Questions tagged [orthornormal]
The orthornormal tag has no usage guidance.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $...
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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 ...
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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 ...
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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 ...
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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\...
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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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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 ...
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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'...
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