Questions tagged [orthornormal]
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13
questions
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68 views
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 ...
4
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2answers
331 views
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 ...
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0answers
32 views
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 ...
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2answers
40 views
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 ...
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0answers
32 views
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 ...
2
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2answers
56 views
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 $...
4
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1answer
1k views
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 ...
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2answers
1k views
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 ...
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1answer
1k views
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 ...
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2answers
69 views
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\...
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2answers
7k 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 ...
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2answers
934 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 ...
0
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1answer
192 views
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'...
