Questions tagged [orthornormal]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
2answers
31 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 ...
0
votes
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 ...
1
vote
2answers
45 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
votes
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 ...
1
vote
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 ψ1(t)and ψ2(t) for the same. Also ...
1
vote
2answers
426 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 ...
1
vote
1answer
944 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 ...
1
vote
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\...
2
votes
2answers
857 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
votes
1answer
182 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'...