Questions tagged [orthornormal]
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10
questions
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33 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
27 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 ...
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2answers
47 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 $...
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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
552 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
6k 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 Ļ1(t)and Ļ2(t) for the same. Also ...
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2answers
885 views
How to calibrate three orthogonal camerasļ¼
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 ...
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1answer
189 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'...
