use of the term “complete”, so what I mean specifically is a set of basis vectors that can be used ...
Dan Boschen's user avatar
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What's a Normalized function?

I'm studing Representations of Random Processes and the book talks about Orthonormal functions, but doesn't make it clear what is it. I was able to realize that a set of functions are orthonormal if ...
Ivo Tebexreni's user avatar
4 votes
2 answers
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Geometric representation of a signal using basis functions

I'm trying to solve the following problem where I need to express $x(t)$ in terms of the given $φ_i(t)$ functions. (It is proven that the $φ_i(t)$ functions are orthonormal).: Here's what I tried: In ...
big sad's user avatar
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Pros/Cons to using Spectral and Diffusive Graph Wavelets

As I understand, there are two major methods of constructing wavelets on graphs. Spectral wavelets, from David K Hammond et. al, and diffusive wavelets from Coifman and Maggioni. I can't quite parse ...
bigdrip's user avatar
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Partitioning the energy of a signal between its components

In physics, the total energy of a system is the summed energy of its component subsystems, and energy must be conserved, ie, adding the energy of the components gives the total energy. In signal ...
kordes's user avatar
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Relationship of input-outputs in Hartley transformation based on few elements in a vector

This question is related also to that question HERE, but with further details and another issue I need to solve. Assuming we have a vector $X = [x_0,x_1,\ldots,x_N]$, its Hartley transformation is ...
Gze's user avatar
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Relationship between input and output sequence in Hartley transformation

As you know that Discrete Hartley transformation is related to the discrete Fourier transformation, $i.e$, assuming we have a vector $X = [x_0,x_1,\ldots,x_N]$, its Hartley transformation is equal to $...
Gze's user avatar
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5 votes
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Orthogonal basis of signal space and the projection of white noise

I am trying to make the relation between linear modulation and nonlinear one by using orthonormal expansion. The purpose is to understand what is orthonormal set in each case and to understand the ...
Anna Noie's user avatar
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2 answers
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The inverse of an orthogonal matrix is its transpose

In the following statement I don't understand the case for $\ i = j$: Let $\mathbf A$ be an $\ m \times \ n$ orthogonal matrix where $\ a_i$ is the $\ i^{th}$ column vector. The $\ ij^{th} $ element ...
Starhowl's user avatar
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1 vote
1 answer
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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 ...
ivan.ukr's user avatar
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2 answers
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What's the meaning of the continuity in spectrum analysis? [closed]

We all know that for any, suitable, kind of signal $f(t)$, there corresponds a Fourier transform function $F(j\omega)$ such that $$ f(t) = \frac{1}{2\pi} \int_{-\infty}^{+\infty} F(j\omega) e^{i\...
user1297181's user avatar
1 vote
2 answers
8k views

How to find orthonormal basis function in the following digital communication problem?

I'm trying to express the following set of signals on orthonormal basis functions. These signals are to be transmitted using a 4-ary modulation scheme.How do i write ψ1(t)and ψ2(t) for the same. Also ...
user12083's user avatar
2 votes
2 answers
1k views

How to calibrate three orthogonal cameras?

I am trying to find out intrinsic parameters(focal length ,principle point,and lens distortion coefficients)as well as the extrinsic parameters(rotation and translation of each camera relative to the ...
oilpig's user avatar
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1 answer
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Orthornormal Wavelet scaling function coefficient calculation (filter design)

I stumbled upon an equation system as shown in the image below while designing an orthonormal wavelet filter. I tried solving the equation (5.63,5.64,5.65 => 5.66) but no avail. I'm not sure if there'...
NcJie's user avatar
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