Questions tagged [orthogonal-signals]
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27
questions
1
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2answers
70 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
votes
2answers
352 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 ...
0
votes
1answer
110 views
Finding set of orthogonal basis functions for composite signals
I've been given a list of 5 composite signals, where each is composed of 10 sinusoids of different frequencies. For instance, the first composite signal $S_1$ is given by
$$
S_1 = \sum_{i=1}^{10} A_i \...
1
vote
0answers
73 views
Non-coherent FSK and Orthogonality and square-law detectors
This is a basic figure that explains how Non-Coherent FSK actually works. The incoming signal
$ r (t)=\sqrt{2 P}{Cos}(2 \pi t (\text{fc}+\text{fi})+\text{n(t)}$
where P denotes the signal power in ...
1
vote
1answer
83 views
How to prove a train of sinc pulses in digital communicaton system are orthogonal to each other?
Consider a train of sinc pulses:
$$\phi_n(t)= \frac{\sin(\omega_M(t-nT_s))}{\omega_M(t-nT_s)}\quad; n=0,\pm1,\pm2,\dots$$
$\quad$where,$\quad T_s=\frac{\pi}{\omega_M}$
Now ,in order to show sinc ...
1
vote
1answer
41 views
About the orthogonality of columns in Zadoff-Chu matrix
As we know that Zadoff-Chu matrix is similar to Walsh-Hadamard matrix where every columns in those matrices is orthogonal with the any other column.
For Walsh-Hadmard matrix, the orthogonality is ...
1
vote
1answer
52 views
How $\Delta f=\frac{1}{2T}$ satifies the orthogonality condition?
Let
$$s_{ml}(t)=\sqrt{\frac{2E}{T}}\exp(j2\pi\Delta fmt)$$
where $T$ is the time-period of signal
$\Delta f$ is the frequency spacing
The text says that two signals $s_{ml}(t)$ and $s_{nl}(t)$ are ...
2
votes
1answer
274 views
Processes: Orthogonal, Uncorrelated, Statistically Independent
How are they all related? You can define them as:
Orthogonal Processes: $E[XY] = 0$
Uncorrelated Processes: $E[XY] = E[(X - \mu_x)(Y - \mu_y)] = 0$
Statistically Independent Processes: $E[XY] = E[X] \...
0
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0answers
26 views
How can we generate an orthogonal sinusodial signal to any other signal?
I have three signals which are
\begin{align}
A&=\cos\left(2\pi ft + \frac \pi2\right)\\
B&=\cos\left(2\pi ft\right)\\
C&=\cos\left(2\pi ft + \frac {5\pi}4\right)
\end{align}
What i need ...
3
votes
2answers
127 views
Orthogonal Codes for Band Limited Channel
In this question orthogonal family and pulse shaping filter the user asked about possible loss of orthogonality of orthogonal codes due to the use of raised cosine pulse shaping and I showed as an ...
5
votes
1answer
133 views
On the Measurement Matrix Used for Compressing Sensing
Assume we have a matrix $x$ of size $(8,8)$ where each column is considered to be sparse with degree of sparsity equals to $4$. it means that every column can have $4$ zeros and $4$ non-zeros values ...
0
votes
1answer
79 views
Orthogonality of filter impulse response to its even shift
I meet this problem but still do not know how to solve it.
Could you guy give me some guides?
Upsampling by 2 ($U_2$) followed by filtering by $g$, with operator $G$
And given: $<g_n,g_{n-2k}>...
1
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0answers
48 views
Detect orthogonal sequence with fading
For a set of $N$ orthogonal sequences $\textbf{A}^i = \{a_1^i,a_2^i,...,a_M^i\}, i =1 ..N$, the detection of these sequences can be done by calculating the inner product (dot product) of receive ...
0
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1answer
46 views
Refinement equation and orthogonal wavelets basis
I have a wavelet function space defined by,
$ \phi(x) = \sqrt(2) \sum_n h_{\phi}(n) \phi(2x-n) $ .
given the Fourier transform of the function is:
$\hat{\phi}(\omega) = \frac{1}{\sqrt(2)} \hat{h}...
1
vote
3answers
1k views
How can I know if these two signal are orthogonal to each other
So the question is to determine if this statement is true or false. The question can be seen below.
I know that two signals are orthogonal if their inner product is equal to 0. I know how this ...
1
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0answers
19 views
Expectation of power spectrum for nonorthogonal wavelets
I'm working through "A Practical Guide to Wavelet Analysis" by Torrence and Compo, and I am confused about section 3d ("Wavelet Power Spectrum").
Let $x_n$ denote the signal, sampled at increments $\...
1
vote
1answer
57 views
Is it possible to spread signal using sum of more than one orthogonal code
I was wondering if we can spread the signal using more than one spreading code. Assume we have the Walsh code used to spread the transmitted signal, the Walsh code is, for example, gotten based on ...
2
votes
1answer
290 views
When Two Sampled Sinusoidal Are Orthogonal?
If two analog sinusoidal are orthogonal with duration T, their minimum frequency difference should be 1/2T in case of no phase offset between them.
And if there is phase offset, the difference is 1/...
0
votes
0answers
233 views
CDMA-DSSS with orthogonal codes and BPSK modulation: proper way to demodulate
I am having problems when demodulating the signal: If I demodulate the sequence chip by chip and then operate only with binary information the "integrate and dump" (correlator) sometimes will provide ...
0
votes
1answer
32 views
Are there analogues to orthogonal transformations in non-orientable surfaces?
I am working on extremely large, symmetric matrices of counts, and attempting to identify patterns/shapes within them. Wavelets are a popular tool in image processing, and have some nice statistical ...
0
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1answer
147 views
Temporal Orthogonality
I'm studying Digital Communication and I couldn't understand the relationship between temporal orthogonality and sampling theorem.
Definition of the Temporal Orthogonality is as follows:
$$\mathrm{...
2
votes
1answer
256 views
struggling to understand why Fourier basis is orthogonal
Studying DSP on my own time on Coursera.
Was given a proof to why the Fourier basis is orthogonal, but I can't figure it out. Here is how it is proof goes.
Consider the Fourier basis
$$
\left\...
1
vote
1answer
104 views
Does Hamming encoding preserve orthogonality?
The question I have is this-- if I have two binary vectors, i.e. $x_1, x_2 \in \mathbb F_2^k$ that are orthogonal, i.e. $x_1^T x_2 = 0$, and let's say I Hamming encode each of them separately with an $...
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 ...
2
votes
1answer
152 views
Absolute maximum number of possible PN sequences for given length
I previously asked if it was possible to use encryption-grade randomness as a CDMA spreading sequence and learned that the codes must be orthogonal, not necessarily random.
I've tried different ways ...
11
votes
7answers
36k views
When are two signals orthogonal?
The classical definition of orthogonality in linear algebra is that two vectors are orthogonal, if their inner product is zero.
I thought this definition might be applied to signals as well, but then ...
1
vote
3answers
576 views
Proving orthogonality
How to prove a cosine signal with irrational period and another cosine signal with a rational period are orthogonal?
For example, $\cos(4t)$ and $\cos(4\pi t)$ sum is aperiodic. Hence it is said that ...
